arXiv subjects

A. Bhattacharyay

Publications and source records attributed to A. Bhattacharyay.

At least 19 recordsLinked to original sources

arXiv2026

A model of thermophoresis of colloidal proteins in water using non-Fickian diffusion currents

In 1928, Chapman generalised Einstein's theory of diffusion for non-uniform fluids to show the presence of a non-Fickian diffusion current, which he considered important in thermodiffusion (Ludwig-Soret effect). In 1941, Kiyosi Itô proposed the formal methods of stochastic calculus in the presence of spatially dependent diffusion, yielding the same non-Fickian diffusion current as shown by Chapman. The phenomenon of thermodiffusion and thermophoresis happens in the presence of a temperature gradient, which makes diffusion space-dependent. The role of solvation forces in thermophoresis will only be clearer once that of diffusion is understood properly. In this paper, we investigate the importance of Chapman's non-Fickian diffusion current on the thermophoretic motion of colloidal particles in water (with weak salt concentration). We show that all the general features of variations of the Soret coefficient $S_T$ with temperature can be captured using Chapman's non-Fickian diffusion current. We compare our theoretical results with experimental plots of the Soret coefficients for three polypeptides in aqueous solution: Lysozyme, BLGA, and Poly-L-Lysine, and find a strong match. We emphasise that, in addition to the yet-to-be-understood details of solvation forces, Chapman's non-Fickian diffusion current is an indispensable element that needs to be taken into account for a complete understanding of thermophoresis and thermodiffusion.

cond-mat.soft↗

arXiv2026

Hydrodynamic Ratchet for Tracer Transport in a Soft Microchannel: A Detailed Analysis

Understanding surface-driven transport is of paramount importance from the perspective of biological applications and the synthesis of microfluidic devices. In this work, we develop an analysis of a local inversion symmetry broken fluid flow model through an undulating microchannel. Surface undulations of a few tens of Hertz in a soft microchannel keep the fluid flow in a low Reynolds number regime, allowing the advantage of a perturbation analysis of fluid flow. Using this, we develop a detailed analysis of the relationship between the fluid velocity and surface undulations, which is crucial for the subsequent numerical analysis of tracer motion. We used this information to study the dynamics of a tracer particle in the velocity field of an undulating microchannel. We show that the tracer particle can undergo ratcheting (which we call the hydrodynamics ratchet effect) in very specific, physically meaningful circumstances. We observe a ratcheting velocity of $\sim 0.15 \;μ$m/sec for a micrometre-sized particle at room temperature in water when the undulations wavelength is of the order of 1 $μ$m.

physics.flu-dyn↗

arXiv2026

A general variational approach for equilibrium phase boundaries of trapped spin-1 Bose-Einstein condensates

We develop a simple and general variational method to estimate the solutions of the Gross-Pitaevskii equations and obtain the corresponding density profiles for all spin states of a trapped spin-1 Bose-Einstein condensate. We further employ this approach to obtain the complete phase diagram of the system under quasi-one-dimensional harmonic confinement, with ferromagnetic or antiferromagnetic spin interactions. We identify a suitable scaling that collapses all phase diagrams for different system sizes (i.e., total particle number) into a universal (system size-independent) phase diagram. The complete phase diagram for a confined system shows some significant qualitative differences compared to that of a condensate with homogeneous density distribution. The phase diagrams reported here could help identify the important parameter regimes in which phase transitions in the confined system, in general, occur. This knowledge of the region of phase boundaries can enable a reliable investigation of the instabilities near the boundaries that drive phase transitions.

cond-mat.quant-gas↗

arXiv2024

Entropic pulling and diffusion diode in an Itô process

Biological environments at micrometer scales and below are often crowded, and experience incessant stochastic thermal fluctuations. The presence of membranes/pores, and multiple biological entities in a constricted space can make the damping/diffusion inhomogeneous. This effect of inhomogeneity is presented by the diffusion becoming coordinate-dependent. In this paper, we analyze the consequence of inhomogeneity-induced coordinate-dependent diffusion on Brownian systems in thermal equilibrium under the Itô's interpretation. We argue that the presence of coordinate-dependent diffusion under Itô's formulation gives rise to an effective diffusion potential (and, equivalently an entropy) that can have substantial contribution to system's transport. This emergent force when looked at as of entropic origin it provides a physical basis of the notion of the entropic pulling postulated in the context of working of some biological systems.

cond-mat.stat-mech↗

arXiv2024

Equilibrium with coordinate dependent diffusion: Comparison of different stochastic processes

We show that, simultaneous local scaling of coordinate and time keeping the velocity unaltered is a symmetry of an Itô-process. Using this symmetry, any Itô-process can be mapped to a universal additive Gaussian-noise form. We use this mapping to separate the canonical and micro-canonical part of stochastic dynamics of a Brownian particle undergoing coordinate dependent diffusion. We identify the equilibrium distribution of the system and associated entropy induced by coordinate dependence of diffusion. Equilibrium physics of such a Brownian particle in a heat-bath of constant temperature is that of an Itô-process.

