Introduction to Electrodynamics
... However, it is noted that these assumptions may not always be valid, even if the medium is pure air. For instance, electromagnetic waves of high strength or specific wavelengths, or the presence of particulate matter in the reacting flow, may cause the violation of these assumptions [23,24,25]. The validity of the aforementioned assumptions in the context of reacting flows must be verified experimentally in the future. ...
... The polarization force arises from the intrinsic or field-induced polarization of atoms and molecules, i.e., the distribution of the electron cloud with respect to the nuclei. When a particle with an electric moment is placed in an inhomogeneous electric field, E, it experiences a polarization force equal to [25]: ...
... Therefore, the magnetization force that is induced on those elementary magnetic moments depends on how these magnetic moments are modelled [64]. However, it is difficult to define a quantum mechanical phenomenon in the context of classical electrodynamics [25]. There has been a lot of debate and scrutiny on the form of the magnetization force [65,64,66,67,68,69,70,71,72,73]. ...
A computational fluid dynamics methodology for the simulation of electromagnetic interactions in compressible reacting flows has been formulated. The developed code, named EMI, is based on the SENGA Direct Numerical Simulation (DNS) software. Static electric and magnetic fields are solved using Gauss's laws of Maxwell's equations. Electromagnetic wave propagation is solved by discretizing Ampere's and Faraday's equations using the explicit Finite-Difference Time-Domain (FDTD) method. The equations for the electromagnetic fields are fully coupled with the Navier-Stokes equations, such that interactions between the electromagnetic fields and the fluid are included in the formulation. The interaction terms include the Lorentz, polarization, and magnetization forces. These forces determine volume forces that affect the transport of momentum, the diffusion velocity, and the energy conservation equations. In addition, the medium's properties affect the propagation of the electromagnetic fields via electrical permittivity and conductivity, charge density, and magnetic permeability. The solution of electromagnetic fields is validated against analytical and numerical solutions. The implementation of the coupling between electromagnetic fields and conservation equations for species, energy, and momentum is validated with laminar reacting flow numerical solutions from the literature. The capabilities of the formulation are investigated for a range of laminar methane-air computations under electrostatic, magnetostatic, and high-frequency electromagnetic waves. The validity of the electrostatic formulation in the presence of currents related to the movement of charged species is also assessed. Results demonstrate that EMI-SENGA can capture the fundamental effects of electromagnetic fields on reacting flows and the dynamics of charged species and their effect on flame shape and reactivity.
... Thus, the resulting interference patterns and structured modulation arise from the resonance between coexisting wave fields, mediated by recursive geometry. The curvature does not generate the structure, but rather refracts and aligns it [6,9]. ...
... In conventional optics, interference arises from the coherent superposition of multiple wavefronts [6,9]. A prototypical example is Young's double-slit experiment, where the intensity distribution is given by ...
... E(a, b) := ⟨ϕ A (a) ϕ B (b)⟩. The effective hidden variable λ in this model is the pre-collapse configuration of Φ in H (6) , constrained by: λ ∈ Λ rec := Φ ∈ C 2 (M (6) ) P n [Φ] ∈ H (3) spin-coherent . Because ϕ A and ϕ B are projections from the same field filtered through a global operator, their correlation function cannot be factorized: ...
We propose a geometric framework in which quantum-like behavior arises from deterministic resonance between classical scalar fields defined on a recursively modulated higher-dimensional manifold. The observable universe is modeled as a three-dimensional spatial hypersurface embedded within a six-dimensional flat Lorentzian space. Recursive curvature, encoded via smooth functions in the extra dimensions, modulates the phase and amplitude of a classical ambient field evaluated on this hypersurface. We show that the resulting field structure exhibits interference, localization, and modulation effects commonly associated with quantum phenomena, without invoking stochastic processes or probabilistic postulates. A confined scalar field sourcing and responding to the ambient field yields an effective Schrödinger-like equation with a dynamically induced potential , suggesting that quantum behavior can emerge from classical field interaction under recursive geometric alignment. Unlike holographic or brane-world models, our framework is not based on boundary duality but on recursive curvature as an organizing principle. The resulting modulation reproduces nodal structures, localization patterns, and decoherence-like suppression as deterministic consequences of classical wave resonance. This model provides a viable testbed for reinterpreting quantum interference as emergent from recursive geometry, with implications for fields, gravity, and fundamental ontology.
... It seems reasonable to use the classical electrodynamics of conducting media based on Maxwell's equations and Ohm's law. This is exactly what is done in all textbooks on electrodynamics that pay attention to this issue, see, e.g., [6][7][8]. However, the attempt to use classical electrodynamics when applied to metals reveals two problems that cannot be ignored: The first problem is that physics handbooks do not contain any information about the speed of light in metals or, what is in fact the same thing, about permittivity of metals. ...
... This equation can be found, e.g., in [8], Section 9.4, [41], Section 10.9, [19], Section 1.2. This is a wave equation with damping, a wave equation for a so-called "lossy" (i.e., dissipative) medium. ...
... With a time ansatz for electromagnetic waves, 7 we can reduce Eq. (6) to the form of a standard wave equation, 8 where ̂ is the complex relative permittivity, which is obtained from ...
We study the behavior of electromagnetic waves near the interface between two media: a dielectric medium and a conducting medium. Solving this problem within the framework of classical electrodynamics, we obtain results that coincide with the known ones, namely: (1) By comparison of the solution to this problem—when obtained within the framework of classical electrodynamics—with experimental data shows that using the values of electrical conductivity of metals given in physics reference books (the values of the so-called static electrical conductivity), we cannot achieve satisfactory agreement between theory and experiment. (2) We can achieve satisfactory agreement between experimental data and the predictions of classical electrodynamics only if we use values of the so-called optical conductivity that differ by two orders of magnitude from the values of the static conductivity. In addition, we propose a re-evaluation of some well-known facts, namely: (1) According to many literary sources, the permittivity of metals changes by several orders of magnitude depending on frequency and becomes negative at frequencies below the plasma frequency. It turns out that when applying Maxwell’s equations in different frequency ranges, it is necessary to use parameters that differ by two orders of magnitude. (2) At the same time, experimentalists interpret optical experiments by using formulae derived from Maxwell’s equations under the assumption that all parameters are constants. In our opinion, if we interpret experimental data using equations with constant coefficients and as a result we see that the coefficients depend significantly on frequency, we should think about using more complex equations to interpret the experimental data. (3) In this paper, we propose a new approach to interpretation of the experimental data. The novelty is that we use the equations of extended electrodynamics, which are three-dimensional analogues of Kirchhoff’s laws for electrical circuits. We show that extended electrodynamics allows us to describe experimental data using handbook values of conductivity and frequency-independent values of permittivity. Thus, we conclude that extended electrodynamics describes experimental data for metals more accurately than classical electrodynamics.
... In this paper, we will theoretically investigate the precision astrophysics phenomenology having the gravitomagnetism related with mass M which is the analogue of the EM [10,11,18,19] associated with charge Q. Next we will study the mass magnetic fields for the spinning compact objects in the gravitomagnetism. ...
