arXiv subjects

R. Adhikari

Publications and source records attributed to R. Adhikari.

At least 19 recordsLinked to original sources

arXiv2021

Relaxation to statistical equilibrium in stochastic Michaelis-Menten kinetics

The equilibration of enzyme and complex concentrations in deterministic Michaelis-Menten reaction networks underlies the hyperbolic dependence between the input (substrates) and output (products). This relationship was first obtained by Michaelis and Menten and then Briggs and Haldane in two asymptotic limits: `fast equilibrium' and `steady state'. In stochastic Michaelis-Menten networks, relevant to catalysis at single-molecule and mesoscopic concentrations, the classical analysis cannot be directly applied due to molecular discreteness and fluctuations. Instead, as we show here, such networks require a more subtle asymptotic analysis based on the decomposition of the network into reversible and irreversible sub-networks and the exact solution of the chemical master equation (CME). The reversible and irreversible sub-networks reach detailed balance and stationarity, respectively, through a relaxation phase that we characterise in detail through several new statistical measures. Since stochastic enzyme kinetics encompasses the single-molecule, mesoscopic and thermodynamic limits, our work provides a broader molecular viewpoint of the classical results, in much the same manner that statistical mechanics provides a broader understanding of thermodynamics.

q-bio.MN↗

arXiv2021

Efficient Bayesian inference of fully stochastic epidemiological models with applications to COVID-19

Epidemiological forecasts are beset by uncertainties about the underlying epidemiological processes, and the surveillance process through which data are acquired. We present a Bayesian inference methodology that quantifies these uncertainties, for epidemics that are modelled by (possibly) non-stationary, continuous-time, Markov population processes. The efficiency of the method derives from a functional central limit theorem approximation of the likelihood, valid for large populations. We demonstrate the methodology by analysing the early stages of the COVID-19 pandemic in the UK, based on age-structured data for the number of deaths. This includes maximum a posteriori estimates, MCMC sampling of the posterior, computation of the model evidence, and the determination of parameter sensitivities via the Fisher information matrix. Our methodology is implemented in PyRoss, an open-source platform for analysis of epidemiological compartment models.

stat.ME↗

arXiv2021

Experimental measurement of relative path probabilities and stochastic actions

For diffusive stochastic dynamics, the probability to observe any individual trajectory is vanishingly small, making it unclear how to experimentally validate theoretical results for ratios of path probabilities. We provide the missing link between theory and experiment, by establishing a protocol to extract ratios of path probabilities from measured time series. For experiments on a single colloidal particle in a microchannel, we extract both ratios of path probabilities, and the most probable path for a barrier crossing, and find excellent agreement with independently calculated predictions based on the Onsager-Machlup stochastic action. Our experimental results at room temperature are found to be inconsistent with the low-noise Freidlin-Wentzell stochastic action, and we discuss under which circumstances the latter is expected to describe the most probable path. Furthermore, while the experimentally accessible ratio of path probabilities is uniquely determined, the formal path-integral action is known to depend on the time-discretization scheme used for deriving it; we reconcile these two seemingly contradictory facts by careful analysis of the time-slicing derivation of the path integral. Our experimental protocol enables us to probe probability distributions on path space, and allows us to relate theoretical single-trajectory results to measurement.

cond-mat.stat-mech↗

arXiv2021

Positive magnetoresistance and chiral anomaly in exfoliated type-II Weyl semimetal $T_\mathrm{d}$-WTe$_{2}$

