May 2000

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145 Reads

Published by

May 2000

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145 Reads

Frequency-dependent fluid flow in electrolytes on microelectrodes subjected to ac voltages has recently been reported. The fluid flow is predominant at frequencies of the order of the relaxation frequency of the electrode-electrolyte system. The mechanism responsible for this motion has been termed ac electro-osmosis: a continuous flow driven by the interaction of the oscillating electric field and the charge at the diffuse double layer on the electrodes. This paper develops the basis of a theoretical approach to this problem using a linear double layer analysis. The theoretical results are compared with the experiments, and a good correlation is found.

May 2000

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207 Reads

Under the influence of an ac electric field, electrolytes on planar microelectrodes exhibit fluid flow. The nonuniform electric field generated by the electrodes interacts with the suspending fluid through a number of mechanisms, giving rise to body forces and fluid flow. This paper presents the detailed experimental measurements of the velocity of fluid flow on microelectrodes at frequencies below the charge relaxation frequency of the electrolyte. The velocity of latex tracer particles was measured as a function of applied signal frequency and potential, electrolyte conductivity, and position on the electrode surface. The data are discussed in terms of a linear model of ac electroosmosis: the interaction of the nonuniform ac field and the induced electrical double layer.

July 1999

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100 Reads

We introduce a lattice gas model of cluster growth via the diffusive aggregation of particles in a closed system obeying a local, deterministic, microscopically reversible dynamics. This model roughly corresponds to placing the irreversible diffusion limited aggregation model (DLA) in contact with a heat bath. Particles release latent heat when aggregating, while singly connected cluster members can absorb heat and evaporate. The heat bath is initially empty, hence we observe the flow of entropy from the aggregating gas of particles into the heat bath, which is being populated by diffusing heat tokens. Before the population of the heat bath stabilizes, the cluster morphology (quantified by the fractal dimension) is similar to a standard DLA cluster. The cluster then gradually anneals, becoming more tenuous, until reaching configurational equilibrium when the cluster morphology resembles a quenched branched random polymer. As the microscopic dynamics is invertible, we can reverse the evolution, observe the inverse flow of heat and entropy, and recover the initial condition. This simple system provides an explicit example of how macroscopic dissipation and self-organization can result from an underlying microscopically reversible dynamics. We present a detailed description of the dynamics for the model, discuss the macroscopic limit, and give predictions for the equilibrium particle densities obtained in the mean field limit. Empirical results for the growth are then presented, including the observed equilibrium particle densities, the temperature of the system, the fractal dimension of the growth clusters, scaling behavior, finite size effects, and the approach to equilibrium. We pay particular attention to the temporal behavior of the growth process and show that the relaxation to the maximum entropy state is initially a rapid nonequilibrium process, then subsequently it is a quasistatic process with a well defined temperature.

December 2000

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36 Reads

We have investigated the onset of avalanches in fine, cohesive granular materials. In our experiments shear stress is generated by tilting an initialized bed of powder and increasing the angle of tilt until the powder avalanches. We find that the angle alpha of the avalanche decreases with increasing bed width. The avalanche depth increases with the bed width and, in all cases, is of the order of several millimeters, which is much greater than the particle size. We carry out a macroscopic analysis of the avalanche process based on Coulomb's method of wedges. This analysis shows the fundamental role played by powder cohesion and boundary conditions on avalanches in fine cohesive powders. This behavior contrasts with the behavior of noncohesive grains, such as dry sand, where avalanches consist of superficial layers of about ten grains. The reason behind this is that for our experimental powders (particle diameter approximately 10 &mgr;m) the van der Waals interparticle adhesive force exceeds several orders of magnitude particle weight. Adhesive forces oppose gravity, and as a result fine cohesive powders settle in very open structures as compared to noncohesive granular materials. Because of the dominance of adhesive forces over particle weight, our materials behave more like wet sand.

