arXiv subjects

Abhik Basu

Publications and source records attributed to Abhik Basu.

At least 37 records · Page 2Linked to original sources

arXiv2023

The Statistical Properties of Superfluid Turbulence in $^4$He from the Hall-Vinen-Bekharevich-Khalatnikov Model

We obtain the von Kármán-Howarth relation for the stochastically forced three-dimensional Hall-Vinen-Bekharvich-Khalatnikov (3D HVBK) model of superfluid turbulence in Helium ($^4$He) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analyitcal studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) $P(γ)$, of the ratio $γ$ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as $P(γ) \sim γ^3$, for $γ\ll 1$, and $P(γ) \sim γ^{-3}$, for $γ\gg 1$. Furthermore, we show that the PDF $P(θ)$, of the angle $θ$ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: $P(θ)\sim θ$ for $θ\ll θ_*$ and $P(θ)\sim θ^{-4}$ for $θ_* \ll θ\ll 1$, where $θ_*$ is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, and the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature $T$, by using the experimentally determined mutual-friction coefficients for superfluid Helium $^4$He, so our results are of direct relevance to superfluid turbulence in this system.

physics.flu-dyn↗

arXiv2023

Anomalous Collective Dynamics of Auto-Chemotactic Populations

While the role of local interactions in nonequilibrium phase transitions is well studied, a fundamental understanding of the effects of long-range interactions is lacking. We study the critical dynamics of reproducing agents subject to autochemotactic interactions and limited resources. A renormalization group analysis reveals distinct scaling regimes for fast (attractive or repulsive) interactions; for slow signal transduction, the dynamics is dominated by a diffusive fixed point. Furthermore, we present a correction to the Keller-Segel nonlinearity emerging close to the extinction threshold and a novel nonlinear mechanism that stabilizes the continuous transition against the emergence of a characteristic length scale due to a chemotactic collapse.

cond-mat.stat-mech↗

arXiv2023

Active XY model on a substrate: Density fluctuations and phase ordering

We explore the generic long wavelength properties of an active XY model on a substrate, consisting of collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte-Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it shows phase ordering which is generically either logarithmically stronger than the conventional quasi long range order (QLRO) found in its equilibrium limit, together with "miniscule number fluctuations", or logarithmically weaker than QLRO along with "giant number fluctuations", showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short range phase-order are found, characterized by the presence or absence of stable clusters of finite sizes.

cond-mat.stat-mech↗

arXiv2023

Mobility-induced order in active XY spins on a substrate

We elucidate that the nearly phase-ordered active XY spins in contact with a conserved, diffusing species on a substrate can be stable. For wide-ranging model parameters, it has stable uniform phases robust against noises. These are distinguished by generalized quasi-long range (QLRO) orientational order logarithmically stronger or weaker than the well-known QLRO in equilibrium, together with miniscule (i.e., hyperuniform) or giant number fluctuations, respectively. This illustrates a direct correspondence between the two. The scaling of both phase and density fluctuations in the stable phase-ordered states is nonuniversal: they depend on the nonlinear dynamical couplings. For other parameters, it has no stable uniformly ordered phase. Our model, a theory for active spinners, provides a minimal framework for wide-ranging systems, e.g., active superfluids on substrates, synchronization of oscillators, active carpets of cilia and bacterial flagella and active membranes.

cond-mat.stat-mech↗

arXiv2023

Stiffening or softening of elastic media: Anomalous elasticity near phase transitions

We present the general theory of Ising transitions in isotropic elastic media with vanishing thermal expansion. By constructing a minimal model with appropriate spin-lattice couplings, we show that in two dimensions near a continuous transition the elasticity is anomalous in unusual ways: the system either significantly stiffens with a hitherto unknown unique positional order logarithmically stronger than quasi-long range order, or, as the inversion-asymmetry of the order parameter in its coupling with strain increases, it destabilizes when system size $L$ exceeds a finite threshold. At three dimensions, stronger inversion-asymmetric couplings induce instability to the long-range positional order for all $L$. Sufficiently strong order parameter-displacement couplings can also turn the phase transition first order at all dimensions, concomitant with finite jumps in the elastic modulii across the transition. Our theory establishes a {\em one-to-one correspondence} between the order of the phase transitions and anomalous elasticity near the transitions.

