Mario Liu

Mario Liu
University of Tuebingen | EKU Tübingen · Institute for Theoretical Physics

Prof. Dr.

About

153
Publications
21,952
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Introduction
Mario Liu currently works at the Institute for Theoretical Physics, University of Tuebingen. Mario does research in Theoretical Physics, Thermodynamics and Fluid Dynamics. The current project is "GSH -- granular solid hydrodynamics."
Additional affiliations
January 1983 - October 2001
Leibniz Universität Hannover
Position
  • Professor

Publications

Publications (153)
Article
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Jamming/un-jamming, the transition between solid- and fluid-like behavior in granular matter, is an ubiquitous phenomenon in need of a sound understanding. As argued here, in addition to the usual un-jamming by vanishing pressure due to a decrease of density, there is also yield (plastic rearrangements and un-jamming that occur) if, e.g., for given...
Chapter
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The effective stress of unsaturated soil media is defined in most rigorous way using Landau’s hydrodynamic procedure, and its structure derived under conditions that are close to thermodynamic equilibrium. This derivation is complete and accurate for soils with negligible cohesion effects (degrees of saturation \(\gtrapprox \) 2–3%). The richness i...
Article
In ‘Rational Mechanics’ the work input per unit element volume can be identified from the local energy balance, itself being derived through localization from the global energy balance of an arbitrary volume. On the other hand, in the search of meaning for an effective stress of partially and fully saturated soil media, in ‘Soil Mechanics’ some def...
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Two approaches exist to account for granular dynamics: The athermal one takes grains as elementary, the thermal one considers the total entropy that includes microscopic degrees of freedom such as phonons and electrons. Discrete element method (DEM), granular kinetic theory and athermal statistical mechanics (ASM) belong to the first, granular soli...
Article
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Granular solid hydodynamics (GSH) is generalized to account for segregation. The necessary change is minimal, and consists in introducing the concentration c as an additional variable. There is no need for the stress and velocity of every population. GSH’s functionality with respect to all other granular phenomena – from elasto-plastic motion and s...
Article
A rigorous thermodynamic treatment of partially saturated soils is developed using a minimal number of assumptions. The derivation is carried out in a way that does not require to explicitly track the complex shapes of interfaces between the solid, fluid and gas domains. Instead, suction is the property being recovered explicitly through the minimi...
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Accounting for elasto-plastic motion in granular media, hypoplasticity is a state-of-the-art constitutive model derived from data accumulated over many decades. In contrast, GSH, a hydrodynamic theory, is derived from general principles of physics, with comparatively few inputs from experiments, yet sporting an applicability ranging from static str...
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As grains are too large to display thermal fluctuations, they are widely taken as particles without any internal structure, and considered "athermal." Though frequently an excellent approximation, this fails in any considerations involving the entropy, because the inner-granular, microscopic degrees of freedom are then the dominating ones. We clari...
Article
Transient elasticity (TE) is a concept useful for a systematic generalization of viscoelasticity. Due to its thermodynamic consistency, it naturally leads to a simple description of non-Newtonian effects displayed by polymeric fluids, granular media, and other soft matter. We employ a continuum-mechanical theory that is derived from TE and tailored...
Article
Transient elasticity is a systematic generalization of viscoelasticity. Its purpose is to give a coherent description of non-Newtonian effects displayed by soft-matter systems, especially polymer melts and solutions. Using the concept of transient elasticity we describe here a hydrodynamic model for polymeric fluids, which is applicable for large a...
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A unified continuum-mechanical theory has been until now lacking for granular media, some believe it could not exist. Derived employing the hydrodynamic approach, GSH is such a theory, though as yet a qualitative one. The behavior being accounted for includes static stress distribution, elastic wave, elasto-plastic motion, the critical state and ra...
Article
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Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for granular media, whose wide range of applicability is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: i) static stress distribution, clogging; ii) elasto-plastic motion: loading and unloading, ap...
