arXiv subjects

Ronojoy Adhikari

Publications and source records attributed to Ronojoy Adhikari.

27 records · Page 2Linked to original sources

arXiv2020

Stochastic action for tubes: Connecting path probabilities to measurement

The trajectories of diffusion processes are continuous but non-differentiable, and each occurs with vanishing probability. This introduces a gap between theory, where path probabilities are used in many contexts, and experiment, where only events with non-zero probability are measurable. Here we bridge this gap by considering the probability of diffusive trajectories to remain within a tube of small but finite radius around a smooth path. This probability can be measured in experiment, via the rate at which trajectories exit the tube for the first time, thereby establishing a link between path probabilities and physical observables. Considering $N$-dimensional overdamped Langevin dynamics, we show that the tube probability can be obtained theoretically from the solution of the Fokker-Planck equation. Expressing the resulting exit rate as a functional of the path and ordering it as a power series in the tube radius, we identify the zeroth-order term as the Onsager-Machlup stochastic action, thereby elevating it from a mathematical construct to a physical observable. The higher-order terms reveal, for the first time, the form of the finite-radius contributions which account for fluctuations around the path. To demonstrate the experimental relevance of this action functional for tubes, we numerically sample trajectories of Brownian motion in a double-well potential, compute their exit rate, and show an excellent agreement with our analytical results. Our work shows that smooth tubes are surrogates for non-differentiable diffusive trajectories, and provide a direct way of comparing theoretical results on single trajectories, such as path-wise definitions of irreversibility, to measurement.

cond-mat.stat-mech↗

arXiv2020

Ritz method for transition paths and quasipotentials of rare diffusive events

The probability of trajectories of weakly diffusive processes to remain in the tubular neighbourhood of a smooth path is given by the Freidlin-Wentzell-Graham theory of large deviations. The most probable path between two states (the instanton) and the leading term in the logarithm of the process transition density (the quasipotential) are obtained from the minimum of the Freidlin-Wentzell action functional. Here we present a Ritz method that searches for the minimum in a space of paths constructed from a global basis of Chebyshev polynomials. The action is reduced, thereby, to a multivariate function of the basis coefficients, whose minimum can be found by nonlinear optimization. For minimisation regardless of path duration, this procedure is most effective when applied to a reparametrisation-invariant "on-shell" action, which is obtained by exploiting a Noether symmetry and is a generalisation of the scalar work [Olender and Elber, 1997] for gradient dynamics and the geometric action [Heyman and Vanden-Eijnden, 2008] for non-gradient dynamics. Our approach provides an alternative to chain-of-states methods for minimum energy paths and saddlepoints of complex energy landscapes and to Hamilton-Jacobi methods for the stationary quasipotential of circulatory fields. We demonstrate spectral convergence for three benchmark problems involving the Muller-Brown potential, the Maier-Stein force field and the Egger weather model.

cond-mat.stat-mech↗

arXiv2018

Flow-induced phase separation of active particles is controlled by boundary conditions

Active particles, including swimming microorganisms, autophoretic colloids and droplets, are known to self-organize into ordered structures at fluid-solid boundaries. The entrainment of particles in the attractive parts of their spontaneous flows has been postulated as a possible mechanism underlying this phenomenon. Here, combining experiments, theory and numerical simulations, we demonstrate the validity of this flow-induced ordering mechanism in a suspension of active emulsion droplets. We show that the mechanism can be controlled, with a variety of resultant ordered structures, by simply altering hydrodynamic boundary conditions. Thus, for flow in Hele-Shaw cells, metastable lines or stable traveling bands can be obtained by varying the cell height. Similarly, for flow bounded by a plane, dynamic crystallites are formed. At a no-slip wall the crystallites are characterised by a continuous out-of-plane flux of particles that circulate and re-enter at the crystallite edges, thereby stabilising them. At an interface where the tangential stress vanishes the crystallites are strictly two-dimensional, with no out-of-plane flux. We rationalize these experimental results by calculating, in each case, the slow viscous flow produced by the droplets and the dissipative, long-ranged, many-body active forces and torques between them. The results of numerical simulations of motion under the action of the active forces and torques are in excellent agreement with experiments. Our work elucidates the mechanism of flow-induced phase separation (FIPS) in active fluids, particularly active colloidal suspensions, and demonstrates its control by boundaries, suggesting new routes to geometric and topological phenomena in active matter.

