arXiv subjects

Abhishek Ghosh

Publications and source records attributed to Abhishek Ghosh.

At least 19 recordsLinked to original sources

arXiv2026

Inverse Identification of Surface Elastic Parameters in Soft Solids Using GA-ANN Surrogate Model

Surface elasticity plays a crucial role in the mechanics of soft solids at the scale of micrometers and may become significant even at the scale of millimeters in exceptional cases. However, despite the efforts made for the identification of surface elastic parameters, accurately determining these values remains challenging due to the complex interplay with bulk elasticity and nonlinearity. To address this issue, a novel GA-based optimization framework is developed by employing an ANN-based surrogate forward model for efficient identification of surface parameters from the force-displacement response of a cylindrical specimen. The ANN is trained on force-displacement data of a soft cylindrical specimen, generated by nonlinear FE model predictions incorporating model elastic surfaces. The data used for training is generated for non-dimensional values of surface tension in the range of 0-5 and surface shear modulus in the range of 0-50. The accuracy and reliability of the trained ANN are established. The key novelty lies in replacing analytical forward models, which rely on idealized boundary conditions, with a data-driven surrogate trained on FE simulations under realistic constraints. The parameter identification is performed for a number of surface parameter sets using numerically generated force-displacement data as well as for noisy data obtained by adding 5% error in simulated data. The maximum error in identified values of parameters in all the cases is less than 8%. Repeatability and uncertainty analyses based on multiple noisy realizations further demonstrate the robustness of the approach, yielding narrow confidence intervals for the predicted parameters. The proposed framework provides a novel, efficient, and robust alternative to FE-based inverse identification of surface parameters, particularly for experimentally relevant boundary conditions.

physics.comp-ph↗

arXiv2026

Constitutive modelling of magneto-active polymers at finite strains: A survey

Magneto-active polymers (MAPs) are field-responsive soft composites whose mechanical behaviour can be actively modified by external magnetic fields. Their ability to exhibit field-induced stiffening, magnetostriction, anisotropy and rate-dependent response makes them attractive for sensors, actuators, adaptive structures, vibration-control devices and soft robotic systems. This article presents a structured survey of constitutive modelling approaches for MAPs at finite strains. The review traces the development from early semi-empirical descriptions to thermodynamically consistent nonlinear continuum theories, with particular attention to isotropic and anisotropic magnetoelastic constitutive models, invariant-based and spectral representations, variational and polyconvex frameworks, microstructurally motivated models, dispersed-chain descriptions and magneto-viscoelastic theories. The principal constitutive variables, energy functions, coupling mechanisms and physical assumptions underlying the main models are discussed. The survey shows that constitutive modelling of MAPs has developed into a broad family of nonlinear, anisotropic and dissipative frameworks capable of describing versatile behaviours observed experimentally. Important challenges remain in resolving thermo-magneto-mechanical coupling and microstructure-sensitive effects, identification of parameters, validation of models as well as robust and efficient implementation on computers.

physics.comp-ph↗

arXiv2026

Bilinear spherical maximal function on the Heisenberg group

We introduce the bilinear Nevo-Thangavelu spherical means on the Heisenberg group $\mathbb{H}^n,$ and derive $L^{p_1}(\mathbb{H}^n) \times L^{p_2}(\mathbb{H}^n) \to L^{p}(\mathbb{H}^n)$ estimates for the single-scale bilinear averaging operators, the (full) bilinear Nevo-Thangavelu maximal operator and finally for the bilinear lacunary maximal operator on $\mathbb{H}^n; n \geq 2$. Our result for the full maximal operator is sharp. The principal tools in our analysis include newly developed estimates for single-scale bilinear averages, Hopf's maximal ergodic theorem, and a $T^*T$ argument adapted to this setting.

math.CA↗

arXiv2026

Spherical maximal functions and Hardy spaces for Fourier integral operators

We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact interval in $(0,\infty)$. These bounds extend to general hypersurfaces with non-vanishing Gaussian curvature, to the complex spherical means, and to geodesic spheres on compact manifolds. We also obtain improved maximal function bounds and pointwise convergence statements for wave equations, both on $\mathbb{R}^{n}$ and on compact manifolds. The maximal function bounds are essentially sharp for all $p\in[1,2]\cup [\frac{2(n+1)}{n-1},\infty)$, for each such hypersurface, every complex spherical mean, and on every manifold.

math.CA↗

arXiv2026

Helical maximal function and weighted estimates

In this article, we characterize the range of $α$ for which the helical maximal function is bounded from $L^p(|x|^α)$ to itself for $3<p<\infty$. Our result is optimal for $4\leq p<\infty,$ except possibly at end-points.