February 2015

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309 Reads

The settling of inertial particles in 2D vertical flows is investigated in
the limit where the particle inertia, the free-fall terminal velocity, and the
flow unsteadiness can be treated as perturbations. The generic case of
recirculation cells bounded by a set of separatrix streamlines forming a
heteroclinic cycle of fluid points' dynamics is considered. The (weak)
unsteadiness of the flow generally induces a chaotic tangle near the
heteroclinic cycle, leading to the apparent diffusion of fluid elements through
the boundary. For inertial particles this complex motion can also exist in
spite of inertia and sedimentation, provided the Stokes number is below some
critical value $St_c$. It is shown that $St_c= Pe^{-1}/|Fr^{-1}\pm u_{0c}^2|$,
where $Pe$ is an effective Peclet number related to the diffusion of fluid
points through the boundary, $Fr$ is the Froude number based on the horizontal
distance between the end points of the separatrix streamline, and $u_0^2$ is
the non-dimensional curvature-weighted average of the squared velocity of the
steady fluid flow along this separatrix. The $\pm$ sign is positive if gravity
and centrifugation act in the same direction, and negative otherwise. When $St
< St_c$, particles moving near the separatrix streamline can enter and exit the
cell in a complex manner. When $St > St_c$ a regular motion takes place.
Trapping can still exist in this case, since particles can be driven towards
the interior of the cell in a regular manner, under the effect of either
gravity or curvature, or both.

November 2016

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932 Reads

Information flow or information transfer the widely applicable general physics notion can be rigorously derived from first principles, rather than axiomatically proposed as an ansatz. Its logical association with causality is firmly rooted in the dynamical system that lies beneath. The principle of nil causality that reads, an event is not causal to another if the evolution of the latter is independent of the former, which transfer entropy analysis and Granger causality test fail to verify in many situations, turns out to be a proven theorem here. Established in this study are the information flows among the components of time-discrete mappings and time-continuous dynamical systems, both deterministic and stochastic. They have been obtained explicitly in closed form, and put to applications with the benchmark systems such as the Kaplan-Yorkemap, R¨ossler system, baker transformation, H´enon map, and stochastic potential flow. Besides unraveling the causal relations as expected from the respective systems, some of the applications show that the information flow structure underlying a complex trajectory pattern could be tractable. For linear systems, the resulting remarkably concise formula asserts analytically that causation implies correlation, while correlation does not imply causation, providing a mathematical basis for the long-standing philosophical debate over causation versus correlation.

March 2015

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445 Reads

Critical states are usually identified experimentally through power-law
statistics or universal scaling functions. We show here that such features
naturally emerge from networks in self-sustained irregular regimes away from
criticality. Power-law statistics are also seen when the units are replaced by
independent stochastic surrogates, and thus are not sufficient to establish
criticality. We rather suggest that these are universal features of large-scale
networks when considered macroscopically. These results put caution on the
interpretation of scaling laws found in nature.

February 2017

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81 Reads

Molecular motors and cytoskeletal filaments mostly work collectively under
opposing forces. This opposing force may be due to cargo carried by motors, or
resistance coming from cell membrane pressing against the cytoskeletal
filaments. Certain recent studies have shown that the collective maximum force
(stall force) generated by multiple cytoskeletal filaments or molecular motors
may not always be just a simple sum of stall force for individual filaments or
motors. To understand this phenomena of excess or deficit collective force
generation, we study a broad class of models of both cytoskeletal filaments and
molecular motors. We argue that the stall force generated by a group of
filaments or motors is additive, i.e., the stall force of N filaments(motors)
is N times the stall force of one filament (motor), when the system is in
equilibrium at stall. Consequently, we show that this additivity typically does
not hold when the system departs from equilibrium at stall. We thus present a
novel and unified understanding of existing models exhibiting such non-
addivity, and generalize our arguments by developing new models that
demonstrate this phenomena. We also propose a quantity similar to thermodynamic
efficiency to provide a simple understanding of deviation from stall-force
additivity for filament and motor collectives.

October 2014

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49 Reads

Fermi acceleration is the process of energy transfer from massive objects in
slow motion to light objects that move fast. The model for such process is a
time-dependent Hamiltonian system. As the parameters of the system change with
time, the energy is no longer conserved, which makes the acceleration possible.
One of the main problems is how to generate a sustained and robust energy
growth. We show that the non-ergodicity of any chaotic Hamiltonian system must
universally lead to the exponential growth of energy at a slow periodic
variation of parameters. We build a model for this process in terms of a
Geometric Brownian Motion with a positive drift, and relate it to the entropy
increase.

