arXiv subjects

D. S. Dean

Publications and source records attributed to D. S. Dean.

At least 19 recordsLinked to original sources

arXiv2024

Self-phoretic oscillatory motion in a harmonic trap

We consider the motion of a harmonically trapped overdamped particle, which is submitted to a self-phoretic force, that is proportional to the gradient of a diffusive field for which the particle itself is the source. In agreement with existing results for free particles or particles in a bounded domain, we find that the system exhibits a transition between an immobile phase, where the particle stays at the center of the trap, and an oscillatory state. We perform an exact analysis giving access to the bifurcation threshold, as well as the frequency of oscillations and their amplitude near the threshold. Our analysis also characterizes the shape of two-dimensional oscillations, that take place along a circle or a straight line. Our results are confirmed by numerical simulations.

cond-mat.stat-mech↗

arXiv2021

Effective diffusivity of Brownian particles in a two dimensional square lattice of hard disks

We revisit the classic problem of the effective diffusion constant of a Brownian particle in a square lattice of reflecting impenetrable hard disks. This diffusion constant is also related to the effective conductivity of non-conducting and infinitely conductive disks in the same geometry. We show how a recently derived Green's function for the periodic lattice can be exploited to derive a series expansion of the diffusion constant in terms of the disk's volume fraction $φ$. Secondly we propose a variant of the Fick-Jacobs approximation to study the large volume fraction limit. This combination of analytical results is shown to describe the behavior of the diffusion constant for all volume fractions.

cond-mat.stat-mech↗

arXiv2021

Steady state of overdamped particles in the non-conservative force field of a simple non-linear model of optical trap

Optically trapped particles are often subject to a non-conservative scattering force arising from radiation pressure. In this paper we present an exact solution for the steady state statistics of an overdamped Brownian particle subjected to a commonly used force field model for an optical trap. The model is the simplest of its kind that takes into account non-conservative forces. In particular, we present exact results for certain marginals of the full three dimensional steady state probability distribution as well as results for the toroidal probability currents which are present in the steady state, as well as for the circulation of theses currents. Our analytical results are confirmed by numerical solution of the steady state Fokker-Planck equation.

cond-mat.stat-mech↗

arXiv2018

Dispersion in two-dimensional periodic channels with discontinuous profiles

The effective diffusivity of Brownian tracer particles confined in periodic micro-channels is smaller than the microscopic diffusivity due to entropic trapping. Here, we study diffusion in two-dimensional periodic channels whose cross-section presents singular points, such as abrupt changes of radius or the presence of thin walls, with openings, delimiting periodic compartments composing the channel. Dispersion in such systems is analyzed using the Fick-Jacobs' approximation. This approximation assumes a much faster equilibration in the lateral than in the axial direction, along which the dispersion is measured. If the characteristic width $a$ of the channel is much smaller than the period $L$ of the channel, i.e. $\varepsilon = a/L$ is small, this assumption is clearly valid for Brownian particles. For discontinuous channels, the Fick-Jacobs' approximation is only valid at the lowest order in $\varepsilon$ and provides a rough, though on occasions rather accurate, estimate of the effective diffusivity. Here we provide formulas for the effective diffusivity in discontinuous channels that are asymptotically exact at the next-to-leading order in $\varepsilon$. Each discontinuity leads to a reduction of the effective diffusivity. We show that our theory is consistent with the picture of effective {\em trapping rates} associated with each discontinuity, for which our theory provides explicit and asymptotically exact formulas. Our analytical predictions are confirmed by numerical analysis. Our results provide a precise quantification of the kinetic entropic barriers associated with profile singularities.

cond-mat.stat-mech↗

arXiv2017

Stresses in non-equilibrium fluids: Exact formulation and coarse grained theory

Starting from the stochastic equation for the density operator, we formulate the exact (instantaneous) stress tensor for interacting Brownian particles, whose average value agrees with expressions derived previously. We analyze the relation between the stress tensor and forces on external potentials, and observe that, out of equilibrium, particle currents give rise to extra forces. Next, we derive the stress tensor for a Landau-Ginzburg theory in non-equilibrium situations, finding an expression analogous to that of the exact microscopic stress tensor, and discuss the computation of out-of-equilibrium (classical) Casimir forces. We use these relations to study the spatio-temporal correlations of the stress tensor in a Brownian fluid, which we derive exactly to leading order in the interaction potential strength. We observe that, after integration over time, the spatial correlations generally decay as power laws in space. These are expected to be of importance for driven confined systems. We also show that divergence-free parts of the stress tensor do not contribute in the Green-Kubo relation for the viscosity.