... Note that the Maxwell type gravitational equations in (2.16) in the gravitomagnetism are the analogs of the Maxwell equations in the EM [18,19]. Note also that in the gravitomagnetism the equations in (2.16) include the time derivative terms related with the dynamics of the gravitomagnetism interactions. ...
... Note that, outside the spinning solid sphere, the direction of ⃗ B M is parallel toω on the equatorial plane. Note also that in the EM the direction of ⃗ B Q circles around the charge current following the right hand thumb rule since the charges interact repulsively [18,19]. In contrast, in the gravitomagnetism the direction of ⃗ B M circles around the mass current following the left hand thumb rule due to the fact that the masses interact attractively. ...
In order to describe properly the gravity interactions including the mass currents, in the gravitomagnetism we construct four Maxwell type gravitational equations which are shown to be analogs of the Maxwell equations in the electromagnetism. Next, exploiting the Maxwell type gravitational equations, we explicitly predict the mass magnetic fields for both the isolated system of the spinning Moon orbiting the spinning Earth and that of the Sun and solar system planets orbiting the spinning Sun, whose phenomenological values have not been evaluated in the precedented Newtonian gravity formalisms. In the gravitomagnetism we also phenomenologically investigate the mass magnetic general relativity (GR) forces associated with the mass magnetic fields, to find that they are extremely small but non-vanishing compared to the corresponding mass electric Newtonian forces. Moreover, the directions of the mass magnetic GR forces for the solar system planets except Venus and Uranus are shown to be anti-parallel to those of their mass electric Newtonian forces. Next we investigate the mass magnetic dipole moment related with the B-ring of Saturn, to evaluate with being the unit vector along the axis direction of the spinning B-ring. The predicted value of is shown to be directly related with the Cassini data on the total mass of the rings of Saturn.
... Interactions between elementary particles are one of the most fundamental features in physics to analyze the evolution and structure of several physical systems presented in nature (Feynman, Leighton, & Sands, 1963;Griffiths, 1999;Kittel, Knight, & Ruderman, 1973). ...
... Energy is defined as the work done by an applied force on a particle that leads to a change in its spatial configuration. In the context of electrical forces, this is known as electrostatic potential energy or simply potential energy (Griffiths, 1999). The concept of potential energy plays an important role in modern technology advances with implications in several branches of science. ...
... This work is organized as follows. In section theoretical framework, we introduce an elementary definition of electrostatic potential energy based on classical literature (Feynman, Leighton, & Sands, 1963;Good, 1999;Griffiths, 1999;Wangsness, 1997). In section potential energy for a discrete arrangement of point charges, we describe the energy stored in a set of point charges in electrostatic equilibrium in empty space, the one-dimensional electrostatic interaction of several point charges located at vertices of a polygon, and inscribed into a unitary imaginary circle interacting with another point charge located along the axis of the circle and out of the plane. ...
The concept of electrostatic potential energy has served as a starting point for a deeper understanding of several models in electromagnetic theory. We use this concept looking for a connection between some of those models, in particular, we analyze the contribution of electrostatic potential energy for different configurations of electric charge with circular symmetry. We study models corresponding to a discrete set of point charges arranged in a polygonal figure, a uni-dimensional continuously charged ring and a continuously charged torus, considering the existing analogies between them. In addition, we contrast the situation between the discrete and continuum models.
... In this paper, we theoretically investigate the precision astrophysics phenomenology with gravitomagnetism related to mass (M), which is the analog of EM [10,11,18,19] associated with charge (Q). Next, we study the mass magnetic fields for the spinning compact objects in gravitomagnetism. ...
... Note that the Maxwell-type gravitational equations in (16) in gravitomagnetism are analogs of the Maxwell equations in EM [18,19]. Note also that in gravitomagnetism, the equations in (16) include the time-derivative terms related to the dynamics of gravitomagnetism interactions. ...
... where J α M ≡ (cρ M , J i M ). Next, (19) has the same form as the EOM for the fields ( ...
In order to properly describe the gravity interactions, including the mass currents, in gravitomagnetism, we construct four Maxwell-type gravitational equations that are shown to be analogs of the Maxwell equations in electromagnetism. Next, exploiting the Maxwell-type gravitational equations, we explicitly predict the mass magnetic fields for both the isolated system of the spinning Moon orbiting the spinning Earth and that of the Sun and solar system planets orbiting the spinning Sun, whose phenomenological values have not been evaluated in the preceding Newtonian gravity formalisms. In gravitomagnetism, we also phenomenologically investigate the mass magnetic general relativity (GR) forces associated with the mass magnetic fields, finding that they are extremely small but non-vanishing compared to the corresponding mass electric Newtonian forces. Moreover, the directions of the mass magnetic GR forces for the solar system planets, except Venus and Uranus, are shown to be anti-parallel to those of their mass electric Newtonian forces. Next, we investigate the mass magnetic dipole moment related to the B ring of Saturn to evaluate m→M(Ring)=−1.141×104m3s−1ω^, with ω^ being the unit vector along the axis direction of the spinning B ring. The predicted value of m→M(Ring) is shown to be directly related to the Cassini data on the total mass of the rings of Saturn.
... The analytical solutions to these equations are provided by the following theorem [48]: ...
... The theorem is validated by substituting equations (3.2) and (3.3) into equation (3.1). Further details can be obtained from [48]. ■ ...
... The superposition of solutions is made possible by the linearity of equation (2.4). The boundary conditions can also be addressed using the method of images [48]. By leveraging the Biot-Savart law of dislocations and Helmholtz decomposition, the plastic deformation gradient F p can be obtained for an arbitrary configuration of dislocations, leading to the analytical expression for the intermediate configuration ℬ of the Riemann-Cartan manifold. ...
Universal mechanical principles may exist behind seemingly unrelated physical phenomena, providing novel insights into their underlying mechanisms. This study sheds light on the geometrical theory of dislocations through an analogy with electromagnetics. In this theory, solving Cartan’s first structure equation is essential for connecting the dislocation density to the plastic deformation field of the dislocations. The additional constraint of a divergence-free condition, derived from the Helmholtz decomposition, forms the governing equations that mirror Ampère’s and Gauss’s law in electromagnetics. This allows for the analytical integration of the equations using the Biot–Savart law. The plastic deformation fields of screw and edge dislocations obtained through this process form both a vortex and an orthogonal coordinate system on the cross-section perpendicular to the dislocation line. This orthogonality is rooted in the conformal property of the corresponding complex function that satisfies the Cauchy–Riemann equations, leading to the complex potential of plastic deformation. We validate the results by comparing them with the classical dislocation theory. The incompatibility tensor is crucial in the generation of the mechanical field. These findings reveal a profound unification of dislocation theories, electromagnetics and complex functions through their underlying mathematical parallels.
... Olson et al. [23] calculated the electrochemical potentials and bound charge densities for a range of (rigid) asperity shapes contacting an elastic half-space. Bound charge is the surface charge σ b = P ·n and volume charge ρ b = −∇ · P produced due to polarisation beneath the surface [32]. They emphasised that shapes that generate higher strain gradients give rise to higher charges, and surface potentials, e.g., pyramids, gave higher values than dome-shaped asperities. ...