January 2015

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61 Reads

Single component pseudo-potential lattice Boltzmann model has been widely
applied in multiphase simulation due to its simplicity and stability. In many
research, it has been claimed that this model can be stable for density ratios
larger than 1000, however, the application of the model is still limited to
small density ratios when the contact angle is considered. The reason is that
the original contact angle adjustment method influences the stability of the
model. Moreover, simulation results in present work show that, by applying the
contact angle adjustment method, the density distribution near the wall is
artificially changed, and the contact angle is dependent on the surface
tension. Hence, it is very inconvenient to apply this method with a fixed
contact angle, and the accuracy of the model cannot be guaranteed. To solve
these problems, a contact angle adjustment method based on the geometry
analysis is proposed and numerically compared with the original method.
Simulation results show that, with the new contact angle adjustment method, the
stability of the model is highly improved when the density ratio is relatively
large, and it is independent of the surface tension.

January 2015

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33 Reads

Plastic events in amorphous solids can be much more than just "shear
transformation zones" when the positional degrees of freedom are coupled
non-trivially to other degrees of freedom. Here we consider magnetic amorphous
solids where mechanical and magnetic degrees of freedom interact, leading to
rather complex plastic events whose nature must be disentangled. In this paper
we uncover the anatomy of the various contributions to some typical plastic
events. These plastic events are seen as Barkhausen Noise or other "serrated
noises". Using theoretical considerations we explain the observed statistics of
the various contributions to the considered plastic events. The richness of
contributions and their different characteristics imply that in general the
statistics of these "serrated noises" cannot be universal, but rather highly
dependent on the state of the system and on its microscopic interactions.

February 2015

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171 Reads

A mesoscopic model of amorphous plasticity is discussed in the wider context
of depinning models. After embedding in a d + 1 dimensional space, where the
accumulated plastic strain lives along the additional dimension, the gradual
plastic deformation of amorphous media can be regarded as the motion of an
elastic manifold in a disordered landscape. While the associated depinning
transition leads to scaling properties, the quadrupolar Eshelby interactions at
play induce specific additional features like shear-banding and weak ergodicity
breakdown. The latters are shown to be controlled by the existence of soft
modes of the quadrupolar interaction, the consequence of which is discussed in
the context of depinning.

February 2015

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48 Reads

A method for analytic continuation of imaginary-time correlation functions
(here obtained in quantum Monte Carlo simulations) to real-frequency spectral
functions is proposed. Stochastically sampling a spectrum parametrized by a
large number of delta-functions, treated as a statistical-mechanics problem, it
avoids distortions caused by (as demonstrated here) configurational entropy in
previous sampling methods. The key development is the suppression of entropy by
constraining the spectral weight to within identifiable optimal bounds and
imposing a set number of peaks. As a test case, the dynamic structure factor of
the S=1/2 Heisenberg chain is computed. Very good agreement is found with Bethe
Ansatz results in the ground state (including a sharp edge) and with exact
diagonalization of small systems at elevated temperatures.

March 2015

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63 Reads

Nonlinear localized magnetic excitations in one dimensional magnonic crystal
is investigated under periodic magntic field. The governing Landau-Lifshitz
equation is transformed into variable coefficient nonlinear Schrodinger
equation(VCNLS) using sterographic projection. The VCNLS equation is in general
nonintegrable, by using painleve analysis necessary conditions for the VCNLS
equation to pass Weiss-Tabor-Carnevale (WTC) Painleve test are obtained. A
sufficient integrability condition is obtained by further exploring a
transformation, which can map the VCNLS equation into the well-known standard
nonlinear Schrodinger equation. The transformation built a systematic
connection between the solution of the standard nonlinear Schrodinger equation
and VC-NLS equation. The results shows the excitation of magnetization in the
form of soliton has spatialperiod exists on the background of spin Bloch waves.
Such solution exisits only certain constrain conditions on the coefficient of
the VCNLS equation are satisfied. The analytical results suggest a way to
control the dynamics of magnetization in the form of solitons by an appropriate
spatial modulation of the nonlinearity coefficient in the governing VCNLS
equation which is determined by the ferromagnetic materials which forms the
magnonic crystal.