Article
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Granular media are considered "athermal", because the grains are too large to display Brownian type thermal fluctuations. Yet being macroscopic, every grain undergoes thermal expansion, possesses a temperature that may be measured with a thermometer, and consists of many, many internal degrees of freedom that in their sum do affect granular dynamic...
Article
Maxwell's stress tensor is well known from electromagnetic theory. But correct application of it to practical problems is by no means general knowledge even among experts. In this article we present a survey of the electromagnetic stress tensor and of the electromagnetic forces in strongly polarizable materials. We relate the observed ponderomotori...
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Vibrating walls, frequently employed to maintain the temperature (i.e., average velocity) in a granular gas, modify the system strongly, rendering it dissimilar to a molecular one in various aspects. As evidenced by microgravity experiments employing a quasi-two-dimensional (quasi-2D) rectangular box and by 2D simulations, the one-peak velocity dis...
Article
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Granular solid hydrodynamics (GSH) is employed to account for granular rheology, both the rate-controlled one, smoothly extending from the critical state to the Bagnold regime, and the stress-controlled one that is discontinuous and hysteretic. Employing GSH, it is shown that a quiescent state is stable below the smaller jamming stress and instable...
Article
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A microgravity experimental study of vibrofluidized granular gas with intermediate number density is performed. Local velocity distributions are investigated, and are found to deviate measurably from a symmetric distribution for the velocity component in the direction of vibration due to the boundary heating mechanism. One generalized granular hydr...
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Propotional paths as summed up by the Goldscheider Rule (GR) -- stating that given a constant strain rate, the evolution of the stress maintains the ratios of its components -- is a characteristics of elasto-plastic motion in granular media. Barodesy, a constitutive relation proposed recently by Kolymbas, is a model that, with GR as input, successf...
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Recent experiments reveal an unexpected dip of the shear stress as the shear rate increases, from the rate-independent regime to Bagnold flow. Employing granular solid hydrodynamics, it is shown that in uniform systems, such dips occur for given pressure or normal stress, but not for given density. If the shear rate is strongly nonuniform, enforcin...
Article
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{\sc gsh} is a continuum mechanical theory constructed to qualitatively account for a broad range of granular phenomena. To probe and demonstrate its width, simple solutions of {\sc gsh} are related to granular phenomena and constitutive models, including (i) for vanishing shear rates: static stress distribution and propagation of elastic waves; (i...
Article
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Vibrating walls, used to maintain the temperature in a granular gas, modify the system strongly. Most conspicuously, the usual one-peak velocity distribution splits into two, asymmetrically positioned. A surgical repair of the usual hydrodynamic description is presented that provides an account for, and an understanding of, the situation.
Article
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Granular Solid Hydrodynamics (GSH) is a broad-ranged continual mechanical description of granular media capable of accounting for static stress distributions, yield phenomena, propagation and damping of elastic waves, the critical state, shear band, and fast dense flow. An important input of GSH is an expression for the elastic energy needed to def...
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The hydrodynamic approach to a continuum mechanical description of granular behavior is reviewed and elucidated. By considering energy and momentum conservation simultaneously, the general formalism of hydrodynamics provides a systematic method to derive the structure of constitutive relations, including all gradient terms needed for nonuniform sys...
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The propagation of elastic waves in a box under direct shear, filled with glass beads and being sheared at constant rates, is studied experimentally and theoretically. The respective velocities are shown to be essentially unchanged from that in a static granular system under the same pressure and shear stress but without a shear band. Influence of...
Article
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Granular solid hydrodynamics, constructed to describe quasi-elastic and plastic motion of granular solid, is shown also capable of accounting for the rheology of granular dense flow. This makes it a unified, though still qualitative, hydrodynamic description, enabling one to tackle fluidization and jamming, the hysteretic transition between elasto-...
Article
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The anisotropic stress-dependent velocity of elastic waves in glass beads--as observed by Khidas and Jia [Phys. Rev. E 81, 021303 (2010)]--is shown to be well accounted for by "granular solid hydrodynamics," a broad-range macroscopic theory of granular behavior. As the theory makes no reference to fabric anisotropy, the influence of which on sound...
