arXiv subjects

Vinayak

Publications and source records attributed to Vinayak.

15 recordsLinked to original sources

arXiv2026

Finite strain homogenization of periodic rod networks with application to semi-flexible biopolymers

In this work, we adopt a finite strain computational homogenization approach to characterize the response of semi-flexible biopolymer networks modeled as idealized 8- and 14-chain periodic networks. We use the geometrically exact special Cosserat rod theory to model the microscale fibers forming these 8- and 14-chain networks. This allows us to capture arbitrarily large microscale deformations. Both macroscopic strain- and stress-driven homogenization are performed to study the macroscopic uniaxial tension, compression and simple shear responses. Several phenomena unique to biopolymer networks are recovered such as strain-stiffening and volume shrinkage under uniaxial tension, softening under compression and reverse Poynting effect under simple shear. We find that nonlinearity and non-affine deformation at microscale, especially bending and buckling of microscale fibers, plays an important role in these phenomena. We obtain the postbuckled solutions of the homogenization problem using a nonlinear, imperfection-free path following approach and also check for their stability. We further compare our homogenization results with experimental data for uniaxial tension and compression of biofilament networks and find good agreement. When the fibers are replaced by helical rods in the 8-chain unit cell, we are also able to capture the enlarged stretching behaviour as shown in recently fabricated compliant metastructures.

cond-mat.soft↗

arXiv2026

Homogenization of one-dimensional periodic rod networks as special Cosserat rods

One-dimensional periodic rod networks are the structures that are obtained by periodically assembling its microstructural unit, a network of rods itself, in just one direction. In this work, we present a scheme for obtaining the nonlinear constitutive response of such structures when homogenized macroscopically as a continuum rod. To accurately capture arbitrary and large deformations, the geometrically exact special Cosserat rod theory is used for modeling the rod at both micro- and macroscales. By assuming the periodic structure to be strained uniformly, at macroscale, along its arc length, the full structure problem is reduced to just that of its microstructural unit but subjected to helically periodic boundary condition. The microscale problem, consisting of a network of rods and formulated in a variational setting, is solved in the presence of rod-joint constraints and helically periodic boundary conditions. The expressions for the macroscale rod's stress resultants, i.e. internal contact force and moment, and stiffnesses are then obtained. Finally, several numerical examples having different microstructural units are presented to demonstrate our method. First, the results corresponding to simpler square and cross microstructural units are presented and validated with the existing literature. Square microstructural units having helical constituent rods are then taken up which have application as artificial muscle fiber material. Eventually, homogenization of auxetic tubular metamaterials is performed. It is shown how various design parameters of these microstructural units can be tuned to obtain the desired macroscopic response.

cond-mat.mtrl-sci↗

arXiv2026

A Polynomial Coreset for Furthest Neighbor in Planar Metrics

A furthest neighbor data structure on a metric space $(V,\mathrm{dist})$ and a set $P \subseteq V$ answers the following query: given $v \in V$, output $p \in P$ maximizing $\mathrm{dist}(v,p)$; in the approximate version, it is allowed to report any $p \in P$ with $\mathrm{dist}(v,p) \geq (1-\varepsilon)\max_{p' \in P} \mathrm{dist}(v,p')$ for an accuracy parameter $\varepsilon \in (0,1)$. A particular type of approximate furthest neighbor data structure is an $\varepsilon$-coreset: a small subset $Q \subseteq P$ such that for every query $v \in V$ there is a feasible answer $p \in Q$. Our main result is that in planar metrics there always exists an $\varepsilon$-coreset for furthest neighbors of size bounded polynomially in $(1/\varepsilon)$. This improves upon an exponential bound of Bourneuf and Pilipczuk [SODA'25] and resolves an open problem of de Berg and Theocharous [SoCG'24] for the case of polygons with holes. On the technical side, we develop a connection between $\varepsilon$-coreset for furthest neighbors and an invariant of a metric space that we call an $\varepsilon$-comatching index -- a sibling of $\varepsilon$-(semi-)ladder index, a.k.a, $\varepsilon$-scatter dimension, as defined by Abbasi et al [FOCS'23]. While the $\varepsilon$-(semi-)ladder index of planar metrics admits an exponential lower bound, we show that the $\varepsilon$-comatching index of planar metrics is polynomial, all in $1/\varepsilon$. The exponential separation between $\varepsilon$-(semi-)ladder and $\varepsilon$-comatching is rather surprising, and the proof is the main technical contribution of our work.