... Since the outermost atomic layers of two interacting surfaces have a finite gap at the atomic scale, the interfacial electric field inside the contact area is generally non-zero; see the first image in the bottom right inset in Fig. 4(a). This electric field induced by flexoelectric polarisation serves as the driving force for the tribo- As the half-space is polarised, the bound charge on the surface is described by σ b = P ·n [32]. At the interface in Fig. 4(a), P produces the bound charge of opposing polarity on two mating surfaces; see the first frame of the inset of Fig. 4(a) placed at the bottom right corner. ...
... represents the Maxwell-stress tensor of the vacuum in the electric limit case, as is also frequently noted in the literature, especially in the case of small deformations [15,22,34]. ...
... By this transformation, Ampère's circuital law can now be expressed with the material time derivative resulting in a formulation which goes back to [13] and can also be found in [15] as ...
An important part for material modeling is the consideration of electromagnetic fields. In this paper, we add them to Hamilton’s principle for mechanical and thermal fields. We begin with a brief introduction to the electric and magnetic limit cases, which allows a non-relativistic formulation. After introducing the thermodynamic fundamentals, we present the Hamilton functionals for the limit cases from which we derive our governing system of equations by applying Hamilton’s principle of stationary action. In order to be able to describe the microstructure as well, we also consider general internal variables. After the derivation of the equations for the dominant fields, we show how to obtain the secondary fields. For both limit cases we show an example where the dominant electromagnetic field and the mechanic field are coupled by material properties.
... Some molecules, called polar, have built-in permanent dipole moments. Additionally, dipoles feel a force and a torque [5,6]. By viewing the dipole as consistent with two charges, +q and −q, at positions displaced by d, the dipole is found to experience the force f f f e and the torque N N N e given by f f f e = (p p p · ∇)E, ...
... The polarization P is defined as the electric dipole moment per unit volume while p = P/ρ is the electric dipole moment per unit mass. The magnetic dipole moment m m m is usually thought of via Ampère's model as a current loop, thus leading to the force f f f m and the torque N N N m as follows [6] (ch. 6): ...
As a generalization of the symmetry of the stress tensor of continuum mechanics, the paper investigates symmetry properties arising in models of magneto- and electro-mechanical interaction. First, the balance of angular momentum is considered, thus obtaining a symmetry condition that is applied as a mathematical constraint on admissible constitutive equations. Next, thermodynamic restrictions are also investigated and, among others, a further symmetry condition is determined. The joint validity of the two symmetry conditions implies that the dependence on electromagnetic fields has to be through variables involving deformation gradients. These variables constitute two classes that prove to be Euclidean invariants. The simplest selection of the variables is just that of Lagrangian fields in the literature. Furthermore, the variables of one class allow a positive magnetostriction and of the other one allow a negative magnetostriction. Some applications to (NO) Fe-Si are outlined. The use of entropy production as a constitutive function allows generalization to dissipative and heat-conducting electromagnetic solids.
... Hence, the change in projectile velocity ∆v = (v − v ′ )× Bohr velocity due to influence of nuclear interaction is 1.3 × 10 7 m/s. This deceleration results in emission of electromagnetic radiation, which can be described by using the Lienard-Wiechert potentials [21]. Such electromagnetic radiations in an inelastic collision produce excitation in the interacting nuclei [16,18,19]. ...
... It can be absorbed by the projectile ion or the target atom. The total power radiated (P ) by the projectile corresponding to nuclear bremsstrahlung radiation can be calculated from the Larmor formula [21] in the center of mass frame as follows ...
In nuclear collisions, nuclear bremsstrahlung can cause nuclear Coulomb excitation via photon exchange in the projectile as well as the target nuclei. Such a process originating in nuclear timescales (zeptoseconds) can also influence the atomic phenomenon, which can be observed if it is delayed at least by a few attoseconds as atomic timescales an attosecond. We have found that this may happen due to a mechanism called the Eisenbud-Wigner-Smith (EWS)time delay process. We have estimated EWS time delays in atomic collisions utilizing the non-relativistic version of random phase approximation with exchange as well as Hartree-Fock methods. We present three representative collision systems through which one can experimentally observe the phenomena in attosecond timescales even though they originate from nuclear bremsstrahlung radiation occurring in zeptoseconds. Thus the present work represents an investigation of parallels between two neighboring areas of physics: atomic and nuclear physics. Furthermore the present work suggests the possibilities for atomic physics research near the Coulomb barrier energies, where the nuclear bremsstrahlung can be used as a zeptosecond x-ray source.
... where ∇ is the del operator ∇ = ∂ ∂xx + ∂ ∂yŷ + ∂ ∂zẑ , and ∇⋅ represents the divergence operator. This equation indicates that the current density vector is divergence-free, and therefore, there exists a vector potential T from which the current density vector can be expressed as [25] ...
Vibration attenuation is a critical aspect of mechanical engineering design, and eddy currents provide an effective damping technique that does not add mass to the system, and it is especially effective at low frequencies. In this context, this paper introduces a methodology tailored for the design of thin non-magnetic metallic beams with eddy current damping. By solving the eddy current problem for a reference beam across various boundary conditions and lengths, a comprehensive database of output variables is generated. These include structural and electrical variables, along with coefficients from two simplified equivalent beam models: an electrome-chanical model and a Kelvin-Voight viscoelastic model. Simplified equations are subsequently derived to predict the behaviour of other beams, eliminating the need to solve complex elec-tromechanical problems individually. The methodology incorporates a parametric study of design variables, including beam geometry, material properties, velocity magnitude, magnetic field strength, and boundary conditions, revealing straightforward relationships between these variables and damping performance. Moreover, insights into eddy current maps are provided, emphasising their dependence on boundary conditions. This approach significantly streamlines the design process, enabling efficient and precise vibration attenuation. The methodology, further supported by a MATLAB application included as supplementary material, constitutes an invaluable resource for engineering design.
... For example, a low field means a low dV dz , resulting in a narrow energy spread, but the lower fields come at the cost of transverse broadening. High dF dz can drastically reduce the energy spread, but Gauss's law (∇ · F = 0) [38] requires that for an electric field to have a gradient in the z direction, there must also be a gradient in the transverse directions, leading to an undesirable lensing effect. ...
The energy spread of a focused ion beam causes chromatic aberration that limits the focal spot size and resolution for imaging and fabrication. Ion beams based on photoionization of neutral atoms can have a much smaller energy spread and higher brightness than conventional liquid metal ion sources and are thus capable of higher resolution. We present a method for using selective ionization of Rydberg atoms to reduce the beam energy spread in a cold atom focused ion beam. We produce experimental maps of the ionization rate of Rubidium-85 near the classical ionization threshold, predict the energy spread of an ion beam produced from these states and demonstrate energy spread reduction in situ in a focused ion beam. We use a novel method to measure the energy spread, using only components present in many commercial FIB systems. Selecting different states changed the energy spread by up to 50%, with opportunities to further reduce the energy spread by constructing a more favorable electric field gradient and finding atomic states with better ionization characteristics.
