arXiv subjects

Lalit Kumar

Publications and source records attributed to Lalit Kumar.

18 recordsLinked to original sources

arXiv2026

Pathology Transport: Optimal-Transport Explanations for Clinical Data, and When Their Heatmaps (Fail to) Localize Disease

Generative models promise a route to explainable clinical AI: rather than probe a classifier, model the distributions of healthy and diseased patients and read explanations off the geometry between them. We build such a system - an optimal-transport rectified flow trained between two clinical distributions - and use it to ask a pointed question the field too rarely tests: do the resulting explanation heatmaps actually localize disease? On tabular tumour biomarkers (Breast Cancer Wisconsin) a single flow yields per-patient counterfactuals, an unsupervised malignancy score (AUROC 0.91; 0.93 +/- 0.01 across five seeds), and a label-free attribution that agrees with a supervised classifier (r ~ 0.5) - a compact, honest interpretability engine, though it never out-predicts logistic regression. Moving to chest X-rays, we show the transport heatmap is a population-level signal, not a localiser; a reconstruction-based, identity-preserving variant does localize synthetic lesions (pointing game 0.52), yet on real RSNA radiologist boxes it collapses to chance while only supervised Grad-CAM stays above it. The central result is a synthetic-to-real gap: label-free heatmaps that look compelling on planted lesions are not evidence of real localisation. We contribute a reusable optimal-transport recipe for generative explanations and a controlled benchmark for stress-testing whether they localize.

cs.LG↗

arXiv2026

Emergent Yielding from Structural Load Transfer in Disordered Soft Solids

Yielding in disordered soft solids originates from the progressive redistribution of load-bearing capacity from recoverable elastic networks to frictional interactions through deformation-induced structural evolution. We present a unified, non-singular constitutive framework demonstrating that this mechanism naturally generates a finite yield stress and a smooth solid-to-fluid transition without prescribed yield criteria, constitutive switching, or divergent viscosities. The framework captures diverse transient and steady rheological phenomena, including Herschel-Bulkley behavior, stress overshoots, hysteresis, viscosity bifurcation, plug-flow formation, and thixotropic steady-state shear banding.

cond-mat.soft↗

arXiv2026

Kinematic Inconsistencies and Initial-Value Boundary Paradoxes in Rate-Dependent Viscoelastic Yield Stress Models

We present a rigorous analysis of the mathematical boundaries and kinematic consistency of a recently proposed rate-dependent relaxation time framework intended to unify pre- and post-yield dynamics in yield-stress fluids. By evaluating the governing constitutive equations under an idealized transient creep protocol from a state of physical rest, we show that the model encounters an unavoidable boundary paradox. To avoid predicting perfectly rigid solid behavior or falling into a division-by-zero mathematical singularity under a constant applied stress below the yield threshold ($\sigma \le \sigma_y$), the framework requires an unphysical, instantaneous velocity or strain-rate step at $t = 0^+$. We show that assuming a non-zero initial strain rate explicitly violates momentum conservation and fluid inertia. Consequently, the framework preserves the piecewise, discontinuous drawbacks of classic viscoplastic models.

cond-mat.soft↗

arXiv2024

Existence and regularity results for space-time fractional integro-differential equation of Kirchhoff type with memory

This paper analyses a Kirchhoff type quasilinear space-time fractional integro-differential equation with memory $(\mathcal{K}^{s}_{\alpha})$. Various a priori bounds are derived in different norms on the solution of the considered equation. Utilizing these a priori bounds, existence and uniqueness of the weak solution to the proposed model are proved. Furthermore, regularity results on the solution of $(\mathcal{K}^{s}_{\alpha})$ are established. The contribution made in this work provides a framework for further investigation of such types of partial integro-differential equation $(\mathcal{K}^{s}_{\alpha})$.

math.AP↗

arXiv2024

Variational Optimization for Constructing Inverse Potentials of Proton-Proton Scattering: A Phase Function Method Study