Article
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The recently published theory named Granular Solid Hydrodynamics (GSH) is outlined, supported and quantified with arguments from physics as well as soil mechanics. Seismodynamic equilibria serve to introduce a granular temperature T g and a related entropy s g , both with gradients. The evolution equations of GSH are first presented without gradi...
Article
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The approach to the critical state -- the transition from partially elastic to perfectly plastic behavior -- is considered the most characteristic of granular phenomena in soil mechanics. By identifying the critical state as the steady-state solution of the elastic strain, and presenting the main results as transparent, analytic expressions, the ph...
Article
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Compaction, of both the reversible and irreversible branch, is deduced from granular solid hydrodynamics. The first is related to the pressure exerted by agitated grains, the second to the slow relaxation of granular deformation. The latter occurs because jiggling grains briefly loose contact with one another, and is what gives rise to the plastic...
Article
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The possibility of dissipative contributions to the mass flux is considered in detail. A general thermodynamically consistent framework is developed to obtain such terms, the compatibility of which with general principles is then checked-including Galilean invariance, the possibility of steady rigid rotation and uniform center-of-mass motion, the e...
Article
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When at rest, sand maintains shear stresses as durably as an elastic medium—see the tilted slopes of a sand dune that persists forever if unperturbed. When being sheared, sand becomes transiently elastic, because grains partially loose contact with one another, during which the elastic stress relaxes. The flip‐flop between permanent and transient e...
Article
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A complete continuum mechanical theory for granular media, including explicit expressions for the energy current and the entropy production, is derived and explained. Its underlying notion is: granular media are elastic when at rest, but turn transiently elastic when the grains are agitated—such as by tapping or shearing. The theory includes the tr...
Chapter
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It is demonstrated how the complete structure of Newtonian ferrofluid dynamics, including magneto-dissipative effects, is derived from general principles. Ferrofluids are taken as homogeneous magnetizable fluids with a magnetic relaxation time sufficiently large to compare with other hydrodynamic time scales. The derivation makes no reference to th...
Chapter
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Nonlinear hydrodynamic equations for non-Newtonian fluids are discussed. We start from the recently derived hydrodynamic-like nonlinear description of a slowly relaxing orientational order parameter tensor. The reversible quadratic nonlinearities in this tensor’s dynamics are material dependent due to the generalized nonlinear flow alignment effect...
Article
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A Comment on the Letter by Hans Christian Öttinger, [Phys. Rev. Lett. 99, 130602 (2007)]. The author of the Letter offers a Reply.
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Granular media are reversible and elastic if the stress increments are small enough. An elastic stress-strain relation, employed previously to determine static stress distributions, in this paper is compared to experiments by Kuwano and Jardine [Geotechnique 52, 727 (2002)] on incremental stress-strain relations, and shown to yield satisfactory agr...
Article
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The larger magnetic particles in ferrofluids are known to form chains, causing the fluid to display non-Newtonian behavior. In this paper, a generalization of the familiar ferrofluid dynamics by Shliomis is shown capable of realistically accounting for these fluids. The modification consists of identifying the relaxing magnetization as that of the...
Article
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"Granular elasticity," useful for calculating static stress distributions in granular media, is generalized by including the effects of slowly moving, deformed grains. The result is a hydrodynamic theory for granular solids that agrees well with models from soil mechanics.
Article
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General boundary conditions for smectic shear flows are derived and their consequences examined. At low frequencies, a new stationary solution is found that exists concurrently with second-sound. At higher frequencies, these two solutions turn diffusive. Experimental implications are studied. Modified impedance, velocity slip, and a "Josephson effe...
Article
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The general hydrodynamic theory of the 3He A → B transition that includes the influence of finite geometries is presented. Lateral walls hold back the normal velocity and confine the range of heat transfer via second sound. This alters the temperature and counterflow fields but not the transition velocity. Its dependence on the diameter and materia...