... The refractive index is in general both a complex-valued and frequency-dependent magnitude, where the real part affects the propagation of light while the imaginary part accounts for the attenuation of the electromagnetic field. 90 The phase velocity of a wave is = ω/ , and thus the real part of refractive index is the ratio of the speed of light in vacuum to its speed in a specific medium (n = Figure 1. Types of chirality with example geometries. ...
Plasmonic nanostructures are important tools in the study of chirality in the nanoscale. They are systems composed of conducting materials that support resonant excitations of the oscillatory motion of their...
... According to the Maxwell stress tensor method, the calculation of the stator axial force can be converted into a surface integral over the air domain enclosing all the coils [22,23]. This conclusion can be proved by numerical calculation [24][25][26][27], since the most classical method to derive the tensor involves using the Gauss flux theorem to obtain the tensor on the closed surface [28][29][30][31]. This conclusion has been widely used in the calculation of magnetic force and electromagnetic torque [32][33][34][35]. ...
Axial flux motors have gained widespread attention in the field of electric vehicles. The stator may exert a unilateral axial force on the dual rotors under uneven air gaps. The unbalanced magnetic pull can influence the production and processing of the motor, leading to issues such as vibrations, bearing degradation, reduced lifespan, and torque reduction attributed to the bearings. Accurate evaluation of the unilateral magnetic pull can reduce costs associated with bearing protection. For dual-rotor motors, the axial forces of the rotors act in opposite directions with nearly equal magnitudes, resulting in the catastrophic cancellation of unbalanced magnetic pull calculations. A similar phenomenon may occur between coils, introducing computational errors. To avoid these errors, the stator was selected as the computational target for unilateral axial force calculations. The integration domain was defined to encompass the entire air region containing all windings, rather than summing individual force components. This merged integration approach was mathematically validated through the Maxwell stress tensor method. Finally, the obtained stator axial force closely matched the rotor axial force in magnitude, demonstrating the accuracy of the proposed method.
... This interdependence reveals a critical flaw: the SI system is not a set of independent standards but a hierarchical structure rooted in the second. The mole, while appearing independent, is effectively a redefinition of the ampere in terms of countable quantities, as electric charge is observed in discrete multiples of 1 3 elementary charges [32]. This discreteness aligns with the Panvitalist Theory's emphasis on rational, countable quantities but highlights the SI system's failure to consistently apply this principle. ...
For nearly a decade, the author has pursued a comprehensive reinterpretation of physics, rooted in a critical analysis of its foundational axioms concerning the nature of reality. The discovery that the conventional understanding of time in both physics and society is fundamentally flawed has led to the identification of a centuries-long misinterpretation of reality, stemming from unsound first principles. This paper proposes a clear, precise, and logically compelling first axiom, paving the way for a radical reformulation of the physical and mathematical foundations of science. Central to this reformulation is the Panvitalist Theory, which introduces a discrete, 12-dimensional spacetime, eliminates all natural constants except the dimension count 12, and develops a rational number theory inspired by the ancient Pythagorean school, eschewing irrational numbers entirely. The theory integrates physics, mathematics, philosophy, and theology, positing life as the fundamental cause of the universe. This paper rigorously derives the 12-dimensional spacetime model, incorporating the projection of elliptical planetary orbits onto circular ones and a detailed error analysis. It presents testable hypotheses, such as the prediction of a third polarization plane for photons, and outlines the philosophical and theological implications of a life-centric cosmos. By summarizing the developmental milestones of the theory, this work offers a holistic framework for understanding spacetime and invites further interdisciplinary exploration.
... where the subscripts i, r, and t represent the incident, reflected, and transmitted waves, respectively. Since B = E·n/c (n: refractive index, n ≡ c/v) where v is the speed of an electromagnetic wave in matter [23], Equation (2) indicates that ...
Physical insight into a material can be first gained by its color, as the reflectance spectrum of an object reflects its microstructure and complex refractive indices. Here, we present a comprehensive overview of electrodynamics and optics related to reflectance spectra and color. We provide an open-source Python code for simulating reflectance spectra and extracting color values. The validity and applicability of the code are demonstrated through a comparative analysis with both the literature and experimental data. For SnO2 and ZnO thin films deposited on SiO2/Si substrates using rf sputtering, the Python code and simulation predict color variations with the film thickness and effectively capture their angular dependence. This code will help in understanding and making use of color-related phenomena. It can be further used and developed for various purposes, particularly machine learning, which requires extensive spectral and color data for model training.
... Using demonstration experiments, electric and magnetic field lines are visualized, for example, by semolina grains (Benimoff, 2006;Küchemann et al., 2021;Lincoln, 2017) or iron filings (Küchemann et al., 2021;Thompson, 1878), respectively. When representing a quantity as a vector field, the fields' properties, its divergence and curl, and further the integral theorems of Gauss and Stokes are of particular importance for physics applications (Griffiths, 2013). Accordingly, a sound understanding of vector calculus is of great importance for undergraduate and graduate physics studies. ...
Multiple external representations (e. g. diagrams, equations) and their interpretations play a central role in science and science learning as research has shown that they can substantially facilitate the learning and understanding of science concepts. Therefore, multiple and particularly visual representations are a core element of university physics. In electrodynamics, which students encounter already at the beginning of their studies, vector fields are a central representation typically used in two forms: the algebraic representation as a formula and the visual representation depicted by a vector field diagram. While the former is valuable for quantitative calculations, vector field diagrams are beneficial for showing many properties of a field at a glance. However, benefiting from the mutual complementarity of both representations requires representational competencies aiming at referring different representations to each other. Yet, previous study results revealed several student problems particularly regarding the conceptual understanding of vector calculus concepts. Against this background, we have developed research-based, multi-representational learning tasks that focus on the visual interpretation of vector field diagrams aiming at enhancing a broad, mathematical as well as conceptual, understanding of vector calculus concepts. Following current trends in education research and considering cognitive psychology, the tasks incorporate sketching activities and interactive (computer-based) simulations to enhance multi-representational learning. In this article, we assess the impact of the learning tasks in a field study by implementing them into lecture-based recitations in a first-year electrodynamics course at the University of Goettingen. For this, a within- and between-subjects design is used comparing a multi-representational intervention group (IG) and a control group (CG) working on traditional calculation-based tasks (N = 81). Group comparisons revealed that students in the intervention group scored significantly higher on a vector field performance test after the intervention (p = 0.04, d = 0.40) while perceiving higher cognitive load during task processing (extraneous p < 0.001, d = 0.75; intrinsic p = 0.02, d = 0.47; germane p = 0.02, d = 0.48). Moreover, students who worked with multi-representational learning tasks achieved higher normalized learning gains in tasks addressing conceptual understanding and representational competencies related to vector field diagrams and vector calculus concepts (gH, IG = 0.35, gH, CG = 0.13). These results provide guidance for the design of multi-representational learning tasks in field-related physics topics and beyond.
... It is unlikely that the training current, which generates an electric field on the order of 10 5 V/cm, can displace the localized states in the barrier if the states are generated by, for example, oxygen deficiencies. However, applying such a field can generate bound charge at the Al 2 O 3 /Hf 0.8 Zr 0.2 O 2 interface with its sign and density determined by the applied field [55]. Even after the training current is switched off, the presence of the bound charge may persist because of the low mobility of bound charge expected at low temperatures. ...