Layered van der Waals semimetallic $T_\mathrm{d}$-WTe$_{2}$, exhibiting intriguing properties which include non-saturating extreme positive magnetoresistance (MR) and tunable chiral anomaly, has emerged as model topological type-II Weyl semimetal system. Here, $\sim$45 nm thick mechanically exfoliated flakes of $T_\mathrm{d}$-WTe$_{2}$ are studied $via$ atomic force microscopy, Raman spectroscopy, low-$T$/high-$μ_{0}H$ magnetotransport measurements and optical reflectivity. The contribution of anisotropy of the Fermi liquid state to the origin of the large positive transverse $\mathrm{MR}_\perp$ and the signature of chiral anomaly of the type-II Weyl fermions are reported. The samples are found to be stable in air and no oxidation or degradation of the electronic properties are observed. A transverse $\mathrm{MR}_\perp$ $\sim$1200\,\% and an average carrier mobility of $5000$\, cm$^{2}$V$^{-1}$s$^{-1}$ at $T=5\,\mathrm{K}$ for an applied perpendicular field $μ_{0}H_{\perp} = 7\,\mathrm{T}$ are established. The system follows a Fermi liquid model for $T\leq50\,\mathrm{K}$ and the anisotropy of the Fermi surface is concluded to be at the origin of the observed positive MR. The anisotropy of the electronic behaviour is also confirmed by optical reflectivity measurements. The relative orientation of the crystal axes and of the applied electric and magnetic fields is proven to give rise to the observed chiral anomaly in the in-plane magnetotransport.

cond-mat.mes-hall↗

arXiv2020

Low temperature and high magnetic field performance of a commercial piezo-actuator probed $via$ laser interferometry

The advances in the fields of scanning probe microscopy, scanning tunneling spectroscopy, point contact spectroscopy and point contact Andreev reflection spectroscopy to study the properties of conventional and quantum materials at cryogenic conditions have prompted the development of nanopositioners and nanoscanners with enhanced spatial resolution. Piezoelectric-actuator stacks as nanopositioners with working strokes $>100~μ\mathrm{m}$ and positioning resolution $\sim$(1-10) nm are desirable for both basic research and industrial applications. However, information on the performance of most commercial piezoelectric-actuators in cryogenic environment and in the presence of magnetic fields in excess of 5\,T is generally not available. In particular, the magnitude, rate and the associated hysteresis of the piezo-displacement at cryogenic temperatures are the most relevant parameters that determine whether a particular piezoelectric-actuator can be used as a nanopositioner. Here, the design and realization of an experimental set-up based on interferometric techniques to characterize a commercial piezoelectric-actuator over a temperature range of $2~\mathrm{K}\leq{T}\leq260~\mathrm{K}$ and magnetic fields up to 6\,T is presented. The studied piezoelectric-actuator has a maximum displacement of $30~μ\mathrm{m}$ at room temperature for a maximum driving voltage of 75\,V, which reduces to $1.2~μ\mathrm{m}$ with an absolute hysteresis of $\left(9.1\pm3.3\right)~\mathrm{nm}$ at $T=2\,\mathrm{K}$. The magnetic field is shown to have no substantial effect on the piezo properties of the studied piezoelectric-actuator stack.

cond-mat.mtrl-sci↗

arXiv2020

Transients generate memory and break hyperbolicity in stochastic enzymatic networks

The hyperbolic dependence of catalytic rate on substrate concentration is a classical result in enzyme kinetics, quantified by the celebrated Michaelis-Menten equation. The ubiquity of this relation in diverse chemical and biological contexts has recently been rationalized by a graph-theoretic analysis of deterministic reaction networks. Experiments, however, have revealed that "molecular noise" - intrinsic stochasticity at the molecular scale - leads to significant deviations from classical results and to unexpected effects like "molecular memory", i.e., the breakdown of statistical independence between turnover events. Here we show, through a new method of analysis, that memory and non-hyperbolicity have a common source in an initial, and observably long, transient peculiar to stochastic reaction networks of multiple enzymes. Networks of single enzymes do not admit such transients. The transient yields, asymptotically, to a steady-state in which memory vanishes and hyperbolicity is recovered. We propose new statistical measures, defined in terms of turnover times, to distinguish between the transient and steady states and apply these to experimental data from a landmark experiment that first observed molecular memory in a single enzyme with multiple binding sites. Our study shows that catalysis at the molecular level with more than one enzyme always contains a non-classical regime and provides insight on how the classical limit is attained.