cond-mat.soft↗

arXiv2017

Dispersion in two dimensional channels - the Fick-Jacobs approximation revisited

We examine the dispersion of Brownian particles in a symmetric two dimensional channel, this classical problem has been widely studied in the literature using the so called Fick-Jacobs' approximation and its various improvements. Most studies rely on the reduction to an effective one dimensional diffusion equation, here we drive an explicit formula for the diffusion constant which avoids this reduction. Using this formula the effective diffusion constant can be evaluated numerically without resorting to Brownian simulations. In addition a perturbation theory can be developed in $\varepsilon = h_0/L$ where $h_0$ is the characteristic channel height and $L$ the period. This perturbation theory confirms the results of Kalinay and Percus (Phys. Rev. E 74, 041203 (2006)), based on the reduction, to one dimensional diffusion are exact at least to ${\cal O}(\varepsilon^6)$. Furthermore, we show how the Kalinay and Percus pseudo-linear approximation can be straightforwardly recovered. The approach proposed here can also be exploited to yield exact results an appropriate limit $\varepsilon \to \infty$, we show that here the diffusion constant remains finite and show how the result can be obtained with a simple physical argument. Moreover we show that the correction to the effective diffusion constant is of order $1/\varepsilon$ and remarkably has a some universal characteristics. Numerically we compare the analytical results obtained with exact numerical calculations for a number of interesting channel geometries.

cond-mat.stat-mech↗

arXiv2017

Geometry controlled dispersion in periodic corrugated channels

The effective diffusivity $D_e$ of tracer particles diffusing in periodically corrugated axisymmetric two and three dimensional channels is studied. The majority of previous studies of this class of problems are based on perturbative analyses about narrow channels, where the problem can be reduced to an effectively one dimensional one. Here we show how to analyze this class of problems using a much more general approach which even includes the limit of infinitely wide channels. Using the narrow and wide channel asymptotics, we provide a Pad{é} approximant scheme that is able to describe the dispersion properties of a wide class of channels. Furthermore, we systematically identify all the exact asymptotic scaling regimes of $D_e$ and the accompanying physical mechanisms that control dispersion, clarifying the distinction between smooth channels and compartmentalized ones, and identifying the regimes in which $D_e$ can be linked to first passage problems.

cond-mat.stat-mech↗

arXiv2017

Universal time dependent dispersion properties for diffusion in a one-dimensional critically tilted potential

We consider the time dependent dispersion properties of overdamped tracer particles diffusing in a one dimensional periodic potential under the influence of an additional constant tilting force $F$. The system is studied in the region where the force is close to the critical value $F_c$ at which the barriers separating neighboring potential wells disappear. We show that, when $F$ crosses the critical value, the shape of the Mean-Square Displacement (MSD) curves is strongly modified. We identify a diffusive regime at intermediate time scales, with an effective diffusion coefficient which is much larger than the late time diffusion coefficient for $F>F_c$, whereas for $F<F_c$ the late time and intermediate time diffusive regimes are indistinguishable. Explicit asymptotic regimes for the MSD curves are identified at all time scales.

cond-mat.stat-mech↗

arXiv2015

Out of equilibrium thermal Casimir effect between Brownian conducting plates

We study the thermal fluctuation induced interactions between two surfaces containing Brownian charges which are held at different temperatures. Using a dynamical form of Debye-Hückel theory implemented within the stochastic equation for the density of mobile Brownian charges, we derive expressions for the average force between the two surfaces as well as its variance. The latter is found both for the normal, of finite mean, as well as the lateral force, of zero mean, between the surfaces.

cond-mat.stat-mech↗

arXiv2015

Phase diagram of a bulk 1d lattice Coulomb gas

The exact solution, via transfer matrix, of the simple one dimensional lattice Coulomb gas (1d LCG) model can reproduce peculiar features of ionic liquid capacitors, such as overscreening, layering, and camel- and bell-shaped capacitance curves. Using the same transfer matrix method, we now compute the bulk properties of the 1d LCG in the constant voltage ensemble. We unveil a phase diagram with rich structure exhibiting a low density disordered and high density ordered phases, separated by a first order phase transition at low temperature; the solid state at full packing can be ordered or not, depending on the temperature. This phase diagram, which is strikingly similar to its three dimensional counterpart, also sheds light on the behaviour of the confined system.