Background: The phase-shift analysis for proton-proton scattering has been studied by various research groups using the realistic potentials to be comprised of various internal interactions based on an exchange of pions and mesons, involving a large number of parameters. Purpose: The goal of the research is to construct inverse potentials for various l-channels of proton-proton (pp) elastic scattering using the 3-parameter Morse function in combination with atomic Hulthen by utilizing the phase function method and variational optimization technique. Methodology: The implementation of variational optimization begins with randomly assigning initial values to the Morse model parameters. Utilizing the Morse + Hulthen potential as input, the phase equations for various l-channels are numerically solved using the RK-5 method for obtaining the simulated Scattering Phase Shift (SPS). Mean Squared error between simulated and expected SPS has been chosen as the cost function. Variational optimization proceeds iteratively by adjusting potential parameters and re-evaluating the cost function until convergence is achieved. Results: All the obtained scattering phase shifts for various l-channels have been found to converge to a mean squared error <= 0.3. The computed cross-sections matched the experimental ones to less than 1% for energies up to 25 MeV. The scattering parameters are also found to closely match the experimental data. Conclusion: The inverse potentials constructed for various l-channels using Morse + atomic Hulthen are on par with the currently available high-precision realistic potentials.

nucl-th↗

arXiv2024

Algorithm to Obtain Inverse Potentials for $\alpha-\alpha$ Scattering using Variable Phase Approach

An algorithm$^{\ref{Fig1}}$ has been developed with the purpose of obtaining inverse potentials, where the Riccati-type non-linear differential equation, also called phase equation, has been kept in tandem with the Variational Monte Carlo method. The optimization of Gaussian function parameters is achieved such that the experimental phase shifts are reproduced. The obtained SPS for various $\ ell$ channels has been compared with experimental ones with mean absolute percentage error (MAPE) as a measure. The model parameters have been optimised by suitable optimisation technique by looking for minimum value of MAPE. The results for $\ell$=0$^+$, 2$^+$ and 4$^+$ partial waves have been obtained, to match with experimental SPS, with MAPE values of $2.9$, $4.6$ and $6.2$ respectively for data up to $23$ MeV, while for higher states 6$^+$, 8$^+$ and 10$^+$ has MAPE of $3.2, 4.5$ and $5.9$ respectively for data from $53-120$ MeV. On extrapolation for data in range E$_{\ell ab.}$ = $23-120$ MeV, using the optimised parameters, the SPS are found to be in close agreement with experimental ones for the first three channels.

nucl-th↗

arXiv2023

Numerical Simulation Study of Neutron-Proton Scattering using Phase Function Method

In this article, we propose a numerical approach to solve quantum mechanical scattering problems, using phase function method, by considering neutron-proton interaction as an example. The nonlinear phase equation, obtained from the time-independent Schrodinger equation, is solved using the Runge-Kutta method for obtaining S-wave scattering phase shifts for neutron-proton interaction modeled using Yukawa and Malfliet-Tjon potentials. While scattering phase shifts of S-states using Yukawa match with experimental data for only lower energies of 50 MeV, Malfliet-Tjon potential with repulsive term gives very good accuracy for all available energies up to 350 MeV. Utilizing these S-wave scattering phase shifts, low energy scattering parameters, and total S-wave cross section have been calculated and found to be consistent with experimental results. This simulation methodology can be easily extended to study scattering phenomenon using phase wave analysis approach in the realms of atomic, molecular, and nuclear physics.

nucl-th↗

arXiv2023

A Linearized L1-Galerkin FEM for Non-smooth Solutions of Kirchhoff type Quasilinear Time-fractional Integro-differential Equation

