15,214 research outputs found
Dynamics and efficiency of a self-propelled, diffusiophoretic swimmer
Active diffusiophoresis - swimming through interaction with a self-generated,
neutral, solute gradient - is a paradigm for autonomous motion at the
micrometer scale. We study this propulsion mechanism within a linear response
theory. Firstly, we consider several aspects relating to the dynamics of the
swimming particle. We extend established analytical formulae to describe small
swimmers, which interact with their environment on a finite lengthscale. Solute
convection is also taken into account. Modeling of the chemical reaction
reveals a coupling between the angular distribution of reactivity on the
swimmer and the concentration field. This effect, which we term "reaction
induced concentration distortion", strongly influences the particle speed.
Building on these insights, we employ irreversible, linear thermodynamics to
formulate an energy balance. This approach highlights the importance of solute
convection for a consistent treatment of the energetics. The efficiency of
swimming is calculated numerically and approximated analytically. Finally, we
define an efficiency of transport for swimmers which are moving in random
directions. It is shown that this efficiency scales as the inverse of the
macroscopic distance over which transport is to occur.Comment: 16 pages, 11 figure
Power law tails of time correlations in a mesoscopic fluid model
In a quenched mesoscopic fluid, modelling transport processes at high
densities, we perform computer simulations of the single particle energy
autocorrelation function C_e(t), which is essentially a return probability.
This is done to test the predictions for power law tails, obtained from mode
coupling theory. We study both off and on-lattice systems in one- and
two-dimensions. The predicted long time tail ~ t^{-d/2} is in excellent
agreement with the results of computer simulations. We also account for finite
size effects, such that smaller systems are fully covered by the present theory
as well.Comment: 11 pages, 12 figure
Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems
This work extends the results of the recently developed theory of a rather
complete thermodynamic formalism for discrete-state, continuous-time Markov
processes with and without detailed balance. We aim at investigating the
question that whether and how the thermodynamic structure is invariant in a
multiscale stochastic system. That is, whether the relations between
thermodynamic functions of state and process variables remain unchanged when
the system is viewed at different time scales and resolutions. Our results show
that the dynamics on a fast time scale contribute an entropic term to the
"internal energy function", , for the slow dynamics. Based on the
conditional free energy , one can then treat the slow dynamics as if
the fast dynamics is nonexistent. Furthermore, we show that the free energy,
which characterizes the spontaneous organization in a system without detailed
balance, is invariant with or without the fast dynamics: The fast dynamics is
assumed to reach stationarity instantaneously on the slow time scale; they have
no effect on the system's free energy. The same can not be said for the entropy
and the internal energy, both of which contain the same contribution from the
fast dynamics. We also investigate the consequences of time-scale separation in
connection to the concepts of quasi-stationaryty and steady-adiabaticity
introduced in the phenomenological steady-state thermodynamics
A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields
Generalized parity (P), time-reversal (T), and charge-conjugation
(C)operators were initially definedin the study of the pseudo-Hermitian
Hamiltonians. We construct a concrete realization of these operators for
Klein-Gordon fields and show that in this realization PT and C operators
respectively correspond to the ordinary time-reversal and charge-grading
operations. Furthermore, we present a complete description of the quantum
mechanics of Klein-Gordon fields that is based on the construction of a Hilbert
space with a relativistically invariant, positive-definite, and conserved inner
product. In particular we offer a natural construction of a position operator
and the corresponding localized and coherent states. The restriction of this
position operator to the positive-frequency fields coincides with the
Newton-Wigner operator. Our approach does not rely on the conventional
restriction to positive-frequency fields. Yet it provides a consistent quantum
mechanical description of Klein-Gordon fields with a genuine probabilistic
interpretation.Comment: 20 pages, published versio
Diffusion of multiple species with excluded-volume effects
Stochastic models of diffusion with excluded-volume effects are used to model
many biological and physical systems at a discrete level. The average
properties of the population may be described by a continuum model based on
partial differential equations. In this paper we consider multiple interacting
subpopulations/species and study how the inter-species competition emerges at
the population level. Each individual is described as a finite-size hard core
interacting particle undergoing Brownian motion. The link between the discrete
stochastic equations of motion and the continuum model is considered
systematically using the method of matched asymptotic expansions. The system
for two species leads to a nonlinear cross-diffusion system for each
subpopulation, which captures the enhancement of the effective diffusion rate
due to excluded-volume interactions between particles of the same species, and
the diminishment due to particles of the other species. This model can explain
two alternative notions of the diffusion coefficient that are often confounded,
namely collective diffusion and self-diffusion. Simulations of the discrete
system show good agreement with the analytic results
Momentum of an electromagnetic wave in dielectric media
Almost a hundred years ago, two different expressions were proposed for the
energy--momentum tensor of an electromagnetic wave in a dielectric. Minkowski's
tensor predicted an increase in the linear momentum of the wave on entering a
dielectric medium, whereas Abraham's tensor predicted its decrease. Theoretical
arguments were advanced in favour of both sides, and experiments proved
incapable of distinguishing between the two. Yet more forms were proposed, each
with their advocates who considered the form that they were proposing to be the
one true tensor. This paper reviews the debate and its eventual conclusion:
that no electromagnetic wave energy--momentum tensor is complete on its own.