Article
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Although fully elastic when static, granular media become transiently elastic when being slowly sheared -- during which both the elastic energy and stress relax. Starting from this observation, we cogently derive the framework for granular hydrodynamics, a set of differential equations consistent with general principles of physics, especially rever...
Article
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Although granular materials are predominantly plastic, preparation-dependent, anisotropic under shear, and incrementally nonlinear, their static stress distribution is well accounted for, in the whole range up to the point of failure, by an isotropic, nonlinear and carefully tailored elasticity theory termed GE, for "granular elasticity". Its usefu...
Article
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Granular materials are predominantly plastic, incrementally nonlinear, preparation-dependent, and anisotropic under shear. Nevertheless, their static stress distribution is well accounted for, in the whole range up to the point of failure, by a judiciously tailored isotropic nonanalytic elasticity theory termed granular elasticity. The first purpos...
Article
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An elastic-strain-stress relation, the result of granular elasticity as introduced in the preceding paper, is employed here to calculate the stress distribution (a) in cylindrical silos and (b) under point loads assuming uniform density. In silos, the ratio k{J} between the horizontal and vertical stress is found to be constant (as conjectured by J...
Article
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The relaxation of magnetization, a well-accepted part of ferrofluid dynamics, is shown to give rise to a broad range of non-Newtonian behaviour in ferrofluids, including shear thinning or shear thickening, normal stress differences, a visco-elastic response and a varying Trouton, or elongational, viscosity.
Article
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A magnetic field rotating on the free surface of a ferrofluid layer is shown to induce considerable fluid motion towards the direction the field is rolling. The measured flow velocity (i) increases with the square of the magnetic field amplitude, (ii) is proportional to the thickness of the fluid layer and (iii) has a maximum at a fluid specific fr...
Article
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We review conventional constitutive equations for non-Newtonian fluids from a hydrodynamic point of view. Using general thermodynamic and symmetry arguments and applying valid physical principles we describe viscoelasticity by setting up nonlinear dynamic equations either for a relaxing (Eulerian) strain tensor or for a transient orientational orde...
Article
Full-text available
A magnetic field rotating on the free surface of a ferrofluid layer is shown to induce considerable fluid motion toward the direction the field is rolling. The measured flow velocity (i) increases with the square of the magnetic field amplitude, (ii) is proportional to the thickness of the fluid layer, and (iii) has a maximum at a driving frequency...
Article
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Jamming is a phenomenon occurring in systems as diverse as traffic, colloidal suspensions, and granular materials. A theory on the reversible elastic deformation of jammed states is presented. First, an explicit granular stress-strain relation is derived that captures many relevant features of sand, including especially the Coulomb yield surface an...
Article
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There is a thermodynamic approach to macroscopic electrodynamics, unfortu-nately far too little known, which is rigoros, powerful, and above all, simple. It yields unambiguous answers to many questions, especially the conceptually sub-tle ones about field dissipation and electromagnetic forces. This article presents a thorough yet pedagogical revie...
Article
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A unified, consistent and simple view of the Faraday law of induction is presented, which consists of two points: discriminating the lab- from the rest-frame electric field and understanding it is the impossibility for both fields to vanish simultaneously, which generates and maintains the circular current. A number of illustrative examples are con...
Article
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Nonlinear hydrodynamic equations for visco-elastic media are discussed. We start from the recently derived fully hydrodynamic nonlinear description of permanent elasticity that utilizes the (Eulerian) strain tensor. The reversible quadratic nonlinearities in the strain tensor dynamics are of the 'lower convected' type, unambiguously. Replacing the...
Article
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A factor of k sound =k shear was missed when we plugged in numbers to estimate the orders of magnitude of the considered effect, where k sound and k shear are the wave vectors of sound and shear, respectively. We took 0 as 1 2 k shear !x 20 Hz, yet Eq. (21) is valid only if 0 is properly identified as 1 2 k sound !x. As a result, in the example tha...
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A self-contained elastic theory is derived which accounts both for mechanical yield and shear-induced volume dilatancy. Its two essential ingredients are thermodynamic instability and the dependence of the elastic moduli on compression.