cs.CG↗

arXiv2025

Optimal Bounds for Spanners and Tree Covers in Doubling Metrics

It is known that any $n$-point set in the $d$-dimensional Euclidean space $\mathbb{R}^d$, for $d = O(1)$, admits: 1) a $(1+\epsilon)$-spanner with maximum degree $\tilde{O}(\epsilon^{-d+1})$ and with lightness $\tilde{O}(\epsilon^{-d})$; 2) a $(1+\epsilon)$-tree cover with $\tilde{O}(n \cdot \epsilon^{-d+1})$ trees and maximum degree of $O(1)$ in each tree. Moreover, all the parameters in these constructions are optimal: there exists an $n$-point set in $\mathbb{R}^d$, for which any $(1+\epsilon)$-spanner has $\tilde{\Omega}(n \cdot \epsilon^{-d+1})$ edges and lightness $\tilde{\Omega}(\epsilon^{-d})$. The upper bounds for Euclidean spanners rely heavily on the spatial property of cone partitioning in $\mathbb{R}^d$, which does not seem to extend to the wider family of doubling metrics, i.e., metric spaces of constant doubling dimension. In doubling metrics, a simple spanner construction from two decades ago, the net-tree spanner, has $\tilde{O}(n \cdot \epsilon^{-d})$ edges, and it could be transformed into a spanner of maximum degree $\tilde{O}(\epsilon^{-d})$ and lightness $\tilde{O}(n \cdot \epsilon^{-(d+1)})$ by pruning redundant edges. Moreover, a careful refinement of the net-tree spanner yields a $(1+\epsilon)$-tree cover with $\tilde{O}(\epsilon^{-d})$ trees. Despite a large body of work, the problem of obtaining tight bounds for spanners and tree covers in the wider family of doubling metrics has remained elusive. We resolve this problem by presenting: 1) a surprisingly simple and tight lower bound, which shows that the net-tree spanner and its pruned version are optimal with respect to all the involved parameters, 2) a new construction of $(1+\epsilon)$-tree covers with $\tilde{O}(n \cdot \epsilon^{-d})$ trees, with maximum degree $O(1)$ in each tree. This construction is optimal with respect to the number of trees and maximum degree.

cs.CG↗

arXiv2025

Breakthrough Asymmetries across Disciplines and Countries: A Network approach to Structural Complexity of Scientific Progress

Science is driven by community endeavors across diverse fields and specializations, forming a complex structure that renders conventional performance evaluation methods inadequate. Using established indicators, the network-based normalized citation score, and the disruptive index, combined with the GENEPY algorithm, we evaluate the complexity rank of countries based on their breakthrough performance across 89 subfields of physical sciences, drawing on nearly 60 million articles (1900-2023). This quality-focused integrated approach reveals pronounced asymmetries: while countries such as the United States, Israel, and several in Europe sustain long-term structural advantages, emerging nations show rapid gains in later decades. A power-law relationship between aggregated breakthrough performance and countries' R&D expenditure underscores the unequal and scale-dependent nature of global science. These results demonstrate that scientific advancement arises not from uniform growth but from asymmetric complexity, offering actionable insights for policymakers and funding agencies aiming to foster sustainable, high-quality research ecosystems.

cs.DL↗

arXiv2020

Predicting the DNA Conductance using Deep Feed Forward Neural Network Model

Double-stranded DNA (dsDNA) has been established as an efficient medium for charge migration, bringing it to the forefront of the field of molecular electronics as well as biological research. The charge migration rate is controlled by the electronic couplings between the two nucleobases of DNA/RNA. These electronic couplings strongly depend on the intermolecular geometry and orientation. Estimating these electronic couplings for all the possible relative geometries of molecules using the computationally demanding first-principles calculations requires a lot of time as well as computation resources. In this article, we present a Machine Learning (ML) based model to calculate the electronic coupling between any two bases of dsDNA/dsRNA of any length and sequence and bypass the computationally expensive first-principles calculations. Using the Coulomb matrix representation which encodes the atomic identities and coordinates of the DNA base pairs to prepare the input dataset, we train a feedforward neural network model. Our NN model can predict the electronic couplings between dsDNA base pairs with any structural orientation with a MAE of less than 0.014 eV. We further use the NN predicted electronic coupling values to compute the dsDNA/dsRNA conductance.

cond-mat.soft↗

arXiv2016

Parametric Number Covariance in Quantum Chaotic Spectra

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the co- variance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal non-invariant cases. A local version of the parametric number variance introduced earlier is also investigated.

quant-ph↗

arXiv2014

Spectral density of the non-central correlated Wishart ensembles

Wishart ensembles of random matrix theory have been useful in modeling positive definite matrices encountered in classical and quantum chaotic systems. We consider nonzero means for the entries of the constituting matrix A which defines the correlated Wishart matrix as W = AA{\dag}, and refer to the ensemble of such Wishart matrices as the non-central correlated Wishart ensemble (nc-CWE). We derive the Pastur self-consistent equation which describes the spectral density of nc-CWE at large matrix dimension.