cond-mat.stat-mech↗

arXiv2024

Flow cross-overs under surface fluctuations in cylindrical nano-channel

We analyse surface-fluctuations-driven fluid flow through nano-channels to investigate the interplay between boundary layer flow structures and the bulk flow of fluid under a pressure-head. Surface fluctuations of a wide range of frequencies (up to several thousands of Hertz) in a nano-channel keep the flow in the low Reynolds number regime. Using this advantage of low Reynolds number flow, we develop a perturbation analysis of the fluid flow that clearly distinguishes the bulk flow under a pressure head around the axis of a nano-tube from its surface flow structure induced by fluctuations. In terms of particle transport under such flow conditions, there exists the opportunity to drag particles near the periphery of the nano-tube in a direction opposite to the bulk flow near the axis. This can potentially find applications in the separation, trapping, and filtration of particles under surface-driven flow through nano-tubes under widely varying conditions.

physics.flu-dyn↗

arXiv2023

Multi-component states for trapped spin-1 Bose-Einstein Condensates in the presence of magnetic field

In presence of a magnetic field, multi-component ground states appear in trapped spin-1 Bose-Einstein condensates for both ferromagnetic and anti-ferromagnetic types of spin-spin interaction. We aim to produce an accurate analytical description of the multi-component states which is of fundamental importance. Despite being in the so-called regime of Thomas-Fermi approximation (condensates with large particle number), the scenario of multi-component states is problematic under this approximation due to large variation in densities of the sub-components. We generalize the variational method that we have introduced in the article [Eur. Phys. J. Plus 137, 547 (2022)] to overcome the limitations of T-F approximation. We demonstrate that the variational method is crucial in identifying multi-component ground states. A comparison of the results of the variational method, which is multi-modal by construction, with that of single-mode approximation is also presented in this paper to demonstrate a marked improvement in accuracy over single-mode approximation. We have also looked into the phase transition between the phase-matched and polar state in a trapped condensate using the variational method and have identified substantial change in the phase boundary. The correspondence of the phase diagram of the trapped case with the homogeneous one identifies other limitations of T-F approximation as opposed to the more accurate variational method.

cond-mat.quant-gas↗

arXiv2023

Spontaneous collective transport in a heat--bath

We investigate emergence of spontaneous filtering of Brownian motion in higher dimensional space by many--body structures of symmetry broken dimer. Interacting dimer form structures which eventually restrict rotational degrees of freedom of individual constituents resulting in spontaneous emergence of collective transport. In this phenomenon, interaction and broken structural symmetry play cooperatively in emergence of collective transport out of thermal fluctuations. As a general phenomenon, spontaneous filtering of Brownian fluctuation might play an important role in the structural transition of complex molecules on top of what is known in terms of Kramers--rate process. This could also be a missing link to completely understand basics of bio--polymers' folding transitions (protein folding) where structure might encode motion in phase space.

cond-mat.stat-mech↗

arXiv2022

Physical interpretation of Itô--distribution on the basis of local measurement of diffusion

In this paper we provide a physical interpretation of Itô-process resulting in thermal equilibrium distribution of a Brownian particle experiencing coordinate dependent diffusion. Since the local quantities like diffusivity would go through large fluctuations in thermal equilibrium, one needs to take these fluctuation into account. We identify that the definition of local diffusivity is an essential ingredient that effectively modifies Hamiltonian of the system to result in a physically relevant Gibbs measure related to the Itô-distribution.

cond-mat.stat-mech↗

arXiv2022

Thermal equilibrium of a Brownian particle with coordinate dependent diffusion: comparison of Boltzmann and modified Boltzmann distributions with experimental results

In this paper we compare the Boltzmann distribution with a modified Boltzmann distribution, that results from an Itô-process considering thermal equilibrium of a Brownian particle with coordinate dependent diffusion, in the light of an existing experiment. The experiment was reported in 1994 by Faucheux and Libchaber. The experiment made use of direct tracking of diffusion of Brownian particles near a wall. Results of this experiment allows us to compare the Boltzmann and the modified Boltzmann distribution without making use of any adjustable parameter. A comparison of these two distributions with the experimental results lends support to the consideration of thermodynamic equilibrium of a Brownian particle with coordinate-dependent diffusion to be an Itô-process.

cond-mat.stat-mech↗

arXiv2021

A variational approach for the ground state profile of a trapped spinor-BEC: A detailed study of phase transition in spin-1 condensate at zero magnetic field