In this article, we study the semi discrete and fully discrete formulations for a Kirchhoff type quasilinear integro-differential equation involving time-fractional derivative of order $\alpha \in (0,1) $. For the semi discrete formulation of the equation under consideration, we discretize the space domain using a conforming FEM and keep the time variable continuous. We modify the standard Ritz-Volterra projection operator to carry out error analysis for the semi discrete formulation of the considered equation. In general, solutions of the time-fractional partial differential equations (PDEs) have a weak singularity near time $t=0$. Taking this singularity into account, we develop a new linearized fully discrete numerical scheme for the considered equation on a graded mesh in time. We derive a priori bounds on the solution of this fully discrete numerical scheme using a new weighted $H^{1}(\Omega)$ norm. We prove that the developed numerical scheme has an accuracy rate of $O(P^{-1}+N^{-(2-\alpha)})$ in $L^{\infty}(0,T;L^{2}(\Omega))$ as well as in $L^{\infty}(0,T;H^{1}_{0}(\Omega))$, where $P$ and $N$ are degrees of freedom in the space and time directions respectively. The robustness and efficiency of the proposed numerical scheme are demonstrated by some numerical examples.

math.NA↗

arXiv2023

Inverse Potentials for all l-channels of Neutron-Proton Scattering using Reference Potential Approach

Reference potential approach (RPA) is successful in obtaining inverse potentials for weakly bound diatomic molecules using Morse function. In this work, our goal is to construct inverse potentials for all available l-channels of np-scattering using RPA. The Riccati-type phase equations for various l-channels are solved using 5th order Runge-Kutta method to obtain scattering phase shifts (SPS) in tandem with an optimization procedure to minimize mean squared error (MSE). Interaction potentials for a total of 18 states have been constructed using only three parameter Morse interaction model. The obtained MSE is < 1% for 1S0 , 3P1 and 3D1 channels and < 2% for 1P1 channel and < 0.1% for rest of the 14 channels. The obtained total scattering cross-sections at various lab energies are found to be matching well with experimental ones. This phase wave analysis study of all channels of np-scattering using RPA has been undertaken using Morse function as zeroth reference, by us, is for the first time.

nucl-th↗

arXiv2023

An algebraic thixotropic elasto-viscoplastic constitutive equation describing pre-yielding solid and post-yielding liquid behaviours

Formulating an appropriate elasto-viscoplastic constitutive equation is challenging, especially for a model describing pre-yielding solid and post-yielding liquid behaviours. Oldroyds 1946 formulation was one of the first models explaining it, however, assumptions of a simple linear elastic and quasi-static deformation before yielding made his model idealistic. At the same time, the quasi-static pre-yielding deformation assumption open-up the possibility for pre-yielding viscous and plastic deformation in the absence of quasi-static conditions. Most early models followed Oldroyds pre-yielding linear elastic assumption. Here, we discuss the structural parameters based thixotropic non-linear elasto-viscoplastic constitutive model valid for reversible and irreversible thixotropic materials. In this work, we have considered non-linear elastic and plastic behaviours before yielding. Despite being a simple algebraic equation, our model explains both the viscosity plateau at low shear rates and the diverging zero shear rate viscosity, using the same parameters but different shear histories. Our model also predicts experimentally observable transient and steady-state shear banding. Furthermore, our model effectively predicts waiting-time-dependent stress overshoot during startup flow, stress hysteresis in shear ramps, sudden stepdown shear rate test results, and viscosity bifurcation phenomena. At the steady state, it reduces to either Bingham, Herschel Bulkley type, or Newtonian fluids model, depending on shear histories. Our model requires only four and five for the irreversible and reversible model, respectively, compared to six or seven parameters required by the existing model. With fewer parameters, our model favourably predicts recent experimental results. The current framework has the potential to provide a possible physical interpretation of the Bingham model.

cond-mat.soft↗

arXiv2023

Synergetic Effect of Wall-Slip and Compressibility During Startup Flow of Complex Fluids

The present letter explains the synergetic effect of wall-slip, compressibility, and thixotropy in a pressurized flow startup operation of various structured fluids. Opposite to the intuition, experimental and numerical simulations suggest that the wall-slip (adhesive failure) is facilitating gel degradation (cohesive failure), revealing a new flow-startup mechanism. The thixotropic rheological model includes structural degradation kinetics at the bulk. Whereas, a static slip-based model addresses the near-wall phenomenon. The near-wall transient variations in axial velocity or strain evolution, and the initial pressure propagation mechanism along the axis of the circular pipe explain the essence of the aforementioned synergy.