September 2014

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36 Reads

Time reversal mirrors have been widely used to achieve wave focusing in
acoustics and electromagnetics. A typical time reversal experiment requires
that a transmitter be initially present at the target focusing point, which
limits the application of this technique. In this letter, we propose a method
to focus waves at an arbitary location inside a complex enclosure using a
numerically calculated wave signal. We use a semi-classical ray algorithm to
calculate the signal that would be received at a transceiver port resulting
from the injection of a short pulse at the desired target location. The
quaility of the reconstruction is quantified in three different ways and the
values of these metrics can be predicted by the statistics of the
scattering-parameter $|S_{21}|^2$ between the transceiver and target points in
the enclosure. We experimentally demonstrate the method using a flat microwave
billiard and quantify the reconstruction quality as a function of enclosure
loss, port coupling and other considerations.

June 2014

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140 Reads

A novel mechanism for the transport of microscale particles in viscous fluids
is demonstrated. The mechanism exploits the trapping of such particles by
rotational streaming cells established in the vicinity of an oscillating
cylinder, recently analyzed in previous work. The present work explores a
strategy of transporting particles between the trapping points established by
multiple cylinders undergoing oscillations in sequential intervals. It is
demonstrated that, by controlling the sequence of oscillation intervals, an
inertial particle is effectively and predictably transported between the stable
trapping points. Arrays of cylinders in various arrangements are investigated,
revealing a quite general technique for constructing arbitrary particle
trajectories. The timescales for transport are also discussed.

October 2014

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62 Reads

Recently, diverse phase transition (PT) types have been obtained in multiplex
networks, such as discontinuous, continuous, and mixed-order PTs. However, they
emerge from individual systems, and there is no theoretical understanding of
such PTs in a single framework. Here, we study a spin model called the
Ashkin-Teller (AT) model in a mono-layer scale-free network; this can be
regarded as a model of two species of Ising spin placed on each layer of a
double-layer network. The four-spin interaction in the AT model represents the
inter-layer interaction in the multiplex network. Diverse PTs emerge depending
on the inter-layer coupling strength and network structure. Especially, we find
that mixed-order PTs occur at the critical end points. The origin of such
behavior is explained in the framework of Landau-Ginzburg theory.

March 2015

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35 Reads

We investigate scaling of work output and efficiency of a photonic Carnot
engine with the number of quantum coherent resources. Specifically, we consider
a generalization of the "phaseonium fuel" for the photonic Carnot engine, which
was first introduced as a three-level atom with two lower states in a quantum
coherent superposition by [M. O. Scully, M. Suhail Zubairy, G. S. Agarwal, and
H. Walther, Science {\bf 299}, 862 (2003)], to the case of $N+1$ level atoms
with $N$ coherent lower levels. Deriving a multilevel mesoscopic master
equation for the system, we evaluate the harvested work by the engine, and its
efficiency. We find that efficiency and extracted work scale quadratically with
the number of quantum coherent levels. Quantum coherence boost to the specific
energy (work output per unit mass of the resource) is a profound fundamental
difference of quantum fuel from classical resources. Besides, we examine the
dependence of cavity loss on the number of atomic levels and find that
multilevel phaseonium fuel can be utilized to beat the decoherence due to
cavity loss. Our results bring the photonic Carnot engines much closer to the
capabilities of current resonator technologies.

March 2015

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18 Reads

Using numerical simulations we examine colloids with a long-range Coulomb
interaction confined in a two-dimensional trough potential undergoing dynamical
compression. As the depth of the confining well is increased, the colloids move
via elastic distortions interspersed with intermittent bursts or avalanches of
plastic motion. In these avalanches, the colloids rearrange to minimize their
colloid-colloid repulsive interaction energy by adopting an average lattice
constant that is isotropic despite the anisotropic nature of the compression.
The avalanches take the form of shear banding events that decrease or increase
the structural order of the system. At larger compressions, the avalanches are
associated with a reduction of the number of rows of colloids that fit within
the confining potential, and between avalanches the colloids can exhibit
partially crystalline or even smectic ordering. The colloid velocity
distributions during the avalanches have a non-Gaussian form with power law
tails and exponents that are consistent with those found for the velocity
distributions of gliding dislocations. We observe similar behavior when we
subsequently decompress the system, and find a partially hysteretic response
reflecting the irreversibility of the plastic events.