q-bio.MN↗

arXiv2020

Controlled Optofluidic Crystallization of Colloids Tethered at Interfaces

We report experiments that show rapid crystallization of colloids tethered to an oil-water interface in response to laser illumination. This light-induced transition is due to a combination of long-ranged thermophoretic pumping and local optical binding. We show that the flow-induced force on the colloids can be described as the gradient of a potential. The nonequilibrium steady state due to local heating thus admits an effective equilibrium description. The optofluidic manipulation explored in this work opens novel ways to manipulate and assemble colloidal particles

cond-mat.soft↗

arXiv2020

PyStokes: phoresis and Stokesian hydrodynamics in Python

We present a modular Python library for computing many-body hydrodynamic and phoretic interactions between spherical active particles in suspension, when these are given by solutions of the Stokes and Laplace equations. Underpinning the library is a grid-free methodology that combines dimensionality reduction, spectral expansion, and Ritz-Galerkin discretization, thereby reducing the computation to the solution of a linear system. The system can be solved analytically as a series expansion or numerically at a cost quadratic in the number of particles. Suspension-scale quantities like fluid flow, entropy production, and rheological response are obtained at a small additional cost. The library is agnostic to boundary conditions and includes, amongst others, confinement by plane walls or liquid-liquid interfaces. The use of the library is demonstrated with six fully coded examples simulating active phenomena of current experimental interest.

cond-mat.soft↗

arXiv2020

Inference, prediction and optimization of non-pharmaceutical interventions using compartment models: the PyRoss library

PyRoss is an open-source Python library that offers an integrated platform for inference, prediction and optimisation of NPIs in age- and contact-structured epidemiological compartment models. This report outlines the rationale and functionality of the PyRoss library, with various illustrations and examples focusing on well-mixed, age-structured populations. The PyRoss library supports arbitrary structured models formulated stochastically (as master equations) or deterministically (as ODEs) and allows mid-run transitioning from one to the other. By supporting additional compartmental subdivision ad libitum, PyRoss can emulate time-since-infection models and allows medical stages such as hospitalization or quarantine to be modelled and forecast. The PyRoss library enables fitting to epidemiological data, as available, using Bayesian parameter inference, so that competing models can be weighed by their evidence. PyRoss allows fully Bayesian forecasts of the impact of idealized NPIs by convolving uncertainties arising from epidemiological data, model choice, parameters, and intrinsic stochasticity. Algorithms to optimize time-dependent NPI scenarios against user-defined cost functions are included. PyRoss's current age-structured compartment framework for well-mixed populations will in future reports be extended to include compartments structured by location, occupation, use of travel networks and other attributes relevant to assessing disease spread and the impact of NPIs. We argue that such compartment models, by allowing social data of arbitrary granularity to be combined with Bayesian parameter estimation for poorly-known disease variables, could enable more powerful and robust prediction than other approaches to detailed epidemic modelling. We invite others to use the PyRoss library for research to address today's COVID-19 crisis, and to plan for future pandemics.

q-bio.PE↗

arXiv2020

Age-structured impact of social distancing on the COVID-19 epidemic in India

The outbreak of the novel coronavirus, COVID-19, has been declared a pandemic by the WHO. The structures of social contact critically determine the spread of the infection and, in the absence of vaccines, the control of these structures through large-scale social distancing measures appears to be the most effective means of mitigation. Here we use an age-structured SIR model with social contact matrices obtained from surveys and Bayesian imputation to study the progress of the COVID-19 epidemic in India. The basic reproductive ratio R0 and its time-dependent generalization are computed based on case data, age distribution and social contact structure. The impact of social distancing measures - workplace non-attendance, school closure, lockdown - and their efficacy with durations are then investigated. A three-week lockdown is found insufficient to prevent a resurgence and, instead, protocols of sustained lockdown with periodic relaxation are suggested. Forecasts are provided for the reduction in age-structured morbidity and mortality as a result of these measures. Our study underlines the importance of age and social contact structures in assessing the country-specific impact of mitigatory social distancing.