Josephson diode (JD) effect found in Josephson tunnel junctions (JTJs) has attracted a great deal of attention due to its importance for developing superconducting circuitry based quantum technologies. So far, the highly desirable electrical control of the JD effect has not been demonstrated in any JTJ prepared by techniques used in semiconductor industry. We report the fabrication of JTJs featuring a composite tunnel barrier of AlO and HfZrO prepared by complementary-metal-oxide-semiconductor (CMOS) compatible atomic layer deposition (ALD). These JTJs were found to show the JD effect in nominally zero magnetic fields with the nonreciprocity controllable using an electric training current, yielding a surprisingly large diode efficiency not achieved previously. The quasiparticle tunneling, through which the Josephson coupling in a JTJ is established, was found to show no nonreciprocity. We attribute these observations to the simultaneous presence of positive and negative Josephson couplings, with the latter originating from indirect tunneling. The resulted spontaneous time-reversal symmetry breaking and the double-minima washboard potential for the ensemble averaged phase difference in the resistively and capacitively shunted junction (RCSJ) model are shown to fully account for the experimentally observed JD effect.
... whereε = ϵ 2 /ϵ 1 is the ratio of the absolute permittivities. Boundary conditions (3) and (4) are consequences of the electrical potential's continuity across the boundary and of Gauss's law, respectively [46]. The far-field condition on the potential V 2 depends upon the generator of E. ...
... This radiation alters the magnetic field in the surrounding area, which in turn affects the electromagnetic waves emitted by the WiFi antenna. WiFi signals, which consist of continuously oscillating in-phase electric and magnetic fields [32], are particularly susceptible to these changes. The energy of an electromagnetic wave, which is derived equally from the electric and magnetic fields [19], can be expressed as: ...
Eavesdropping on sounds emitted by mobile device loudspeakers can capture sensitive digital information, such as SMS verification codes, credit card numbers, and withdrawal passwords, which poses significant security risks. Existing schemes either require expensive specialized equipment, rely on spyware, or are limited to close-range signal acquisition. In this paper, we propose a scheme, CSI2Dig, for recovering digit content from Channel State Information (CSI) when digits are played through a smartphone loudspeaker. We observe that the electromagnetic interference caused by the audio signals from the loudspeaker affects the WiFi signals emitted by the phone's WiFi antenna. Building upon contrastive learning and denoising autoencoders, we develop a two-branch autoencoder network designed to amplify the impact of this electromagnetic interference on CSI. For feature extraction, we introduce the TS-Net, a model that captures relevant features from both the temporal and spatial dimensions of the CSI data. We evaluate our scheme across various devices, distances, volumes, and other settings. Experimental results demonstrate that our scheme can achieve an accuracy of 72.97%.
... A very well known application of this technique is the determination of the potential induced by a charge distribution q outside of a conductor, while still obeying the zero potential at the conductor, by inserting an imaginary negative charge distribution -q on the opposite side. (Griffiths, 2005). The same abstraction may be applied to punctual electromagnetic sources, which allows one to write a Green's function that vanishes at a boundary (Scales, 1995;Schneider, 1978). ...
One of the objectives of the ESA/HERA mission is to perform 3D tomography of the two asteroids within the Didymos binary asteroid system. This presents unique challenges in synthetic aperture radar (SAR) imaging due to the specificities and limitations associated with small body ground penetrating SAR imaging and complex asteroid surfaces. Current methods for achieving 3D tomography of small celestial bodies using SAR imaging exhibit limitations, particularly in the presence of curved surfaces.This dissertation addresses these challenges by adapting the Kirchhoff Migration technique, a well-established method in seismic wave inversion, for asteroid SAR tomography. The optical path determination plays a significant role in inverting the signal backscattered from objects inside the asteroid, and is obtained by a minimization method based on Fermat’s Principle. Also, superellipsoidal shapes are employed to model the complex geometries of spinning-top shaped asteroids during the SAR data inversion process.The results of this research demonstrate significant advancements in the precision in retrieving the position of a scatterer embedded in bodies with curved surfaces while showing good elevation resolution in a multipass scenario. However, when applied to the imaging of irregularly shaped asteroids like Itokawa and Ryugu, the precision of target positioning is affected due to the challenging surface characteristics which can not be exactly modeled by any shape. Nevertheless, the approximation of spinning-top shaped asteroids to superellipsoids shows reasonable results, indicating the potential of this approach to invert SAR data from real spinning-top shaped asteroids as Didymain.
... Both times are real times, and their relationship is similar to that in Section 12.1.2 of Chapter 12 in Griffiths's "Introduction to Electrodynamics" (Griffiths, 2013) Wherein, v is the velocity of the charge movement in the wire, analogous to the gravitational field,v represents the motion speed of the ground relative to the GPS satellite. The "gamma factor" here reduces the electric field intensity. ...
By analogy with an infinitely long straight conductor carrying a current, this paper proposes modified formulas for electric field strength and magnetic field strength. Using these formulas, it is possible to calculate the time difference in GPS and the particle motion period in a cyclotron, with results consistent with those of relativity. However, the physical logic of these formulas differs from relativity. Relativity suggests that the increase in the particle period in a cyclotron is due to an increase in the particle's mass, whereas these formulas attribute it to a decrease in the magnetic field strength perceived by the particles.
... Electromagnetic phenomena are described by Maxwell's equations, see e.g. [23], ...
The use of topology optimization methods for the design of electric machines has become increasingly popular over the past years. Due to a desired increase in power density and a recent trend to high speed machines, thermal aspects play a more and more important role. In this work, we perform multi-material topology optimization of an electric machine, where the cost function depends on both electromagnetic fields and the temperature distribution generated by electromagnetic losses. We provide the topological derivative for this coupled multi-physics problem consisting of the magnetoquasistatic approximation to Maxwell's equations and the stationary heat equation. We use it within a multi-material level set algorithm in order to maximize the machine's average torque for a fixed volume of permanent-magnet material, while keeping the temperature below a prescribed value. Finally, in order to ensure mechanical stability, we additionally enforce a bound on mechanical stresses. Numerical results for the optimization of a permanent magnet synchronous machine are presented, showing a significantly improved performance compared to the reference design while meeting temperature and stress constraints.
... A special category of soft actuators is dielectric elastomer actuators (DEAs), consisting of a dielectric material sandwiched between two elastic electrodes [7,8]. Electrostatic actuation of DEAs induces Maxwell stress, which leads to a deformation of the actuator [9]. Compared to other soft actuators, DEAs ...
