arXiv subjects

Debasish Roy

Publications and source records attributed to Debasish Roy.

31 records · Page 2Linked to original sources

arXiv2018

Time-resolved quantitative visualization of complex flow field emanating from an open-ended shock tube by using wavefront measuring camera

Quantitative visualization of shock-induced complex flow field emanating from the open end of a miniaturized hand-driven shock tube (Reddy tube) is presented. During operation, the planar shock wave of Mach number Mi=1.3 is discharged through the low-pressure driven-section, kept open to ambient atmosphere. From the moment of shock discharge, its aftereffects of evolving flow field are recorded quantitatively for 300us near the exit of the tube by using our newly developed high resolution (16Mpixel) in-house developed wavefront measuring camera setup.

physics.flu-dyn↗

arXiv2017

A simple alteration of the peridynamics correspondence principle to eliminate zero-energy deformation

We look for an enhancement of the correspondence model of peridynamics with a view to eliminating the zero-energy deformation modes. Since the non-local integral definition of the deformation gradient underlies the problem, we initially look for a remedy by introducing a class of localizing corrections to the integral. Since the strategy is found to afford only a reduction, and not complete elimination, of the oscillatory zero-energy deformation, we propose in the sequel an alternative approach based on the notion of sub-horizons. A most useful feature of the last proposal is that the setup, whilst providing the solution with the necessary stability, deviates only marginally from the original correspondence formulation. We also undertake a set of numerical simulations that attest to the remarkable efficacy of the sub-horizon based methodology.

physics.comp-ph↗

arXiv2016

Quantifying Uncertainties in the 2004 Sumatra-Andaman Earthquake Source Parameters by Stochastic Inversion

Usual inversion for earthquake source parameters from tsunami wave data incorporates subjective elements. Noisy and possibly insufficient data also results in instability and non-uniqueness in most deterministic inversions. Here we employ the satellite altimetry data for the 2004 Sumatra-Andaman tsunami event to invert the source parameters. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a non-linear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large variance and skewness in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest the need for objective inversion strategies that should incorporate more sophisticated physical models in order to significantly improve the performance of early warning systems.

physics.geo-ph↗

arXiv2016

A peridynamic approach to flexoelectricity

A flexoelectric peridynamic (PD) theory is proposed. Using the PD framework, the formulation introduces, perhaps for the first time, a nanoscale flexoelectric coupling that entails non-uniform strain in centrosymmetric dielectrics. This potentially enables PD modeling of a large class of phenomena in solid dielectrics involving cracks, discontinuities etc. wherein large strain gradients are present and the classical electromechanical theory based on partial differential equations do not directly apply. Derived from Hamilton's principle, PD electromechanical equations are shown to satisfy the global balance requirements. Linear PD constitutive equations reflect the electromechanical coupling effect, with the mechanical force state affected by the polarization state and the electrical force state in turn by the displacement state. An analytical solution of the PD electromechanical equations in the integral form is presented for the static case when a point mechanical force and a point electric force act in a three dimensional infinite solid dielectric. A parametric study on how the different length scales influence the response is also undertaken.

physics.comp-ph↗

arXiv2015

A Stochastically Evolving Non-local Search and Solutions to Inverse Problems with Sparse Data

Building upon our earlier work of a martingale approach to global optimization, a powerful stochastic search scheme for the global optimum of cost functions is proposed on the basis of change of measures on the states that evolve as diffusion processes and splitting of the state-space along the lines of a Bayesian game. To begin with, the efficacy of the optimizer, when contrasted with one of the most efficient existing schemes, is assessed against a family of Np-hard benchmark problems. Then, using both simulated- and experimental data, potentialities of the new proposal are further explored in the context of an inverse problem of significance in medical imaging, wherein the superior reconstruction features of a global search vis-à-vis the commonly adopted local or quasi-local schemes are brought into relief.

stat.ME↗

arXiv2015

A peridynamic theory for linear elastic shells

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one physical dimension much smaller than the other two. A new notion of curved bonds is exploited to cater for force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states beget the necessary force and deformation vectors governing the motion of the shell. Correctness of our proposal on the peridynamic shell theory is numerically assessed against static deformation of spherical and cylindrical shells and flat plates.

physics.comp-ph↗

arXiv2015

Internal noise driven generalized Langevin equation from a nonlocal continuum model

Starting with a micropolar formulation, known to account for nonlocal microstructural effects at the continuum level, a generalized Langevin equation (GLE) for a particle, describing the predominant motion of a localized region through a single displacement degree-of-freedom (DOF), is derived. The GLE features a memory dependent multiplicative or internal noise, which appears upon recognising that the micro-rotation variables possess randomness owing to an uncertainty principle. Unlike its classical version, the new GLE qualitatively reproduces the experimentally measured fluctuations in the steady-state mean square displacement of scattering centers in a polyvinyl alcohol slab. The origin of the fluctuations is traced to nonlocal spatial interactions within the continuum. A constraint equation, similar to a fluctuation dissipation theorem (FDT), is shown to statistically relate the internal noise to the other parameters in the GLE.