cond-mat.stat-mech↗

arXiv2022

Statistical mechanics of phase transitions in elastic media with vanishing thermal expansion

We consider the elastic theory for Ising transitions in an isotropic elastic medium in the zero thermal expansion (ZTE) limit. We use this theory to study the nature of the fluctuations in the system near the second phase transitions at $T_c$ in the ZTE limit given by $dT_c/dV=0$, where $V$ is the system volume, and explore anomalous elasticity. Allowing for the local strain to couple {\em asymmetrically} with the states of the order parameter, we uncover the dramatic effects of these couplings on the fluctuations of the local displacements near $T_c$, and also on the nature of the phase transition itself. Near second order phase transitions and with weak asymmetry in the order parameter - strain couplings, the variance of the displacement fluctuations in two dimensions scale with the system size $L$ in a universal fashion as $[\ln (L/a_0)]^{2/3}$; $a_0$ is a small-scale cutoff. Likewise, the correlation functions of the difference of the local displacements at two different points separated by $r$ scale as $[\ln (r/a_0)]^{2/3}$ for large $r$. For stronger asymmetry, this variance diverges as $L$ exceeds beyond a (nonuniversal) size, determined by the model parameters, signaling a transition to a phase with only short range order or the loss of the positional order of the elastic medium. At dimensions higher than two, for sufficiently weak selectivity, the variance of the displacement fluctuations is $L$-independent corresponding to long range order. However, if the selectivity parameters rise beyond a dimension-dependent threshold values, again the positional order is lost with a concomitant transition to a phase with short range order. Large values of the order parameter - strain couplings can turn the phase transition into a first order as well.

cond-mat.stat-mech↗

arXiv2022

Universal scaling regimes in rotating fluid turbulence

We analyse the scaling properties of the energy spectra in fully developed incompressible turbulence in forced, rotating fluids in three dimensions (3D), which are believed to be characterised by universal scaling exponents in the inertial range. To elucidate the scaling regimes, we set up a scaling analysis of the 3D Navier-Stokes equation for a rotating fluid that is driven by large-scale external forces. We use scaling arguments to extract the scaling exponents, which characterise the different scaling regimes of the energy spectra. We speculate on the intriguing possibility of two-dimensionalisation of 3D rotating turbulence within our scaling theory. Our results can be tested in large scale simulations and relevant laboratory-based experiments.

cond-mat.stat-mech↗

arXiv2022

Rough or crumpled: Phases in kinetic growth with surface relaxation

We show that generic kinetic growth processes with surface relaxations can exhibit a new crumpled phase with short-range orientational order at dimensions $d<4$. A sufficiently strong spatially non-local part of the chemical potential associated with the particle current above a threshold in the system can trigger this crumpling. The system can also be in a perturbatively accessible rough phase with long range orientational order but short range positional order at $d<4$ with known scaling exponents. Intriguingly, in $d>4$ we argue that there is no crumpling transition; instead, there is a roughening transition from a smooth to a rough phase for large enough non-local particle current. Experimental and theoretical implications of these results are discussed.

cond-mat.stat-mech↗

arXiv2022

Disorders can induce continuously varying universal scaling in driven systems

We elucidate the nature of universal scaling in disordered driven models. We in particularly explore the intriguing possibility of whether coupling with quenched disorders can lead to continuously varying universality classes. We examine this question in the context of the Kardar-Parisi-Zhang (KPZ) equation, with and without a conservation law, coupled with quenched disorders of appropriate structures. By using a renormalisation group (RG) framework, we show when the disorder is relevant in the RG sense, the scaling exponents can depend continuously on a dimensionless parameter that defines the disorder variance. This result is generic and holds for quenched disorders with or without spatially long ranged correlations, as long as the disorder remains "relevant perturbation" on the pure system in a renormalisation group sense and a dimensionless parameter naturally exists in its variance. We speculate on its implications for generic driven systems with quenched disorders, and compare and contrast with the scaling displayed in the presence of annealed disorders.