With the ongoing journey of automation advancements and a trend towards miniaturization, the choice of actuator plays a crucial role. Over recent years, soft actuators have demonstrated their usefulness in various applications, especially where light weight and high strain are required. Dielectric elastomer actuators (DEAs) are a class of soft actuators that provide high-strain actuation possibilities in applications like biomedicine, logistics, or consumer electronics. A variety of work featuring DEAs for actuation has been carried out in recent years, but a single work detailing the design conception, fabrication, modeling and experimental validation is lacking, especially in the context of achieving high strains with the integration of multiple electrodes and their interaction. This work discusses these issues with an equibiaxial DEA, enabling optimized equibiaxial strain patterns due to full use of the available actuation area. The developed DEA can achieve an equibiaxial strain of 12.75% for actuation at 60 V μm⁻¹ over an active area of 7 cm² which is an improvement of 1.3 times compared to traditional dot actuators. These properties position the device as a promising alternative for various applications like cell cultures or microassembly and provide an advantage of optimized use of passive regions within the actuator.
... a. Example -Long Pole and Short Barn Paradox Indeed, since the Aharonov-Bohm interaction is a 1∕c 2 relativistic effect, the point of view can be very different depending upon the inertial frame from which the interaction is described. This different-perspective situation, which is unfamiliar in nonrelativistic physics, is familiar in some of the "relativity paradoxes," such as the long-pole-and-short-barn paradox [15][16][17]. In the frame of the barn, the Lorentz contraction of the moving pole allows it to fit into the short barn. ...
Although the magnitude of the shift in the double-slit interference pattern when two electron beams pass outside a long solenoid has been confirmed in beautiful experiments, the direction of the deflection does not seem to appear in the published literature. It is claimed that careful quantum analysis gives a deflection direction opposite from that given by a classical electrodynamic analysis. Here we give a classical analysis of the interaction, and emphasize that the angle of deflection does not involve Planck’s constant. It is again suggested that a classical lag effect of order forms the basis for the observed shift in the particle interference pattern. The effect is claimed to be the analogue of a nonrelativistic electric effect, and the analogous magnetic and electric forces are given for the two different situations. The magnetic interaction is considered in two different inertial frames where different electromagnetic fields are involved. An optical analogy is also mentioned. Finally, we note that electromagnetic fluctuations might wash out the lag effect for macroscopic solenoids.
... Por ejemplo, el potencial armónico puede representar el confinamiento producido por una trampa óptica [9][10][11][12], mientras que el término logarítmico está asociado con la solución de la ecuación de Poisson para una partícula cargada en dos dimensiones. Además, éste puede representar la interacción electrostática de dos "varillas" cargadas [5,13], de tal manera que esta interacción puede usarse para modelar polielectrolitos y segmentos de ADN, en cuyo caso ξ está relacionado con la longitud de Bjerrum [14]. Un potencial logarítmico ha sido asociado también con la interacción efectiva entre dos polímeros de estrella, siendo ξ una medida relacionada con el radio de giro de los polímeros [15]. ...
Se propone un sistema unidimensional simple de dos partículas interactuantes cuyo comportamiento puede calcularse analíticamente. Se muestra en detalle el cálculo de la función de partición así como también el de cantidades fundamentales como la energía interna y la capacidad calorífica. La estructura espacial del sistema de dos partículas es analizada en términos de las distribuciones que describen la distancia de separaración entre las partículas y la posición de su centro de masa. La evolución del sistema hacia el equilibrio es descrita usando ecuaciones de Langevin en conjunto con las respectivas ecuaciones de Fokker-Planck. Los resultados analíticos son contrastados con los que se obtienen por medio de simulaciones computacionales sencillas basadas en dinámica browniana. En todos los casos el comportamiento del sistema se explica de manera simple y detallada de tal forma que la discusión y el modelo presentado pueden ser usados como un recurso pedagógico en cursos intermedios de mecánica estadística.
... where (a) follows the binomial approximation √ 1 + ≈ 1 + ∕2 as given in Reference [22] and (b) follows the condition v ≫ , and nv ≫ nv, , nv, . Furthermore, the channel model for VT and NVT considers the LoS channel that can be derived [23]. ...
Simultaneous Vortex and Non‐vortex based Transmission. Simultaneous vortex and non‐vortex‐based transmission (SVNT) is proposed to cover multiple users (UEs) (new and legacy). The element distance is derived based on the coordinates between the transmitter and receiver. Line‐of‐sight (LoS) channel models are approximated and derived with a modified Bessel function for legacy UEs (LUEs) and new UEs (NUEs). Three scenarios (S1, S2, S3) are proposed to compare the vortex‐based transmission (VT) and non‐vortex‐based transmission (NVT), SVNT (S1: LUEs only, S2: NUEs only, S3: Both LUEs and NUEs). For average capacity (AC), the coexistence of LUEs and NUEs is analyzed to account for backward compatibility. For outage probability (OP), connectivity parameters are introduced to error factor in antenna alignment. For throughput, the trade‐off between AC and OP is assessed concurrently. image
... A different interpretation of quantum mechanics, called Bohmian mechanics or hidden variables, was formulated by David Bohm in his seminal papers [5,6]. Bohmian claims that the wave function does not give a complete description of reality [11]. ...
In this article, we present a view that the interpretation of quantum mechanics lacks unanimous approval among physicists. To show its inadequacy, we describe the well-known measurement problem and discuss two solutions: an orthodox solution and hidden variables. We provide a brief overview of Bohmian mechanics. We then derive the continuity equation for quantum mechanics and show that a realist interpretation of the quantum probability current ->j leads to the guiding equation for Bohmian mechanics.
... with the specimen at the atomic scale induces a dipole moment ( ⃗ ) that defines the polar izability ( ) as [13]: If the molecular polarizability is expanded into a Taylor series to the first order for a generalized coordinate r = r 0 cos(ω 0 t), which is expressed as follows: ...
The World Health Organization (WHO) cancer agency predicts that more than 35 million cases of cancer will be experienced in 2050, a 77% increase over the 2022 estimate. Currently, the main cancers diagnosed are breast, lung, and colorectal. There is no standardized tool for cancer diagnoses; initially, clinical procedures are guided by the patient symptoms and usually involve biochemical blood tests, imaging, and biopsy. Label-free non-linear optical approaches are promising tools for tumor imaging, due to their inherent non-invasive biosafe contrast mechanisms and the ability to monitor collagen-related disorders, and biochemical and metabolic changes during cancer progression. In this review, the main non-linear microscopy techniques are discussed, according to three main contrast mechanisms: biochemical, metabolic, and structural imaging.
... Dirac [1] proposed the existence of magnetic monopoles with the purpose of achieving this symmetry in the Maxwell equations. The hypothesis of magnetic monopoles can be explored from the theoretical point of view through the duality transformations in the Maxwell equations [2][3][4][5]. It has also been used in the search for unified gauge theories [6][7][8][9][10]. ...
We discuss the missing He-McKellar-Wilkens geometric quantum phase in Landau levels for a neutral particle with a permanent electric dipole moment in the presence of an infinity wall. We also discuss the influence of the missing He-McKellar-Wilkens geometric quantum phase on the energy levels of a neutral particle confined to a one-dimensional quantum ring. Further, we explore this influence of the missing He-McKellar-Wilkens geometric quantum phase on the energy levels by calculating the persistent spin currents.
... Biot-Savart's law [68], and is given by ...