q-bio.PE↗

arXiv2020

Periodic Orbits of Active Particles induced by Hydrodynamic Monopoles

Terrestrial experiments on active particles, such as Volvox, involve gravitational forces, torques and accompanying monopolar fluid flows. Taking these into account, we analyse the dynamics of a pair of self-propelling, self-spinning active particles between widely separated parallel planes. Neglecting flow reflected by the planes, the dynamics of orientation and horizontal separation is symplectic, with a Hamiltonian exactly determining limit cycle oscillations. Near the bottom plane, gravitational torque damps and reflected flow excites this oscillator, sustaining a second limit cycle that can be perturbatively related to the first. Our work provides a theory for dancing Volvox and highlights the importance of monopolar flow in active matter.

cond-mat.soft↗

arXiv2019

Ferromagnetic phase transition in topological crystalline insulator thin films: interplay of anomalous Hall angle and magnetic anisotropy

In magnetic topological phases of matter, the quantum anomalous Hall (QAH) effect is an emergent phenomenon driven by ferromagnetic doping, magnetic proximity effects and strain engineering. The realization of QAH states with multiple dissipationless edge and surface conduction channels defined by a Chern number $\mathcal{C}\geq1$ was foreseen for the ferromagnetically ordered SnTe class of topological crystalline insulators (TCIs). From magnetotransport measurements on Sn$_{1-x}$Mn$_{x}$Te ($0.00\leq{x}\leq{0.08}$)(111) epitaxial thin films grown by molecular beam epitaxy on BaF$_{2}$ substrates, hole mediated ferromagnetism is observed in samples with $x\geq0.06$ and the highest $T_\mathrm{c}\sim7.5\,\mathrm{K}$ is inferred from an anomalous Hall behavior in Sn$_{0.92}$Mn$_{0.08}$Te. The sizable anomalous Hall angle $\sim$0.3 obtained for Sn$_{0.92}$Mn$_{0.08}$Te is one of the greatest reported for magnetic topological materials. The ferromagnetic ordering with perpendicular magnetic anisotropy, complemented by the inception of anomalous Hall effect in the Sn$_{1-x}$Mn$_{x}$Te layers for a thickness commensurate with the decay length of the top and bottom surface states, points at Sn$_{1-x}$Mn$_{x}$Te as a preferential platform for the realization of QAH states in ferromagnetic TCIs.

cond-mat.mes-hall↗

arXiv2019

Competing chemical and hydrodynamic interactions in autophoretic colloidal suspensions

At the surfaces of autophoretic colloids, slip velocities arise from local chemical gradients that are many-body functions of particle configuration and activity. For rapid chemical diffusion, coupled with slip-induced hydrodynamic interactions, we deduce the chemohydrodynamic forces and torques between colloids. Near a no-slip wall, the forces can be expressed as gradients of a non-equilibrium potential which, by tuning the type of activity, can be varied from repulsive to attractive. When this potential has a barrier, we find arrested phase separation with a mean cluster size set by competing chemical and hydrodynamic forces. These are controlled in turn by the monopolar and dipolar contributions to the active chemical surface fluxes.

cond-mat.soft↗

arXiv2018

Magnetotransport in phase-separated (Ga,Fe)N with $γ$'-Ga$_y$Fe$_{4-y}$N nanocrystals

The magnetotransport in phase-separated (Ga,Fe)N containing $γ$'-Ga$_y$Fe$_{4-y}$N (0\,$<$\,y\,$<$1) nanocrystals (NCs) is studied in the temperature range between 2\,K and 300\,K. The evolution of the resistivity and of the magnetoresistance (MR) as a function of temperature points at two conduction mechanisms: namely a conventional Arrhenius-type one down to 50\,K, and Mott variable range hopping at lower temperatures, where the spin-polarized current is transported between NCs in a regime in which phonon-scattering effects are not dominant. Below 25\,K, the MR shows a hysteretic contribution at magnetic fields $<$1\,T and proportional to the coercive field. Anisotropic magnetoresistance with values one order of magnitude greater than those previously reported for $γ$'-Fe$_4$N thin films over the whole considered temperature range, confirms that the observed MR in these layers is determined by the embedded nanocrystals.