math.CA↗

arXiv2025

PyGraph: Robust Compiler Support for CUDA Graphs in PyTorch

Machine learning (ML) workloads launch hundreds to thousands of short-running GPU kernels per iteration. With GPU compute throughput growing rapidly, CPU-side launch latency of kernels is emerging as a bottleneck. CUDA Graphs promise to address this by replaying a set of kernels with a single dispatch of the graph, removing per-kernel launch costs. However, CUDA Graphs remain surprisingly difficult to deploy correctly and efficiently. We present PyGraph - a compiler framework to maximize the coverage and benefits of CUDA Graphs for ML workloads. It introduces three novel optimizations: it applies automatic code transformations to make ML applications amenable to CUDA Graphs; it eliminates the parameter copy overheads for kernels executing in CUDA Graphs, and it selectively deploys CUDA Graphs guided by a cost-benefit analysis. For 25 ML workloads from TorchBench, HuggingFace, and TIMM, PyGraph more than doubles the benefit from deploying CUDA Graph compared to the most popular and widely used ML compiler, PyTorch2. PyGraph is built atop PyTorch2's compilation framework and requires no programmer intervention.

cs.LG↗

arXiv2025

Dimension free estimates for the vector-valued Hardy--Littlewood maximal function on the Heisenberg group

In this article, we establish dimension-free Fefferman-Stein inequalities for the Hardy-Littlewood maximal function associated with averages over Korányi balls in the Heisenberg group. We also generalize the result to more general UMD lattices. As a key stepping stone, we establish the $L^p$- boundedness of the vector-valued Nevo-Thangavelu spherical maximal function, which plays a crucial role in our proofs of the main theorems.

math.CA↗

arXiv2024

Weighted estimates for lacunary maximal functions on homogeneous groups

In this article, we study weighted estimates for a general class of lacunary maximal functions on homogeneous groups. As an application we derive improved weighted estimates for the lacunary maximal function associated to the Korányi spherical means as well as for the lacunary maximal function associated to codimension two spheres in the Heisenberg group.

math.CA↗

arXiv2024

An embedding-aware continuum thin shell formulation

Cutting-edge smart materials are transforming the domains of soft robotics, actuators, and sensors by harnessing diverse non-mechanical stimuli, such as electric and magnetic fields. Accurately modelling their physical behaviour necessitates an understanding of the complex interactions between the structural deformation and the fields in the surrounding medium. For thin shell structures, this challenge is addressed by developing a shell model that effectively incorporates the three-dimensional field it is embedded in by appropriately accounting for the relevant boundary conditions. This study presents a model for the nonlinear deformation of thin hyperelastic shells, incorporating Kirchhoff-Love assumptions and a rigorous variational approach. The shell theory is derived from 3D nonlinear elasticity by dimension reduction while preserving the boundary conditions at the top and bottom surfaces of the shell. Consequently, unlike classical shell theories, this approach can distinguish between pressure loads applied at the top and bottom surfaces, and delivers a platform to include multi-physics coupling. Numerical examples are presented to illustrate the theory and provide a physical interpretation of the novel mechanical variables of the model.

physics.class-ph↗

arXiv2024

Sharp asymptotic of solutions to some nonlocal parabolic equations

We show that if $u$ solves the fractional parabolic equation $(\partial_t - Δ)^s u = Vu$ in $B_5 \times (-25, 0]$ ($0<s<1$) such that $u(\cdot, 0) \not\equiv 0$, then the maximal vanishing order of $u$ in space-time at $(0,0)$ is upper bounded by $C\left(1+\|V\|_{C^{1}_{(x,t)}}^{1/2s}\right)$. As $s \to 1$, it converges to the sharp maximal order of vanishing due to Donnelly-Fefferman and Bakri. This quantifies a space like strong unique continuation result recently proved in [3]. The proof is achieved by means of a new quantitative Carleman estimate that we derive for the corresponding extension problem combined with a quantitative monotonicity in time result and a compactness argument.

math.AP↗

arXiv2023

A fully-coupled nonlinear magnetoelastic thin shell formulation

A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical fields are generalised to the magnetic variables to derive a consistent two-dimensional theory based on a rigorous variational approach. The general deformation map, as opposed to the mid-surface deformation, is considered as the primary variable resulting in a more accurate description of the nonlinear deformation. The commonly used plane stress assumption is discarded due to the Maxwell stress in the surrounding free-space requiring careful treatment on the upper and lower shell surfaces. The complexity arising from the boundary terms when deriving the Euler-Lagrange governing equations is addressed via a unique application of Green's theorem.The governing equations are solved analytically for the problem of an infinite cylindrical magnetoelastic shell. This clearly demonstrates the model's capabilities and provides a physical interpretation of the new variables in the modified variational approach. This novel formulation for magnetoelastic shells serves as a valuable tool for the accurate design of thin magneto-mechanically coupled devices.

physics.class-ph↗

arXiv2023

Modulating thermoelectric properties in oxygen-passivated Sb2Te3 thin film through grain boundary engineering