physics.flu-dyn↗

arXiv2022

Deuteron Structure and Form Factors: Using Inverse Potentials for S-waves

In this paper, we determine deuteron's static properties, low energy scattering parameters, total cross-section and form factors from inverse S-wave potentials constructed using Morse function. The scattering phase shifts (SPS) at different lab energies are determined using phase function method. The model parameters are optimised using both machine learning algorithm and traditional data analysis by choosing mean squared error as cost function. The mean absolute error between experimental and obtained SPS for states 3S1 and 1S0 are found to be 0.35 and 0.70 respectively. The low energy scattering parameters are matching well with expected values. The contribution due to S-waves SPS towards total cross-section at various energies have been obtained and are matching well with experimental values. The analytical ground state deuteron wave-function (DWF) is obtained by utilizing the experimental value for Quadrupole moment. Other static properties and form factors determined from obtained DWF are found to be in close agreement with experimental ones.

nucl-th↗

arXiv2022

Phase Shift Analysis of Light Nucleon-Nucleus Elastic Scattering using Reference Potential Approach

The neutron and proton scattering with either deuteron or stable alpha particle can be modeled as a two particle system. In this paper, using Morse function as reference potential, inverse potentials have been computationally constructed directly from scattering phase shifts (SPS) data for light nucleon-nucleus systems. The phase equation for various l-channels has been numerically solved using 5th order Runge-Kutta (RK-5) method in each iteration within the optimization procedure to obtain best model parameters of Morse function that minimize mean absolute percentage error (MAPE). The inverse potentials for S-wave of neutron-deuteron and proton-deuteron systems have been obtained with MAPE of 1.95 and 2.05% respectively. Those corresponding to various P and D channels of neutron-alpha(n-alpha) and proton-alpha(p-alpha) systems, have been determined to less than 1.53 and 2.17% respectively. The obtained(experimental) resonance energies for p1/2 and p3/2, from their partial cross-sections plots, respectively are 4.1(4) and 0.93(0.89) for n-alpha and 5.21(5) and 1.96(1.96) for p-alpha system. While total cross-section for n-alpha has been found to be matching with values available in literature, that of p-alpha is seen to be following the correct trend.

nucl-th↗

arXiv2022

Error Estimates for a Linearized Fractional Crank-Nicolson FEM for Kirchhoff type Quasilinear Subdiffusion Equation with Memory

In this paper, we develop a linearized fractional Crank-Nicolson-Galerkin FEM for Kirchhoff type quasilinear time-fractional integro-differential equation $\left(\mathcal{D}^{\alpha}\right)$. In general, the solutions to the time-fractional problems exhibit a weak singularity at time $t=0$. This singular behavior of the solutions is taken into account while deriving the convergence estimates of the developed numerical scheme. We prove that the proposed numerical scheme has an accuracy rate of $O(M^{-1}+N^{-2})$ in $L^{\infty}(0,T;L^{2}(\Omega))$ as well as in $L^{\infty}(0,T;H^{1}_{0}(\Omega))$, where $M$ and $N$ are the degrees of freedom in the space and time directions respectively. A numerical experiment is presented to verify the theoretical results.

math.NA↗

arXiv2021

Finite Element Analysis of Time Fractional Integro-differential Equations of Kirchhoff type for Non-homogeneous Materials

In this paper, we study a time-fractional initial-boundary value problem of Kirchhoff type involving memory term for non-homogeneous materials. The energy argument is applied to derive the a priori bounds on the solution of the considered problem. Consequently, we prove the existence and uniqueness of the weak solution to the problem under consideration. We keep the time variable continuous and discretize the space domain using a conforming FEM to obtain the semi discrete formulation of the problem. The semi discrete error analysis is carried out by modifying the standard Ritz-Volterra projection operator. To obtain the numerical solution to the problem efficiently, we develop a new linearized L1 Galerkin FEM. This numerical scheme is shown to have a convergence rate of $O(h+k^{2-\alpha})$, where $\alpha~ (0<\alpha<1)$ is the fractional derivative exponent, $h$ and $k$ are the discretization parameters in the space and time directions respectively. Further, this convergence rate is improved in the time direction by proposing a novel linearized L2-1$_{\sigma}$ Galerkin FEM. We prove that this numerical scheme has an accuracy rate of $O(h+k^{2})$. Finally, a numerical experiment is conducted to validate our theoretical claims.