September 2014

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105 Reads

Small-scale heat exchanges have recently been modeled with resource theories
intended to extend thermodynamics to the nanoscale and quantum regimes. We
generalize these theories to exchanges of quantities other than heat, to baths
other than heat baths, and to free energies other than the Helmholtz free
energy. These generalizations are illustrated with "grand-potential" theories
that model movements of heat and particles. Free operations include unitaries
that conserve energy and particle number. From this conservation law and from
resource-theory principles, the grand-canonical form of the free states is
derived. States are shown to form a quasiorder characterized by free
operations, d-majorization, the hypothesis-testing entropy, and rescaled Lorenz
curves. We calculate the work distillable from, and we bound the work cost of
creating, a state. These work quantities can differ but converge to the grand
potential in the thermodynamic limit. Extending thermodynamic resource theories
beyond heat baths, we open diverse realistic systems to modeling with one-shot
statistical mechanics. Prospective applications such as electrochemical
batteries are hoped to bridge one-shot theory to experiments.

September 2013

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90 Reads

We study the mean field dynamics of self-trapping in Bose-Einstein
condensates loaded in deep optical lattices with Gaussian initial conditions.
We calculate a detailed dynamical phase diagram accurately describing the
different dynamical regimes (such as diffusion and self-trapping) that markedly
differs from earlier predictions based on variational dynamics. The phase
diagram exhibits a very complex structure which could readily be tested in
current experiments. We derive an explicit theoretical estimate for the
transition to self-trapping in excellent agreement with our numerical findings.

February 2014

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105 Reads

We report analytical and numerical modelling of active elastic networks,
motivated by experiments on crosslinked actin networks contracted by myosin
motors. Within a broad range of parameters, the motor-driven collapse of active
elastic networks leads to a critical state. We show that this state is
qualitatively different from that of the random percolation model.
Intriguingly, it possesses both euclidean and scale-free structure with Fisher
exponent smaller than $2$. Remarkably, an indistinguishable Fisher exponent and
the same euclidean structure is obtained at the critical point of the random
percolation model after absorbing all enclaves into their surrounding clusters.
We propose that in the experiment the enclaves are absorbed due to steric
interactions of network elements. We model the network collapse, taking into
account the steric interactions. The model shows how the system robustly drives
itself towards the critical point of the random percolation model with absorbed
enclaves, in agreement with the experiment.

July 2009

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351 Reads

A general lattice Boltzmann (LB) model is proposed for solving nonlinear partial differential equations with the form $\partial_t \phi+\sum_{k=1}^{m} \alpha_k \partial_x^k \Pi_k (\phi)=0$, where $\alpha_k$ are constant coefficients, and $\Pi_k (\phi)$ are the known differential functions of $\phi$, $1\leq k\leq m \leq 6$. The model can be applied to the common nonlinear evolutionary equations, such as (m)KdV equation, KdV-Burgers equation, K($m,n$) equation, Kuramoto-Sivashinsky equation, and Kawahara equation, etc. Unlike the existing LB models, the correct constraints on moments of equilibrium distribution function in the proposed model are given by choosing suitable \emph{auxiliary-moments}, and how to exactly recover the macroscopic equations through Chapman-Enskog expansion is discussed in this paper. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies. Comment: 18 pages, 4 figures

September 2014

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51 Reads

We present a characterization of short-term stability of random Boolean
networks under \emph{arbitrary} distributions of transfer functions. Given any
distribution of transfer functions for a random Boolean network, we present a
formula that decides whether short-term chaos (damage spreading) will happen.
We provide a formal proof for this formula, and empirically show that its
predictions are accurate. Previous work only works for special cases of
balanced families. It has been observed that these characterizations fail for
unbalanced families, yet such families are widespread in real biological
networks.

March 2015

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212 Reads

Parameterization of reaction rates for thermal desorption are often analyzed
using the Arrhenius equation. Data analysis procedures typically impose the
empirical constraint of compensation, such that the different parameters in the
equation balance each other out thereby leading to an implicitly assumed
constant reaction rate for a wide range of thermally activated processes.
However, the compensation effect has not been generally demonstrated and its
origins are not completely understood. Using kinetic Monte Carlo simulations on
a model interface, we explore how site and adsorbate interactions influence
surface coverage during a typical desorption process. We find that the
traditional criterion for the existence of a compensation effect for
interacting species breaks down and the time characterizing desorption
increases with increasing interaction strength due to an increase in the
effective activation energy. At the molecular-site level these changes are the
result of enhanced site correlations with increasing adsorbate interaction
strength suppressing the onset of desorption. Our results show that the
parameters vary as a result of interactions, however they do not offset or
compensate each other completely as predicted with traditional methods of
analysis.