cond-mat.stat-mech↗

arXiv2021

Hydrodynamic theory of flocking at a solid-liquid interface: long range order and giant number fluctuations

We construct the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface. The polar order parameter and concentration of a collection of "active" (self-propelled) particles at a planar interface between a passive, isotropic bulk fluid and a solid surface are dynamically coupled to the bulk fluid. We find that such systems are stable, and have long-range orientational order, over a wide range of parameters. When stable, these systems exhibit "giant number fluctuations", i.e., large fluctuations of the number of active particles in a fixed large area. Specifically, these number fluctuations grow as the $3/4$th power of the mean number within the area. Stable systems also exhibit anomalously rapid diffusion of tagged particles suspended in the passive fluid along any directions in a plane parallel to the solid-liquid interface, whereas the diffusivity along the direction perpendicular to the plane is non-anomalous. In other parameter regimes, the system becomes unstable.

cond-mat.soft↗

arXiv2021

Swarming bottom feeders: Flocking at solid-liquid interfaces

We present the hydrodynamic theory of coherent collective motion ("flocking") at a solid-liquid interface, and many of its predictions for experiment. We find that such systems are stable, and have long-range orientational order, over a wide range of parameters. When stable, these systems exhibit "giant number fluctuations", which grow as the 3/4th power of the mean number. Stable systems also exhibit anomalous rapid diffusion of tagged particles suspended in the passive fluid along any directions in a plane parallel to the solid-liquid interface, whereas the diffusivity along the direction perpendicular to the plane is not anomalous. In the remaining parameter space, the system becomes unstable.

cond-mat.soft↗

arXiv2021

Scaling or multiscaling: Varieties of universality in a driven nonlinear model

Physical understanding of how the interplay between symmetries and nonlinear effects can control the scaling and multiscaling properties in a coupled driven system, such as magnetohydrodynamic turbulence or turbulent binary fluid mixtures, remains elusive till the date. To address this generic issue, we construct a conceptual nonlinear hydrodynamic model, parametrised jointly by the nonlinear coefficients, and the spatial scaling of the variances of the advecting stochastic velocity and the stochastic additive driving force, respectively. By using a perturbative one-loop dynamic renormalisation group method, we calculate the multiscaling exponents of the suitably defined equal-time structure functions of the dynamical variable. We show that depending upon the control parameters the model can display a variety of universal scaling behaviours ranging from simple scaling to multiscaling.

cond-mat.stat-mech↗

arXiv2020

Direct Numerical Simulations of Three-dimensional Magnetohydrodynamic Turbulence with Random, Power-law Forcing

We present pseudospectral direct-numerical-simulation (DNS) studies of the three-dimensional magnetohydrodynamic (MHD) equations (3DRFMHD) with a stochastic force that has zero mean and a variance $\sim k^{-3}$, where $k$ is the wavenumber, because 3DRFMHD is used in field-theoretic studies of the scaling of energy spectra in MHD turbulence. We obtain velocity and magnetic-field spectra and structure functions and, from these, the multiscaling exponent ratios $ζ_p/ζ_3$, by using the extended self similarity (ESS) procedure. These exponent ratios lie within error bars of their counterparts for conventional three-dimensional MHD turbulence (3DMHD). We then carry out a systematic comparison of the statistical properties of 3DMHD and 3DRFMHD turbulence by examining various probability distribution functions (PDFs), joint PDFs, and isosurfaces of of, e.g., the moduli of the vorticity and the current density for three magnetic Prandtl numbers ${\rm Pr_M} = 0.1,~1$, and $10$.