cond-mat.soft↗

arXiv2014

A global optimization paradigm based on change of measures

A global optimization framework, acronymed COMBEO (Change OfMeasure Based Evolutionary Optimization), is proposed. An important aspect in the development is a set of derivative-free additive directional terms obtainable through a change of measures en route to the imposition of any stipulated conditions aimed at driving the realized design variables (particles) to the global optimum. The generalized setting offered by the new approach also enables several basic ideas, used with other global search methods such as the particle swarm or the differential evolution, to be rationally incorporated in the proposed setup via a change of measures. The global search may be further aided by imparting to the directional update terms additional layers of random perturbations such as scrambling and selection. Depending on the precise choice of the optimality conditions and the extent of random perturbation, the search can be readily rendered either greedy or more exploratory. As numerically demonstrated, the new proposal appears to provide for a more rational, more accurate and faster alternative to most available evolutionary optimization schemes, prominent amongst which are the differential evolution and the particle swarm methods.

stat.ME↗

arXiv2014

A Micropolar Peridynamic Theory in Linear Elasticity

A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems.

physics.comp-ph↗

arXiv2014

An ensemble Kushner-Stratonovich-Poisson filter for recursive estimation in nonlinear dynamical systems

Despite the numerous applications that may be expeditiously modelled by counting processes, stochastic filtering strategies involving Poisson-type observations still remain somewhat poorly developed. In this work, we propose a Monte Carlo stochastic filter for recursive estimation in the context of linear/nonlinear dynamical systems with Poisson-type measurements. A key aspect of the present development is the filter-update scheme, derived from an ensemble approximation of the time-discretized nonlinear filtering equation, modified to account for Poisson-type measurements. Specifically, the additive update through a gain-like correction term, empirically approximated from the innovation integral in the filtering equation, eliminates the problem of particle collapse encountered in many conventional particle filters. Through a few numerical demonstrations, the versatility of the proposed filter is brought forth, first with application to filtering problems with diffusive or Poisson-type measurements and then to an automatic control problem wherein the extremization of the associated cost functional is achieved simply by an appropriate redefinition of the innovation process.

stat.ME↗

arXiv2014

Evolutionary global optimization posed as a randomly perturbed martingale problem and applied to parameter recovery of chaotic oscillators

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to a directional update term, which parallels the conventional Gateaux derivative used in a local search for the extrema of smooth cost functionals, additional layers of random perturbations referred to as 'coalescence' and 'scrambling'. A selection scheme, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method apparently provides for a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.

stat.ME↗

arXiv2014

An Ensemble Kushner-Stratonovich (EnKS) Nonlinear Filter: Additive Particle Updates in Non-Iterative and Iterative Forms

Despite the cheap availability of computing resources enabling faster Monte Carlo simulations, the potential benefits of particle filtering in revealing accurate statistical information on the imprecisely known model parameters or modeling errors of dynamical systems, based on limited time series data, have not been quite realized. A major numerical bottleneck precipitating this under-performance, especially for higher dimensional systems, is the progressive particle impoverishment owing to weight collapse and the aim of the current work is to address this problem by replacing weight-based updates through additive ones. Thus, in the context of nonlinear filtering problems, a novel additive particle update scheme, in its non-iterative and iterative forms, is proposed based on manipulations of the innovation integral in the governing Kushner-Stratonovich equation. Numerical evidence for the identification of nonlinear and large dimensional dynamical systems indicates a substantively superior performance of the non- iterative version of the EnKS vis-à-vis most existing filters. The costlier iterative version, though conceptually elegant, mostly appears to effect a marginal improvement in the reconstruction accuracy over its non-iterative counterpart. Prominent in the reported numerical comparisons are variants of the Ensemble Kalman Filter (EnKF) that also use additive updates, albeit with many inherent limitations of a Kalman filter.

stat.ME↗

arXiv2013

Iterated Gain-based Stochastic Filters for Dynamic System Identification: Annealing-type Iterations and the Filter Bank

A novel form of nonlinear stochastic filtering employing an annealing-type iterative update scheme, aided by the introduction of an artificial diffusion parameter and based on the Gaussian sum approximations of the prior and posterior densities, is presented. The proposed Monte Carlo filter bank conforms in structure to the parent nonlinear filtering (Kushner-Stratonovich) equation, as reflected in the additive gain-based updates, and possesses excellent mixing properties enabling better explorations of the phase space of the state vector. The performance of the filter bank, presently assessed against a few carefully chosen numerical examples, provide ample evidence of its substantively improved performance in terms of filter convergence and estimation accuracy vis-à-vis a few other competing filters especially in higher dimensional dynamic system identification problems including cases that may demand estimating relatively minor variations in the parameter values from their reference states.

stat.ME↗