math.NA↗

arXiv2021

Neutron-Proton Interaction Modeled using Morse Function: Constructing Inverse Potentials Using Variational Monte-Carlo and Phase Function Method

Understanding neutron-proton(np) interaction has been one of the most studied problems. One way to construct model interaction has been using inversion potentials obtained from experimental scattering phase shifts(SPS). Here, we show that, inverse potentials corresponding to SPS for various l-channels of np interaction can be obtained using variational Monte-Carlo(VMC) technique in tandem with phase function method(PFM) by modeling np-interaction as a Morse function. The S-channel SPS for 3S1 and 1S0 have been obtained, with a mean percentage error with respect to experimental multiple energy analysis data for lab energies up to 1050 MeV, to less than 5%. Similarly, inverse potential for 1S0 pp interaction, with Coulomb term modeled as proportional to erf(), has also been obtained to match experimental values to less than 4%. Non-local and spin-orbit terms are included to obtain inverse potentials for P and D channels and results match with available data to a good extent.

nucl-th↗

arXiv2021

Effect of Serum Starvation on Rheology of Cell Monolayers

The rheological properties of cells and tissues are central to embryonic development and homoeostasis in adult tissues and organs and are closely related to their physiological activities. In this work, we present our study of rheological experiments on cell monolayer under serum starvation compared to that of healthy cell monolayer with full serum. The normal functioning of cells depends on the micronutrient supply provided by the serum in the growth media. Serum starvation is one of the most widely used procedures in cell biology. Serum deficiency may lead to genomic instability, variation in protein expression, chronic diseases, and some specific types of cancers. However, the effect of deprivation of serum concentration on the material properties of cells is still unknown. Therefore, we performed the macro-rheology experiments to investigate the effect of serum starvation on a fully confluent Madin Darby Canine Kidney (MDCK) cell monolayer. The material properties such as storage modulus (G') and loss modulus (G''), of the monolayer, were measured using oscillatory shear experiments under serum-free (0% FBS) and full serum (10% FBS) conditions. Additionally, the step strain experiments were performed to gain more insights into the viscoelastic properties of the cell monolayer. Our results indicate that without serum, the loss and storage moduli decrease and do not recover fully even after small deformation. This is because of the lack of nutrients, which may result in many permanent physiological changes. Whereas, the healthy cell monolayer under full serum condition, remains strong & flexible, and can fully recover even from a large deformation at higher strain.

physics.bio-ph↗

arXiv2017

Using the SLEUTH urban growth model to simulate the impacts of future policy scenarios on urban land use in the Tehran metropolitan area in Iran

The SLEUTH model, based on the Cellular Automata (CA), can be applied to city development simulation in metropolitan areas. In this study the SLEUTH model was used to model the urban expansion and predict the future possible behavior of the urban growth in Tehran. The fundamental data were five Landsat TM and ETM images of 1988, 1992, 1998, 2001 and 2010. Three scenarios were designed to simulate the spatial pattern. The first scenario assumed historical urbanization mode would persist and the only limitations for development were height and slope. The second one was a compact scenario which makes the growth mostly internal and limited the expansion of suburban areas. The last scenario proposed a polycentric urban structure which let the little patches grow without any limitation and would not consider the areas beyond the specific buffer zone from the larger patches for development. Results showed that the urban growth rate was greater in the first scenario in comparison with the other two scenarios. Also it was shown that the third scenario was more suitable for Tehran since it could avoid undesirable effects such as congestion and pollution and was more in accordance with the conditions of Tehran city.

cs.CV↗