The present study demonstrates the effectiveness of incorporating oxygen atoms into the Sb2Te3 thin film, leading to an improved power factor and reduction in thermal conductivity. Based on the experimental evidence, it can be inferred that oxygen-related impurities preferentially wet the grain boundary (GB) and introduce a double Schottky barrier at the GB interface, promoting energy-dependent carrier scattering, ultimately leading to a rise in the Seebeck coefficient. Additionally, the introduction of chemisorbed oxygen creates a high mobility state within the valence band of Sb2Te3, as corroborated by theoretical calculations, resulting in a significantly increased electrical mobility. These factors collectively contribute to improved thermoelectric performance. A set of Scanning probe (SPM) techniques is used to experimentally confirm the alteration in charge transport resulting from the oxygen-passivated grain boundary. Additionally, Scanning Thermal Microscopy (SThM) is employed to observe the spatial variations of thermal conductivity at the nanoscale regime. This study presents a comprehensive microscopic investigation of the impact of oxygen on the phonon and charge carrier transport characteristics of Sb2Te3 thermoelectric materials and indicates that incorporating oxygen may represent a feasible approach to improve the thermoelectric efficiency of these materials.

cond-mat.mtrl-sci↗

arXiv2023

Decay at infinity for solutions to some fractional parabolic equations

For $s \in [1/2, 1)$, let $u$ solve $(\partial_t - Δ)^s u = Vu$ in $\mathbb R^{n} \times [-T, 0]$ for some $T>0$ where $||V||_{ C^2(\mathbb R^n \times [-T, 0])} < \infty$. We show that if for some $0< c< T$ and $ε>0$ $$\frac{1}{c} \int_{[-c,0]} u^2(x, t) dt \leq Ce^{-|x|^{2+ε}}\ \forall x \in \mathbb R^n,$$ then $u \equiv 0$ in $\mathbb R^{n} \times [-T, 0]$.

math.AP↗

arXiv2023

On some operator-valued Fourier pseudo-multipliers associated to Grushin operators

This is a continuation of our work [BBGG23, BBGG22] where we have initiated the study of sparse domination and quantitative weighted estimates for Grushin pseudo-multipliers. In this article, we further extend this analysis to study analogous estimates for a family of operator-valued Fourier pseudo-multipliers associated to Grushin operators $G = - Δ_{x^{\prime}} - |x^{\prime}|^2 Δ_{x^{\prime \prime}}$ on $\mathbb{R}^{n_1+n_2}.$

math.AP↗

arXiv2023

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

In this article, we prove sharp quantitative weighted $L^p$-estimates for Grushin pseudo-multipliers satisfying Hörmander's condition as an application of pointwise domination of Grushin pseudo-multipliers by appropriate sparse operators.

math.AP↗

arXiv2023

Tuning thermoelectric properties of Sb$_2$Te$_3$-AgSbTe$_2$ nanocomposite thin film -- synergy of band engineering and heat transport modulation

The present study demonstrates a large enhancement in the Seebeck coefficient and ultralow thermal conductivity (TE) in Sb$_2$Te$_3$-AgSbTe$_2$ nanocomposite thin film. The addition of Ag leads to the in-situ formation of AgSbTe$_2$ secondary phase nanoaggregates in the Sb$_2$Te$_3$ matrix during the growth resulting in a large Seebeck coefficient and reduction of the thermal conductivity. A series of samples with different amounts of minor AgSbTe$_2$ phases are prepared to optimize the TE performance of Sb$_2$Te$_3$ thin films. Based on the experimental and theoretical evidence, it is concluded that a small concentration of Ag promotes the band flattening and induces a sharp resonate-like state deep inside the valence band of Sb$_2$Te$_3$, concurrently modifying the density of states (DOS) of the composite sample. In addition, the electrical potential barrier introduced by the band offset between the host TE matrix and the secondary phases promotes strong energy-dependent carrier scattering in the composite sample, which is also responsible for enhanced TE performance. A contemporary approach based on scanning thermal microscopy is performed to experimentally obtain thermal conductivity values of both the in-plane and cross-plane directions, showing a reduced in-plane thermal conductivity value by ~ 58% upon incorporating the AgSbTe$_2$ phase in the Sb$_2$Te$_3$ matrix. Benefitting from the synergistic manipulation of electrical and thermal transport, a large ZT value of 2.2 is achieved at 375 K. The present study indicates the importance of a combined effect of band structure modification and energy-dependent charge carrier scattering along with reduced thermal conductivity for enhancing TE properties.

cond-mat.mtrl-sci↗

arXiv2023

Sparse bounds for oscillating multipliers on stratified groups

In this article, we address sparse bounds for a class of spectral multipliers that include oscillating multipliers on stratified Lie groups. Our results can be applied to obtain weighted bounds for general Riesz means and for solutions of dispersive equations.

math.CA↗

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↗