math-ph↗

arXiv2014

Spectral Domain of Large Nonsymmetric Correlated Wishart Matrices

We study {the} complex eigenvalues of the Wishart model defined for nonsymmetric correlation matrices. The model is defined for two statistically equivalent but different Gaussian real matrices, as $\mathsf{C}=\mathsf{AB}^{t}/T$, where $\mathsf{B}^{t}$ is the transpose of $\mathsf{B}$ and both matrices $\mathsf{A}$ and $\mathsf{B}$ are of dimension $N\times T$. We consider {\it actual} correlations between the matrices so that on the ensemble average $\mathsf{C}$ does not vanish. We derive a loop equation for the spectral density of $\mathsf{C}$ in {the} large $N$ and $T$ limit where the ratio $N/T$ is finite. The actual correlations changes the complex eigenvalues of $\mathsf{C}$, and hence their domain from the results known for the vanishing $\mathsf{C}$ or for the uncorrelated $\mathsf{A}$ and $\mathsf{B}$. Using the loop equation we derive {a} result for the contour describing the domain of {the} bulk of the eigenvalues of $\mathsf{C}$. If the nonvanishing-correlation matrix is diagonal with the same element $c\ne0$, the contour is no longer a circle centered at origin but a shifted ellipse. In this case, the loop equation is analytically solvable and we explicitly derive {a} result for the spectral density. For more general cases, our analytical result implies that the contour depends on its symmetric and anti-symmetric parts if the nonvanishing-correlation matrix is nonsymmetric. On the other hand, if it is symmetric then the contour depends only on the spectrum of the correlation matrix. We also provide numerics to justify our analytics.

math-ph↗

arXiv2014

Spectral analysis of finite-time correlation matrices near equilibrium phase transitions

We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be derived from the spatial correlations. In practice time series are short in the sense that they are either not stationary over long time intervals or not available over long time intervals. Also we usually do not have time series for all variables available. We shall make numerical simulations on a two-dimensional Ising model with the usual Metropolis algorithm as time evolution. Using all spins on a grid with periodic boundary conditions we find a power law, that is, for large grids, compatible with the analytic result. We still find a power law even if we choose a fairly small subset of grid points at random. The exponents of the power laws will be smaller under such circumstances. For very short time series leading to singular correlation matrices we use a recently developed technique to lift the degeneracy at zero in the spectrum and find a significant signature of critical behavior even in this case as compared to high temperature results which tend to those of random matrix models.

math-ph↗

arXiv2013

Time series, correlation matrices and random matrix models

In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null hypothesis or a minimum information hypothesis for the description of a quantum system or subsystem. In the former case various forms of correlation matrices of time series associated with the classical observables of some system. The fact that such series are necessarily finite, inevitably introduces noise and this finite time influence lead to a random or stochastic component in these time series. By consequence random correlation matrices have a random component, and corresponding ensembles are used. In the latter we use random matrices to describe high temperature environment or uncontrolled perturbations, ensembles of differing chaotic systems etc.

math-ph↗

arXiv2013

Emerging spectra of singular correlation matrices under small power-map deformations

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used this implies an analysis of highly singular correlation matrices. We attack this problem by using the so called {\it power map} which was introduced to reduce noise. Its non-linearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

math-ph↗

arXiv2013

Spectral density of a Wishart model for nonsymmetric Correlation Matrices

The Wishart model for real symmetric correlation matrices is defined as $\mathsf{W}=\mathsf{AA}^{t}$, where matrix $\mathsf{A}$ is usually a rectangular Gaussian random matrix and $\mathsf{A}^{t}$ is the transpose of $\mathsf{A}$. Analogously, for nonsymmetric correlation matrices, a model may be defined for two statistically equivalent but different matrices $\mathsf{A}$ and $\mathsf{B}$ as $\mathsf{AB}^{t}$. The corresponding Wishart model, thus, is defined as $\mathbf{C}=\mathsf{AB}^{t}\mathsf{BA}^{t}$. We study the spectral density of $\mathbf{C}$ for the case when $\mathsf{A}$ and $\mathsf{B}$ are not statistically independent. The ensemble average of such nonsymmetric matrices, therefore, does not simply vanishes to a null matrix. In this paper we derive a Pastur self-consistent equation which describes spectral density of large $\mathbf{C}$. We complement our analytic results with numerics.

math-ph↗

arXiv2012

Statistics of Resonances in a One-Dimensional Chain: a Weak Disorder Limit

We study statistics of resonances in a one-dimensional disordered chain coupled to an outer world simulated by a perfect lead. We consider a limiting case for weak disorder and derive some results which are new in these studies. The main focus of the present study is to describe statistics of the scattered complex energies. We derive compact analytic statistical results for long chains. A comparison of these results has been found to be in good agreement with numerical simulations.

cond-mat.dis-nn↗

arXiv2012

Subsystem dynamics under random Hamiltonian evolution

We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and fluctuations. We show that the reduced density matrix can be described in terms of a noncentral correlated Wishart ensemble for which we are able to perform analytical calculations of the eigenvalue density. Our description accounts for a transition from an arbitrary initial state towards a random state at large times, enabling us to determine the convergence time after which random states are reached. We identify and describe a number of other interesting features, like a series of collisions between the largest eigenvalue and the bulk, accompanied by a phase transition in its distribution function.

quant-ph↗