cond-mat.soft↗

arXiv2017

Deep Learning the Indus Script

Standardized corpora of undeciphered scripts, a necessary starting point for computational epigraphy, requires laborious human effort for their preparation from raw archaeological records. Automating this process through machine learning algorithms can be of significant aid to epigraphical research. Here, we take the first steps in this direction and present a deep learning pipeline that takes as input images of the undeciphered Indus script, as found in archaeological artifacts, and returns as output a string of graphemes, suitable for inclusion in a standard corpus. The image is first decomposed into regions using Selective Search and these regions are classified as containing textual and/or graphical information using a convolutional neural network. Regions classified as potentially containing text are hierarchically merged and trimmed to remove non-textual information. The remaining textual part of the image is segmented using standard image processing techniques to isolate individual graphemes. This set is finally passed to a second convolutional neural network to classify the graphemes, based on a standard corpus. The classifier can identify the presence or absence of the most frequent Indus grapheme, the "jar" sign, with an accuracy of 92%. Our results demonstrate the great potential of deep learning approaches in computational epigraphy and, more generally, in the digital humanities.

cs.CV↗

arXiv2014

Do liquid drops roll or slide on inclined surfaces?

We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analysed by decomposing the gradient of the velocity inside the droplet into a shear and a residual flow. This decomposition helps in distinguishing sliding versus rolling motion of the drop. Our detailed study confirms intuition, in that rolling motion dominates as the droplet shape approaches a circle, and the viscosity contrast between the droplet and the ambient fluid becomes large. As a consequence of kinematics, the amount of rotation in a general droplet shape follows a universal curve characterised by geometry, and independent of Bond number, surface inclination and equilibrium contact angle, but determined by the slip length and viscosity contrast. Our results open the way towards a rational design of droplet-surface properties, both when rolling motion is desirable (as in self-cleaning hydrophobic droplets) or when it must be prevented (as in insecticide sprays on leaves).

cond-mat.soft↗

arXiv2012

Lattice operators from discrete hydrodynamics

We present a general scheme to derive lattice differential operators from the discrete velocities and associated Maxwell-Boltzmann distributions used in lattice hydrodynamics. Such discretizations offer built-in isotropy and recursive techniques to increase the convergence order. This provides a simple and elegant procedure to derive isotropic and accurate discretizations of differential operators, which are expected to apply across a broad range of problems in computational physics.

physics.comp-ph↗

arXiv2012

Isotropic discrete Laplacian operators from lattice hydrodynamics

We show that discrete schemes developed for lattice hydrodynamics provide an elegant and physically transparent way of deriving Laplacians with isotropic discretisation error. Isotropy is guaranteed whenever the Laplacian weights follow from the discrete Maxwell-Boltzmann equilibrium since these are, by construction, isotropic on the lattice. We also point out that stencils using as few as 15 points in three dimensions, generate isotropic Laplacians. These computationally efficient Laplacians can be used in cell-dynamical and hybrid lattice Boltzmann simulations, in favor of popular anisotropic Laplacians, which make use of larger stencils. The method can be extended to provide discretisations of higher order and for other differential operators, such the gradient, divergence and curl.

physics.comp-ph↗

arXiv2011

Lattice Boltzmann - Langevin simulations of binary mixtures

We report a hybrid numerical method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes are solved using the stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretisation of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations.

cond-mat.stat-mech↗

arXiv2002

Interactions and Correlations of Particulate Inclusions in a Columnar Phase

We calculate the elastic field mediated interaction between macroscopic particles in a columnar hexagonal phase. The interaction is found to be long-ranged and non-central, with both attractive and repulsive parts. We show how the interaction modifies the particle correlations and the column fluctuations. We also calculate the interaction of particles with the topological defects of the columnar phase. The particle-defect interaction reduces the mobility of the defects.

cond-mat.soft↗