Article
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Derived from general principles, the recently introduced ferrofluid dynamics is structurally identical to Shliomis’ theory for incompressional flows, yet distinctly different for compressional ones. It provides a complementary point of view for the first case, but also shows that the standard theory partially violates general principles. Overemphas...
Article
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The damping of sound waves in magnetized ferrofluids is investigated and shown to be considerably higher than in the nonmagnetized case. This fact may be interpreted as a field-enhanced, effective compressional viscosity-in analogy to the ubiquitous field-enhanced shear viscosity that is known to be the reason for many unusual behaviors of ferroflu...
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A Comment on the Letter by G. L. J. A. Rikken and B. A. van Tiggelen, Phys. Rev. Lett. 78, 847 (1997). The authors of the Letter offer a Reply.
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Perceptible sound is shown to be excited in ferrofluids by the shear motion of a rigid plate, if the fluid is exposed to a magnetic field oblique both to the plate and to the direction of propagation. This is in contrast to other fluids, including anisotropic ones such as nematic liquids.
Article
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Nonlinear hydrodynamic equations for polymeric uids with permanent or transient orientational order are discussed. We start from a description that utilizes the well-known nematohydrodynamic equations for low molecular weight uniaxial nematics. We concentrate on the reversible nonlinearities in the dynamic equation for the orientational tensor orde...
Article
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Introduction The hydrodynamic description of lowmolecular -weight nematic liquid crystals is well established. Nematic-like degrees of freedom are not only relevant for truly thermodynamic nematic phases, but also play a role for isotropic phases close to the transition temperature. To describe these nematic uctuations a second rank tensor, the ful...
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In superconductors, both the persistent electric current and the magnetic field are shown here to be quantities that relax quickly if off equilibrium, with a characteristic time of order 10−15 s. Therefore, they do not belong to the set of independent variables needed to construct the superconducting hydrodynamic theory. This fact renders the theor...
Article
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The general structure of the hydrodynamic equations for ferrofluids is derived, with the grain in rigor paid by a loss of specific information on the transport parameters. The validity of the approach is corroborated by the ease with which two previous experiments associated with magnetodissipation: "negative viscosity" and "magnetovortical resonan...
Article
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Nonlinear hydrodynamic equations for polymeric fluids with permanent or transient orientational order are discussed. We start from a description that utilizes the well-known nematohydrodynamic equations for low molecular weight uniaxial nematics. We concentrate on the reversible nonlinearities in the dynamic equation for the orientational tensor or...
Article
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Two facts are pointed out: 1 Only when the diffusion equation is inadmissibly applied, outside its defined range of validity, does it lead to acausal predictions; 2 although there are many instances in which usually diffusive hydrodynamic variables propagate wave-like in condensed systems, none of them are connected with this appearance of acausali...
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A Reply to the Comment by A. Engel
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A Reply to the Comment by Antony N. Beris et al.
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We derive nonlinear hydrodynamic equations for visco-elastic media using the Eulerian description for all macroscopic quantities and especially for the strain tensor. The form of the convective nonlinearities is xed by the requirement that in the appropriate limit the hydrodynamic equations for solids have to emerge. Dierences to previous descripti...
Book
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While the electromagnetic force is microscopically simply the Lorentz force, its macroscopic form is more complicated, and given by expressions such as the Maxwell stress tensor and the Kelvin force. Their derivation is fairly opaque, at times even confusing, and their range of validity all but a well kept secret. These circumstances unnecessarily...
Article
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 We derive nonlinear hydrodynamic equations for visco-elastic media using the Eulerian description for all macroscopic quantities and especially for the strain tensor. The form of the convective nonlinearities is fixed by the requirement that in the appropriate limit the hydrodynamic equations for solids have to emerge. Differences to previous desc...
Article
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Direct and unambiguous experimental evidence for the magnetic force density being of the form $M\nabla B$ in a certain geometry - rather than being the Kelvin force $M\nabla H$ - is provided for the first time. (M is the magnetization, H the field, and B the flux density.) Comment: 4 pages, 4 figures