Coherent structures (CS) are known to be part of the foundations of turbulent flow dynamics. For a long time, their appearance was believed to be chaotic and unorganized. However, it has been demonstrated through numerical simulations and experiments that a high degree of organization of CS could be attributed to the constitution of a turbulent state. Understanding these organizational dynamics promises to bring valuable theoretical and applied predictions, such as the average lifetime of turbulent structures and understanding the role of CS in particulate transport. The identification of CS was achieved by selecting the most energetic mode in the flow direction within a specified reference shell. Furthermore, the transition dynamics between the identified CS was investigated as a stochastic process, revealing a non-Markovian effect through an algebraic decay of the temporal self-correlation of the identified CS. Finally, the non-Markovian behavior observed between the transitions of CS was reproduced by a low-level Markovian model, which takes into account the degeneracy effects in the definition of the identified CS. In order to obtain an algorithm capable of simulating the quasi-static regime in magnetohydrodynamic (MHD) flows a multiple-relaxation-time (MRT) model and a distance-dependent boundary condition were introduced for the lattice Boltzmann method (LBM) associated with the induction equation for MHD flows. Finally, a turbulent pipe flow simulation was performed by the LBM with a MRT model for hydrodynamic distributions. The identification of CS revealed a non-trivial memory effect with respect to the force that triggered the turbulent state. The transition dynamics of CS revealed a Markovian behavior for finely resolved time data, indicating that experimental behavior could be recovered for larger time separations and, consequently, a larger dataset.
... Biot-Savart's law [68], and is given by ...
Coherent structures (CS) are known to be part of the foundations of turbulent flow dynamics. For a long time, their appearance was believed to be chaotic and unorganized. However, over the past two decades, it has been demonstrated through numerical simulations and experiments that a high degree of organization of CS could be attributed to the constitution of a turbulent state. Understanding these organizational dynamics promises to bring valuable theoretical and applied predictions, such as the average lifetime of turbulent structures, understanding the role of CS in particulate transport, and in the development of fusion reactors since a reduction of heat transfer is expected for less turbulent flows.
In this Ph.D. dissertation, a statistical analysis of an experimental database of a turbulent pipe flow --aimed to investigate the dynamics of CS for a wide range of turbulent intensities-- was carried out at the Interdisciplinary Center for Fluid Dynamics - UFRJ. The identification of CS was achieved by selecting the most energetic mode in the flow direction within a specified reference shell. Furthermore, the transition dynamics between the identified CS was investigated as a stochastic process, revealing a non-Markovian effect through an algebraic decay of the temporal self-correlation of the identified CS. Finally, the non-Markovian behavior observed between the transitions of CS was reproduced by a low-level Markovian model, which takes into account the degeneracy effects in the definition of the identified CS.
In order to obtain an algorithm capable of simulating the quasi-static regime in magnetohydrodynamic (MHD) flows --relevant in most industrial applications-- a multiple-relaxation-time (MRT) model and a distance-dependent boundary condition were introduced for the lattice Boltzmann method (LBM) associated with the induction equation for MHD flows. Finally, a turbulent pipe flow simulation was performed by the LBM with a MRT model for hydrodynamic distributions. The identification of CS revealed a non-trivial memory effect with respect to the force that triggered the turbulent state. The transition dynamics of CS revealed a Markovian behavior for finely resolved time data, indicating that experimental behavior could be recovered for larger time separations and, consequently, a larger dataset.
... Recall in the far-field approximation for a magnetic dipole, the field strength goes as B ∝ 1 R 3 . 39 In this experiment, we will satisfy our goal by in principle allowing the magnetic field strength to be completely determined by the label R. This is done for 1) ease as measuring R is much easier than measuring the external magnetic field strength directly, and 2) performance as typically we would like evenly and linearly sampled targets for our regression task 40 . ...
The axion is a compelling hypothetical particle that could account for the dark matter in our universe, while simultaneously explaining why quark interactions within the neutron do not appear to give rise to an electric dipole moment. The most sensitive axion detection technique in the 1 to 10 GHz frequency range makes use of the axion-photon coupling and is called the axion haloscope. Within a high Q cavity immersed in a strong magnetic field, axions are converted to microwave photons. As searches scan up in axion mass, towards the parameter space favored by theoretical predictions, individual cavity sizes decrease in order to achieve higher frequencies. This shrinking cavity volume translates directly to a loss in signal-to-noise, motivating the plan to replace individual cavity detectors with arrays of cavities. When the transition from one to (N) multiple cavities occurs, haloscope searches are anticipated to become much more complicated to operate: requiring N times as many measurements but also the new requirement that N detectors function in lock step. To offset this anticipated increase in detector complexity, we aim to develop new tools for diagnosing low temperature RF experiments using neural networks for pattern recognition. Current haloscope experiments monitor the scattering parameters of their RF receiver for periodically measuring cavity quality factor and coupling. However off-resonant data remains relatively useless. In this paper, we ask whether the off resonant information contained in these VNA scans could be used to diagnose equipment failures/anomalies and measure physical conditions (e.g., temperatures and ambient magnetic field strengths). We demonstrate a proof-of-concept that AI techniques can help manage the overall complexity of an axion haloscope search for operators.
A common technique used in factories to shape metal panels is shot peen forming, where the panel is sprayed with a high-velocity stream of small steel pellets called shot. The impacts between the hard steel shot and softer aluminum panel cause localized plastic deformation, both improving the fatigue properties of the material's surface and imparting a residual stress distribution that results in bending. Thus, a torque is associated with the through-thickness shot peen stress distribution. We conceptualize shot peen forming as the application of spatially varying torques, which are modeled with the input of applied temperatures. In this paper, we derive the bending equations for a thermally loaded homogeneous Kirchhoff plate in order to predict the effects of shot peen forming. A simple test is devised to extract the value of an equivalent applied torque from the bending response of uniformly shot peened plates, which circumvents the difficulty of accounting for surface plasticity. This torque can be used as an input to a model which predicts the shape of rectangular plates under more complicated shot peen conditions. An experiment is designed and carried out which investigates the agreement between the model and real shot peen operations. The effect of uncertainty in the experiment is estimated with Monte Carlo methods.