physics.flu-dyn↗

arXiv2020

Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes

We develop the hydrodynamic theory for number conserving asymmetric exclusion processes with short-range random quenched disordered hopping rates, which is one-dimensional Kardar-Parisi- Zhang (KPZ) equation with quenched columnar disorder. We show that when the system is away from half-filling, the universal spatio-temporal scaling of the density fluctuations is indistinguishable from its pure counterpart, with the model belonging to the one-dimensional Kardar-Parisi-Zhang universality class. In contrast, close to half-filling, the quenched disorder is relevant, leading to a new universality class. We physically argue that the irrelevance of the quenched disorder when away from half-filling is a consequence of the averaging of the disorder by the propagating density fluctuations in the system. In contrast, close to half-filling the density fluctuations are overdamped, and as a result, are strongly influenced by the quenched disorder.

cond-mat.stat-mech↗

arXiv2020

Asymmetric exclusion processes with fixed resources: Reservoir crowding and steady states

We study the nonequilibrium steady states of an asymmetric exclusion process (TASEP) coupled to a reservoir of unlimited capacity. We elucidate how the steady states are controlled by the interplay between the reservoir population that dynamically controls both the entry and exit rates of the TASEP, and the total particle number in the system. The TASEP can be in the low density, high density, maximal current and shock phases. We show that such a TASEP is different from an open TASEP for all values of available resources: here, the TASEP can support only localised domain walls for any (finite) amount of resources as opposed to delocalised domain walls in open TASEPs. Furthermore, in the limit of infinite resources, the TASEP can be found in its high density phase only for any finite values of the control parameters, in contrast to an open TASEP.

cond-mat.stat-mech↗

arXiv2020

Dynamic scaling in the quenched disordered classical $N$-vector model

We revisit the effects of short-ranged random quenched disorder on the universal scaling properties of the classical $N$-vector model with cubic anisotropy. We set up the nonconserved relaxational dynamics of the model, and study the universal dynamic scaling near the second order phase transition. We extract the critical exponents and the dynamic exponent in a one-loop dynamic renormalisation group calculation with short-ranged isotropic disorder. We show that the dynamics near a critical point is generically slower when the quenched disorder is relevant than when it is not, independent of whether the pure model is isotropic or cubic anisotropic. We demonstrate the surprising thresholdless instability of the associated universality class due to perturbations from rotational invariance breaking quenched disorder-order parameter coupling, indicating breakdown of dynamic scaling. We speculate that this may imply a novel first order transition in the model, induced by a symmetry-breaking disorder.

cond-mat.stat-mech↗

arXiv2020

Smooth or shock: universality in closed inhomogeneous driven single file motions

We study the nonequilibrum steady states in a unidirectional {or driven} single file motion (DSFM) of a collection of particles with hard-core repulsion in a closed system. For driven propulsion that is {spatially} smoothly varying with a few discontinuities, we show that the steady states are broadly classified into two classes, independent of any system detail: (i) when the steady state current depends explicitly on the {conserved} number density $n$, and (ii) when it is independent of $n$. This manifests itself in the universal topology of the phase diagrams {and fundamental diagrams (i.e., the current versus density curves) } for DSFM, which are determined solely by the interplay between {two control parameters} $n$ and the minimum propulsion speed along the chain. Our theory can be tested in laboratory experiments on driven particles in a closed geometry.

cond-mat.stat-mech↗

arXiv2020

When Hopf meets saddle: bifurcations in the diffusive Selkov model for glycolysis

We study the linear instabilities and bifurcations in the Selkov model for glycolysis with diffusion. We show that this model has a zero wave-vector, finite frequency Hopf bifurcation to a growing oscillatory but spatially homogeneous state and a saddle-node bifurcation to a growing inhomogeneous state with a steady pattern with a finite wavevector. We further demonstrate that by tuning the relative diffusivity of the two concentrations, it is possible to make both the instabilities to occur at the same point in the parameter space, leading to an unusual type of codimension-two bifurcation. We then show that in the vicinity of this bifurcation the initial conditions decide whether a spatially uniform oscillatory or a spatially periodic steady pattern emerges in the long time limit.

nlin.PS↗