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Abhishek Ghosh

Publications and source records attributed to Abhishek Ghosh.

30 records · Page 2Linked to original sources
arXiv2022

Computational bifurcation analysis of hyperelastic thin shells

The inflation of hyperelastic thin shells is an important and highly nonlinear problem that arises in multiple engineering applications involving severe kinematic and constitutive nonlinearities in addition to various instabilities. We present an isogeometric approach to compute the inflation of hyperelastic thin shells, following the Kirchhoff-Love hypothesis and associated large deformation. Both the geometry and the deformation field are discretized using Catmull-Clark subdivision bases which provide the C1-continuous finite element framework required for the Kirchhoff-Love shell formulation. To follow the complex nonlinear response of hyperelastic thin shells, the inflation is simulated incrementally, and each incremental step is solved via the Newton-Raphson method enriched with arc-length control. Eigenvalue analysis of the linear system after each incremental step allows for inducing bifurcation to a lower energy mode in case stability of the equilibrium is lost. The proposed method is first validated using benchmarks, and then applied to engineering applications, where we demonstrate the ability to simulate large deformation and associated complex instabilities.

math.NA↗
arXiv2022

Strong unique continuation for variable coefficient parabolic operators with Hardy type potential

In this paper, we prove the strong unique continuation property at the origin for solutions of the following scaling critical parabolic differential inequality \[ |\operatorname{div} (A(x,t) \nabla u) - u_t| \leq \frac{M}{|x|^{2}} |u|,\ \ \ \ \] where the coefficient matrix $A$ is Lipschitz continuous in $x$ and $t$. Our main result sharpens a previous one of Vessella concerned with the subcritical case as well as extends a recent result of one of us with Garofalo and Manna for the heat operator.

math.AP↗
arXiv2022

Pointwise and Weighted Hessian Estimates for Kolmogorov-Fokker-Planck type operators

In this article, we obtain hessian estimates for Kolmogorov-Fokker-Planck operators in non-divergence form in several Banach function spaces. Our approach relies on a representation formula and newly developed sparse domination techniques in Harmonic Analysis. Our result when restricted to weighted Lebesgue spaces yields sharp quantitative hessian estimates for the Kolmogorov-Fokker-Planck operators.

math.AP↗
arXiv2022

Sparse bounds for pseudo-multipliers associated to Grushin operators, II

In this article, we establish pointwise sparse domination results for Grushin pseudo-multipliers corresponding to various symbol classes, as a continuation of our investigation initiated in [BBGG21]. As a consequence, we deduce quantitative weighted estimates for these pseudo-multipliers.

math.AP↗
arXiv2022

Weighted estimates for bilinear fractional integral operator on the Heisenberg group

In this article, we introduce an analogue of Kenig and Stein's bilinear fractional integral operator on the Heisenberg group $\mathbb{H}^n$. We completely characterize exponents $α, β$ and $γ$ such that the operator is bounded from $L^{p}(\mathbb{H}^n, |x|^{αp})\times L^{q}(\mathbb{H}^n, |x|^{βq})$ to $L^{r}(\mathbb{H}^n, |x|^{-γr})$.

math.CA↗
arXiv2021

Stretchable patterns on elastomeric substrates

Compression-induced buckling instability of metal thin films on a compliant base result in surface wrinkles. A stiff thin film, perfectly bonded to an infinitely deep pre-stretched dielectric elastomer (DE) substrate, is considered. Linear perturbation analysis reveals the critical strain in the layer at the onset of wrinkling. A fully coupled Finite-Element (FE) scheme, based on large deformation electroelasticity, where domains of the mechanical and electrical problems coincide, is developed to model the elastomer. The procedure can handle nearly incompressible materials, which require careful considerations. The thin film is modeled as a beam. The numerical technique is used to study the post-buckling behavior upon relaxation of the pre-strained substrate. The FE domain is a unit cell of twice the characteristic wavelength. Assuming that there is no wrinkling-induced delamination at the film/substrate interface, the numerical analyses overview various tunable surface configurations distinctly different from the sinusoidal shape. The several topographic options broaden the functional horizon of surface instability patterns. Again, corrugation is essential to provide a degree of electrode compliance when the elastomer elongates in the lateral direction due to an applied electric potential. Simulations show the response of DE for the different surface profiles and also demonstrate the failure mechanisms that limit the actuation.

physics.comp-ph↗
arXiv2020

Swapping Intra-photon entanglement to Inter-photon entanglement using linear optical devices

We propose a curious protocol for swapping the intra-photon entanglement between path and polarization degrees of freedom of a single photon to inter-photon entanglement between two spatially separated photons which have never interacted. This is accomplished by using an experimental setup consisting of three suitable Mach-Zehnder interferometers along with number of beam splitters, polarization rotators and detectors. Using the same setup, we have also demonstrated an interesting quantum state transfer protocol, symmetric between Alice and Bob. Importantly, the Bell-basis discrimination is not required in both the swapping and state transfer protocols. Our proposal can be implemented using linear optical devices.

quant-ph↗
arXiv2012

Dithered quantizers with negligible in-band dither power

Subtractive dithered quantizers are examined to minimize the signal-band dither power. The design of finite impulse response(FIR) filters that shape most of the dither-power out of the signal band while maintaining the benefits of dithering are dealt with in detail. Simulation results for low-medium resolution quantizers are presented to highlight the overall design consideration.

cs.IT↗
arXiv2009

Classification of Cellular Automata Rules Based on Their Properties

This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the figures at some particular iteration might be helpful for some specific application. The hardware circuit implementation can be done using opto-electronic components [1-7].

cs.DM↗