The advancement of miniaturized, high-efficiency nanogenerators for energy harvesting demands precise
characterization of piezoelectric and triboelectric outputs. This study employs a unique methodology to isolate and characterize
the piezoelectric and triboelectric signals from the as-received piezoelectric output, enabling an accurate evaluation of the true
piezoelectric response. Ground shielding layers were employed to suppress triboelectric interference, contributing toward precise
evaluation and optimization of the actual piezoelectric output. A detailed investigation of the signal generation mechanisms based on
dynamic electric field formation was conducted, revealing distinct charge redistribution behaviors governing piezoelectric and
triboelectric contributions. The triboelectric signal exhibited its typical characteristics, including a longer response time and a
smoother curve than that of the piezoelectric signal. Additionally, nanocapacitor-based mechanisms owing to nanoparticle inclusion
were explored to enhance charge storage and polarization effects within the system, leading to improved energy conversion
efficiency. These insights were leveraged to develop an integrated hybrid piezo/tribo nanogenerator (PTNG), where triboelectric
interference was strategically utilized as a functional amplification mechanism. The final optimized PTNG exhibited a peak-to-peak
output voltage of 81.58 V, a current density of ∼6.4 μA/cm2, and a power density of ∼240 μW/cm2, demonstrating its potential for
efficient energy harvesting in portable electronics. These findings establish a robust framework for precise piezoelectric performance
evaluation while highlighting the potential of compact and integrated hybrid devices for achieving device miniaturization without
sacrificing efficiency. This work paves the way for sustainable energy solutions in flexible electronics and wearable sensor
applications
The annual periodicity present in spectral remote sensing reflectances (Rrs(λ)) derived from ocean color satellite data processed by NASA's Ocean Biology Processing Group has been shown to diverge from that observed in situ, with the source of the discrepancies remaining unresolved. Here we investigate such periodicity in reflectances derived from four satellite sensors and seven in situ locations. Periodicity in the time series of Rrs(λ) spectra are examined without prior assumption of the main constituent frequency through application of the floating-mean Lomb-Scargle periodogram. We show that a 1-term sinusoidal function specified at the annual frequency with a constant offset reproduces seasonal trends observed at various regional oceanic sites. Although unique regional features in mean, amplitude, and phase are generally well captured by Rrs(λ) derived from satellite measurements, discrepancies perpetuate the annual frequency into the satellite-to-in situ Rrs(λ) matchup difference. Specifying the origin of the discrepancy is challenging because the annual frequency is significantly contained in time series of many physical measurements, corrections, and ancillary data required for Rrs(λ) retrievals. Until differences in amplitude and phase between satellite and in situ Rrs(λ) time series are reduced, improved uncertainty estimates should be incorporated into downstream product analyses.
This paper corrects the formulas for electric and magnetic field strengths, deriving an expression similar to the gamma factor. Using the modified formulas for electric and magnetic fields, the time difference in GPS and the time dilation in a cyclotron were calculated, yielding results consistent with relativity. However, the advantage of the formulas presented in this paper is that they do not require the bending of spacetime.
We review Maxwell’s equations, incorporating magnetic monopoles, and derive the electric and magnetic fields applying the Helmholtz decomposition. By extending this decomposition to symmetric traceless tensors, we obtain the gravitoelectric and gravitomagnetic fields through the Maxwell-like equations of gravitoelectromagnetism with gravitomagnetic monopoles naturally present in them.
The aeroacoustic analogy is reviewed. The importance of generalized functions is demonstrated deriving Gauss like theorems in three and two dimensions. It is shown how the Dirac delta function plays an essential part in the theory of fundamental solutions (Green’s function). The concept of generalized derivatives as introduced by Farassat is derived in a consistent way for the time derivative and vector operations, for example gradient, divergence and curl. Applied to the wave equation, the impact of these operators when acting on surface distributions is presented. The compatibility conditions which apply at static and moving surfaces are derived in a unique manner. New source terms are found for the FW-H equation which steam from second order generalized derivatives, whereas all terms with the mass flux vector cancel out due to symmetry conditions. This procedure is validated by the derivation of the same result from the Lighthill equation directly and a term-by-term comparison with the Kirchhoff formula. Finally, it is shown how terms, containing the curvature of the integration surface, appear in the final solutions. The role of the δ ′ ( f ) factor in generating dipole as well as monopole sources is outlined. Essential knowledge provided from electromagnetic research is transferred to aeroacoustic theory. The vector wave equation is proposed instead of the scalar version to mitigate spurious noise effects.
In cosmological special relativity theory, we study Maxwell equations, electromagnetic wave equations and functions. In the cosmological special theory of relativity, we study energy-momentum relations, the Klein-Gordon equation and wave functions. If we solve the Klein-Gordon equation, we obtain the Yukawa potential in the cosmological inertial frame. We derive the Schrodinger equation from Klein-Gordon free particle’s wave function in the cosmological special theory of relativity. We derive the uncertainty principle in cosmological quantum mechanics in cosmological special relativity theory. The Dirac equation is a one order wave equation. The wave function is used as a probability amplitude in quantum mechanics. We derive the Dirac equation from the wave function, Type A in the cosmological inertial frame. The Dirac equation satisfies the Klein-Gordon equation in the cosmological inertial frame. We found equations of complex scalar fields and electromagnetic fields on the interaction of complex scalar fields and electromagnetic fields in Klein-Gordon-Maxwell theory from Type A of the wave function and Type B of the expanded distance in the cosmological inertial frame. In the cosmological special theory of relativity, we quantized the Klein-Gordon scalar field. We treat the Lagrangian density and Hamiltonian in a quantized Klein-Gordon scalar field. We address the particle’s force and kinetic energy in the cosmological special theory of relativity. In the expanded universe, we found the gravity field equation and solution. We found the Schwarzschild solution and Kerr-Newman solution in an expanded universe. Hence, we found a new general relativity theory-the Cosmological General Theory of Relativity (CGTR).
PC steel material inside pre-stressed concrete bridges is prone to corrosion due to the effect of salt, which leads to cross-sectional losses and fractures if proper maintenance is not carried out, affecting the girders’ structural performance. In Japan, pre-tensioned girders incorporating small-diameter PC steel material with a span length of 13 m or less were used until the early 1980s. Thus, it is essential to understand the fracture conditions of PC steel material and the factors affecting section loss due to corrosion, in order to properly assess the residual strength of salt-affected pre-tensioned girders. Hence, the current research clarifies the accuracy of techniques used for detecting deterioration in a pre-tensioned PC girder that had been out of service for about 40 years, caused by exposure to the severely saline environment of the Okinawa coast. Visual and hammer-tapping investigation of the actual bridge in addition to fracture investigation of the PC steel material using the triaxial magnetic method and destructive investigation of the concrete cover on the bottom of the girder were carried out and correlated. The final results confirmed that the triaxial magnetic method could detect PC steel material fractures accurately, and valuable information was obtained regarding fracture-detection technology for application in PC girders via non-destructive testing.
Recently light-driven microdrones have been demonstrated, making use of plasmonic nanomotors based on directional resonant chiral light scattering. These nanomotors can be addressed individually, without requiring the tracking of a focused laser, leading to exceptional 2D maneuverability which renders microdrones a versatile robotic platform in aqueous environments. Here, we incorporate a light-operated manipulator, a plasmonic nano-tweezer, into the microdrone platform, rendering it a microrobot by enabling precise, all-optical transport and delivery of single nanoparticles suspended in solution. The plasmonic nano-tweezer consists of a resonant cross-antenna nanostructure exhibiting a central near-field hot spot, extending the ability of traditional optical tweezers based on focused laser beams to the trapping of nanoparticles. However, most of plasmonic nano-tweezers are fixed to the substrates and lack mobility. Our plasmonic microrobot utilizes circularly polarized light to control both motors and for stable trapping of a 70-nanometer fluorescent nanodiamond in the cross-antenna center. Complex sequences of microrobot operations, including trap-transport-release-trap-transport actions, demonstrate the microrobot’s versatility and precision in picking up and releasing nanoparticles. Our microrobot design opens potential avenues in advancing nanotechnology and life sciences, with applications in targeted drug delivery, single-cell manipulation, and by providing an advanced quantum sensing platform, facilitating interdisciplinary research at the nanoscale.
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