cond-mat.mtrl-sci↗

arXiv2018

Fast Bayesian inference of the multivariate Ornstein-Uhlenbeck process

The multivariate Ornstein-Uhlenbeck process is used in many branches of science and engineering to describe the regression of a system to its stationary mean. Here we present an $O(N)$ Bayesian method to estimate the drift and diffusion matrices of the process from $N$ discrete observations of a sample path. We use exact likelihoods, expressed in terms of four sufficient statistic matrices, to derive explicit maximum a posteriori parameter estimates and their standard errors. We apply the method to the Brownian harmonic oscillator, a bivariate Ornstein-Uhlenbeck process, to jointly estimate its mass, damping, and stiffness and to provide Bayesian estimates of the correlation functions and power spectral densities. We present a Bayesian model comparison procedure, embodying Ockham's razor, to guide a data-driven choice between the Kramers and Smoluchowski limits of the oscillator. These provide novel methods of analyzing the inertial motion of colloidal particles in optical traps.

cond-mat.stat-mech↗

arXiv2018

Generalized Stokes laws for active colloids and their applications

The force per unit area on the surface of a colloidal particle is a fundamental dynamical quantity in the mechanics and statistical mechanics of colloidal suspensions. Here we compute it in the limit of slow viscous flow for a suspension of $N$ spherical active colloids in which activity is represented by surface slip. Our result is best expressed as a set of linear relations, the "generalized Stokes laws", between the coefficients of a tensorial spherical harmonic expansion of the force per unit area and the surface slip. The generalized friction tensors in these laws are many-body functions of the colloidal configuration and can be obtained to any desired accuracy by solving a system of linear equations. Quantities derived from the force per unit area - forces, torques and stresslets on the colloids and flow, pressure and entropy production in the fluid - have succinct expressions in terms of the generalized Stokes laws. Most notably, the active forces and torques have a dissipative, long-ranged, many-body character that can cause phase separation, crystallization, synchronization and a variety of other effects observed in active suspensions. We use the results above to derive the Langevin and Smoluchowski equations for Brownian active suspensions, to compute active contributions to the suspension stress and fluid pressure, and to relate the synchrony in a lattice of harmonically trapped active colloids to entropy production. Our results provide the basis for a microscopic theory of active Brownian suspensions that consistently accounts for momentum conservation in the bulk fluid and at fluid-solid boundaries

cond-mat.soft↗

arXiv2017

Fluctuating hydrodynamics and the Brownian motion of an active colloid near a wall

The traction on the surface of a spherical active colloid in a thermally fluctuating Stokesian fluid contains passive, active, and Brownian contributions. Here we derive these three parts systematically, by "projecting out" the fluid using the boundary-domain integral representation of slow viscous flow. We find an exact relation between the statistics of the Brownian traction and the thermal forces in the fluid and derive, thereby, fluctuation-dissipation relations for every irreducible tensorial harmonic traction mode. The first two modes give the Brownian force and torque, from which we construct the Langevin and Smoluchowski equations for the position and orientation of the colloid. We emphasize the activity-induced breakdown of detailed balance and provide a prescription for computing the configuration-dependent variances of the Brownian force and torque. We apply these general results to an active colloid near a plane wall, the simplest geometry with configuration-dependent variances, and show that the stationary distribution is non-Gibbsian. We derive a regularization of the translational and rotational friction tensors, necessary for Brownian dynamics simulations, that ensures positive variances at all distances from the wall. The many-body generalization of these results is indicated.

cond-mat.soft↗

arXiv2017

Direct verification of the fluctuation-dissipation relation in viscously coupled oscillators

The fluctuation-dissipation relation, a central result in non-equilibrium statistical physics, relates equilibrium fluctuations in a system to its linear response to external forces. Here we provide a direct experimental verification of this relation for viscously coupled oscillators, as realized by a pair of optically trapped colloidal particles. A theoretical analysis, in which interactions mediated by slow viscous flow are represented by non-local friction tensors, matches experimental results and reveals a frequency maximum in the amplitude of the mutual response which is a sensitive function of the trap stiffnesses and the friction tensors. This allows for its location and width to be tuned and suggests the utility of the trap setup for accurate two-point microrheology.

cond-mat.soft↗