cond-mat.stat-mech↗

arXiv2015

Kubo formulas for dispersion in heterogeneous periodic non-equilibrium systems

We consider the dispersion properties of tracer particles moving in non-equilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drift, eventually with the presence of obstacles. We derive a Kubo-like formula for the time dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite time corrections to these transport coefficients. In one dimension, we give closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary non-equilibrium periodic advection-diffusion systems.

cond-mat.stat-mech↗

arXiv2013

On the fluctuation of thermal van der Waals forces due to dipole fluctuations

Fluctuations of the thermal or classical component of the van der Waals force between two dielectric slabs, modelled as an ensemble of polarizable dipoles which interact via the usual electrostatic dipole-dipole interaction, are evaluated. In the model the instantaneous force is a deterministic function of the dipole configurations in the slabs and its fluctuations are purely due to dipole fluctuations (no background thermal fluctuations of the electromagnetic field are considered). The average of the force and its variance are computed. The fluctuations of the force exhibit normal thermodynamic scaling in that they are proportional to the area of the two plates, and even more importantly, do not depend on any microscopic cut-off in the theory. The average and the variance of the thermal van der Waals forces give a unique fingerprint of these fluctuation interactions.

cond-mat.stat-mech↗

arXiv2011

Thermal Casimir drag in fluctuating classical fields

A uniformly moving inclusion which locally suppresses the fluctuations of a classical thermally excited field is shown to experience a drag force which depends on the dynamics of the field. It is shown that in a number of cases the linear friction coefficient is dominated by short distance fluctuations and takes a very simple form. Examples where this drag can occur are for stiff objects, such as proteins, nonspecifically bound to more flexible ones such as polymers and membranes.

cond-mat.stat-mech↗

arXiv2011

A perturbative path integral study of active and passive tracer diffusion in fluctuating fields

We study the effective diffusion constant of a Brownian particle linearly coupled to a thermally fluctuating scalar field. We use a path integral method to compute the effective diffusion coefficient perturbatively to lowest order in the coupling constant. This method can be applied to cases where the field is affected by the particle (an active tracer), and cases where the tracer is passive. Our results are applicable to a wide range of physical problems, from a protein diffusing in a membrane to the dispersion of a passive tracer in a random potential. In the case of passive diffusion in a scalar field, we show that the coupling to the field can, in some cases, speed up the diffusion corresponding to a form of stochastic resonance. Our results on passive diffusion are also confirmed via a perturbative calculation of the probability density function of the particle in a Fokker-Planck formulation of the problem. Numerical simulations on simplified systems corroborate our results.

cond-mat.stat-mech↗

arXiv2010

Drag forces on inclusions in classical fields with dissipative dynamics

We study the drag force on uniformly moving inclusions which interact linearly with dynamical free field theories commonly used to study soft condensed matter systems. Drag forces are shown to be nonlinear functions of the inclusion velocity and depend strongly on the field dynamics. The general results obtained can be used to explain drag forces in Ising systems and also predict the existence of drag forces on proteins in membranes due to couplings to various physical parameters of the membrane such as composition, phase and height fluctuations.

cond-mat.soft↗

arXiv2010

Visualization of membrane loss during the shrinkage of giant vesicles under electropulsation

We study the effect of permeabilizing electric fields applied to two different types of giant unilamellar vesicles, the first formed from EggPC lipids and the second formed from DOPC lipids. Experiments on vesicles of both lipid types show a decrease in vesicle radius which is interpreted as being due to lipid loss during the permeabilization process. We show that the decrease in size can be qualitatively explained as a loss of lipid area which is proportional to the area of the vesicle which is permeabilized. Three possible mechanisms responsible for lipid loss were directly observed: pore formation, vesicle formation and tubule formation.

cond-mat.soft↗

arXiv2009

Thermal Casimir effect between random layered dielectrics

We study the thermal Casimir effect between two thick slabs composed of plane-parallel layers of random dielectric materials interacting across an intervening homogeneous dielectric. It is found that the effective interaction at long distances is self averaging and is given by a description in terms of effective dielectric functions. The behavior at short distances becomes random (sample dependent) and is dominated by the local values of the dielectric function proximal to each other across the dielectrically homogeneous slab.

cond-mat.dis-nn↗

arXiv2007

Path integrals for stiff polymers applied to membrane physics

Path integrals similar to those describing stiff polymers arise in the Helfrich model for membranes. We show how these types of path integrals can be evaluated and apply our results to study the thermodynamics of a minority stripe phase in a bulk membrane. The fluctuation induced contribution to the line tension between the stripe and the bulk phase is computed, as well as the effective interaction between the two phases in the tensionless case where the two phases have differing bending rigidities.

cond-mat.soft↗