When the appropriate accompanying energy--momentum tensor for the material
medium is also considered, experimental predictions of all the various proposed
tensors will always be the same, and the preferred form is therefore
effectively a matter of personal choice.Comment: 23 pages, 3 figures, RevTeX 4. Removed erroneous factor of mu/mu_0
from Eq.(44
Energy and entropy of relativistic diffusing particles
We discuss energy-momentum tensor and the second law of thermodynamics for a
system of relativistic diffusing particles. We calculate the energy and entropy
flow in this system. We obtain an exact time dependence of energy, entropy and
free energy of a beam of photons in a reservoir of a fixed temperature.Comment: 14 pages,some formulas correcte
The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions
We utilize nonequilibrium covariant transport theory to determine the region
of validity of causal Israel-Stewart dissipative hydrodynamics (IS) and
Navier-Stokes theory (NS) for relativistic heavy ion physics applications. A
massless ideal gas with 2->2 interactions is considered in a 0+1D Bjorken
scenario, appropriate for the early longitudinal expansion stage of the
collision. In the scale invariant case of a constant shear viscosity to entropy
density ratio eta/s ~ const, we find that Israel-Stewart theory is 10% accurate
in calculating dissipative effects if initially the expansion timescale exceeds
half the transport mean free path tau0/lambda0 > ~2. The same accuracy with
Navier-Stokes requires three times larger tau0/lambda0 > ~6. For dynamics
driven by a constant cross section, on the other hand, about 50% larger
tau0/lambda0 > ~3 (IS) and ~9 (NS) are needed. For typical applications at RHIC
energies s_{NN}**(1/2) ~ 100-200 GeV, these limits imply that even the
Israel-Stewart approach becomes marginal when eta/s > ~0.15. In addition, we
find that the 'naive' approximation to Israel-Stewart theory, which neglects
products of gradients and dissipative quantities, has an even smaller range of
applicability than Navier-Stokes. We also obtain analytic Israel-Stewart and
Navier-Stokes solutions in 0+1D, and present further tests for numerical
dissipative hydrodynamics codes in 1+1, 2+1, and 3+1D based on generalized
conservation laws.Comment: 30 pages, 26 EPS figures, revtex stylefil
Bulk viscosity of the massive Gross-Neveu model
A calculation of the bulk viscosity for the massive Gross-Neveu model at zero
fermion chemical potential is presented in the large- limit. This model
resembles QCD in many important aspects: it is asymptotically free, has a
dynamically generated mass gap, and for zero bare fermion mass it is scale
invariant at the classical level (broken through the trace anomaly at the
quantum level). For our purposes, the introduction of a bare fermion mass is
necessary to break the integrability of the model, and thus to be able to study
momentum transport. The main motivation is, by decreasing the bare mass, to
analyze whether there is a correlation between the maximum in the trace anomaly
and a possible maximum in the bulk viscosity, as recently conjectured. After
numerical analysis, I find that there is no direct correlation between these
two quantities: the bulk viscosity of the model is a monotonously decreasing
function of the temperature. I also comment on the sum rule for the spectral
density in the bulk channel, as well as on implications of this analysis for
other systems.Comment: v2: 3->3 processes included, conclusions unchanged. Comments and
references added. Typos corrected. To appear in Phys. Rev.
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