In this article we introduce a multi-modal variational method to analytically estimate the full number- and corresponding energy-density profile of a spin-1 Bose-Einstein condensate (BEC) for a number of particles as low as 500 under harmonic confinement. To apply this method, we consider a system of spin-1 BEC under three-dimensional isotropic and effective one-dimensional harmonic confinement in the absence (negligible presence) of the magnetic field which has ground state candidates of comparable energy. It should be noted that in such circumstances kinetic energy contribution to the ground state cannot be neglected which puts the applicability of Thomas-Fermi approximation to question. For anti-ferromagnetic condensates, the T-F approximated energy difference between the competing stationary states (ground state and the first excited state) is approximately 0.3\%. As T-F approximation is only good for condensates with a large number of particles, T-F approximated predictions can completely go wrong especially for small condensates. This is where comes the role of a detailed analysis using our variational method, which incorporates the kinetic energy contribution and accurately estimates the number- and energy-density profile even for condensates having a small number of particles. Results of our analytical method are supported by numerical simulation. This variational method is general and can be extended to other similar/higher-dimensional problems to get results beyond the accuracy of the Thomas-Fermi approximation.

cond-mat.quant-gas↗

arXiv2021

Room temperature flashing Ratcheting in nano-channels

We consider the surface-induced ratcheting transport of particles in nano-channels, particularly at room temperature. We show that at room temperature it is possible to achieve ratcheting of about 10 nm size particles in a nano-channel of about 100 nm width. The typical ratcheting velocity in such a case could be of the order of a few hundred nano-meter when the surface undulations are of a wavelength of a few hundred nano-meter and of the amplitude of a few tens of nano-meter. At room temperature, the viscosity of the fluid enabling such transport in the nano-channels comes out to be that of water. We show here a considerably large effect under realistic conditions which could be used for application in efficient filtration of particles and probably are in use in biological systems which typically work at room temperature.

cond-mat.stat-mech↗

arXiv2020

Galaxy rotation curves from external influence on Schwarzschild geometry

We present a modified Schwarzschild metric to introduce a weak breakdown of asymptotic flatness. The kinematics of the metric captures a wide range of galaxy rotation curves. We show baryonic Tully-Fisher relation on the basis of this modified Schwarzschild metric. On the basis of the kinematics of this modified metric we also show some connections between the size and ordinary matter content of the observable universe and the rotation curves of spiral galaxies.

gr-qc↗

arXiv2020

Random walk model for coordinate dependent diffusion in a force field

In this paper we develop a random walk model on lattice for coordinate dependent diffusion at constant temperature in contact with a heat bath. We employ here a coordinate dependent waiting time of the random walker to make the diffusivity coordinate dependent. The presence of a confining conservative force is modeled by appropriately breaking the isotropy of the jumps of the random walker to its nearest neighbors. We show that the equilibrium is characterized by the position distribution which is of modified Boltzmann form. We also show that, in such systems with coordinate dependent diffusivity, the modified Boltzmann distribution correctly captures the transition over a potential barrier as opposed to the Boltzmann distribution.

cond-mat.stat-mech↗

arXiv2020

Conversion of heat to work: An efficient inchworm

The paper discusses the natural emergence of directed motion in a dimer system due to a structural symmetry breaking. A generalised solution is obtained for the transport of such a system which is driven entirely by bath fluctuations. The result shows the existence of possibility of ratcheting driven by bath fluctuations. If this component of energy conversion driven by bath is taken into account the high efficiency of molecular motors as opposed to paradigmatic ratcheting models can probably be explained.

cond-mat.stat-mech↗

arXiv2020

Ratcheting in Nanofluids : Role of confining surface fluctuations

We consider the effect of surface undulations of nanochannels on the motion of particles in it. We report the mechanism of surface induced ratcheting transport of particles against fluid flow in nano channels. We show that, the typical number for the velocity of ratcheting particles could be of the order of 50 nm/sec. This is a considerably large effect which could be used for application in efficient filtration of particles smaller than the width of nanopores.

cond-mat.stat-mech↗

arXiv2019

Generalization of Stokes-Einstein relation to coordinate dependent damping and diffusivity: An apparent conflict

Brownian motion with coordinate dependent damping and diffusivity is ubiquitous. Understanding equilibrium of a Brownian particle with coordinate dependent diffusion and damping is a contentious area. In this paper, we present an alternative approach based on already established methods to this problem. We solve for the equilibrium distribution of the over-damped dynamics using Kramers-Moyal expansion. We compare this with the over-damped limit of the generalized Maxwell-Boltzmann distribution. We show that the equipartition of energy helps recover the Stokes-Einstein relation at constant diffusivity and damping of the homogeneous space. However, we also show that, there exists no homogeneous limit of coordinate dependent diffusivity and damping with respect to the applicability of Stokes-Einstein relation when it does not hold locally. In the other scenario where the Stokes-Einstein relation holds locally, one needs to impose a restriction on the local maximum velocity of the Brownian particle to make the modified Maxwell-Boltzmann distribution coincide with the modified Boltzmann distribution in the over-damped limit.

cond-mat.stat-mech↗

arXiv2018

Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution

Fick's law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers-Moyal expansion. We have obtained the equilibrium solution of the corresponding Smoluchowski equation. The equilibrium distribution is a generalization of the Boltzmann distribution. This generalized Boltzmann distribution involves an effective potential which is a function of coordinate dependent diffusivity. We discuss various implications of the existence of this generalized Boltzmann distribution for equilibrium of systems with coordinate dependent diffusivity and damping.

cond-mat.stat-mech↗