arXiv subjects

Priyanka D. Bhoyar

Publications and source records attributed to Priyanka D. Bhoyar.

8 recordsLinked to original sources

arXiv2026

Universal Boolean Computation in Negatively Coupled Circle Map Lattices

We investigate the computational capabilities of a one-dimensional lattice of negatively coupled circle maps in its traveling wave regime. We interpret propagating waves as information carriers and exploit their interactions to implement Boolean logic. The logical states are encoded by the propagation direction of the traveling waves, while the presence or absence of a wave at a designated output location represents the logical output. Using controlled wave collisions, we demonstrate the realization of NAND and NOR gates along with other basic gates. Since NAND and NOR operations are functionally complete, the results establish that the traveling wave regime of the negatively coupled circle-map lattice supports universal Boolean computation in principle. The demonstrated logical operations remain valid over a finite range of the coupling strength εand map parameter ω, indicating robustness of the computational scheme to parameter variations. Our results therefore demonstrate that computational functionality can emerge from the collective nonlinear dynamics of a coupled map lattice, providing a con- nection between the dynamical properties of traveling wave states and collision based information processing.

cond-mat.stat-mech↗

arXiv2026

Gap distributions between successive personal bests in cricket: Data and Models

Successive personal best performances provide a natural measure of progression in an athlete's career. Classical record theory predicts a universal gap distribution, $P(g)\sim 1/g$, for independent and identically distributed (i.i.d.) sequences. However, sporting careers are shaped by learning, aging, changes in ability, and external influences that violate these assumptions. We investigate the statistics of inter-record gaps, defined as the number of innings between successive personal best scores, in cricket. Using career records of leading Test, ODI, and T20 players obtained from ESPN Cricinfo. We find that the empirical distributions are well described by truncated power law $P(g) \propto g^{-α} e^{-λg}$ with exponents in the range (0.799 $\leq α\leq$ 0.843). Much of this deviation disappears when the temporal ordering of innings is destroyed, indicating that career evolution plays a key role in shaping record occurrence. Bootstrap-shuffled careers, which preserve individual score distributions and career lengths while removing temporal ordering, yield significantly larger exponents ($α\approx 0.939\text{--}0.979$). These findings show that the progression of personal best performances retains information about the temporal organization of a player's career and cannot be fully explained by simple stochastic record processes. More generally, they illustrate how record statistics are altered in nonstationary and path-dependent systems.

cond-mat.stat-mech↗

arXiv2026

Deterministic cascade coarsening in a Bistable Gene Toggle model

We investigate deterministic coarsening dynamics in a spatially extended bistable gene toggle model with diffusive coupling. Unlike classical curvature-driven coarsening, where domain walls move continuously and annihilate gradually, the present system exhibits a qualitatively different mechanism. The domain walls remain pinned for long intervals and disappear abruptly through collective cascade events. The density of domain walls decays approximately as $ρ(t)\sim t^{-δ}$, but the coarsening exhibits clear log-periodic oscillations superimposed on the power-law behavior. For all values of the promoter strength $α$ considered, the measured exponent satisfies $δ<0.5$, indicating a systematic deviation from the classical Allen--Cahn prediction $δ=1/2$ for curvature-driven coarsening. We show that log-periodic oscillations are not controlled by the density of domain walls, but by the \emph{domains that disappear} in each cascade. The average size of disappearing domains grows roughly linearly with cascade index, producing a constant geometric spacing of cascade times, consistent with discrete scale invariance.

cond-mat.stat-mech↗

arXiv2026

Zigzag ordering, defects, and anomalous relaxation in antiferromagnetic Kuramoto lattices

We investigate the nonequilibrium ordering dynamics of coupled Kuramoto oscillators with negative nearest-neighbor coupling, which induces a zigzag antiferromagnetic ordering. In one dimension, the defect density exhibits anomalously slow coarsening, decaying as $(D(t)\sim t^{-1/4})$ before saturating at a system-size-dependent time $(t_c(N)\sim N^z)$ with (z=2). The local persistence probability follows a stretched-exponential form, $(P(t)\sim \exp(-c t^α))$, with $(α=1/4)$. These exponents are observed are independent of the magnitude of the coupling, which merely rescales the characteristic time scale. The equality $(α=δ=1/4)$ together with (z=2) is consistent with a distinct universality class. These results demonstrate that deterministic nonlinear dynamics and geometric frustration alone are sufficient to generate slow relaxation and anomalous scaling, without quenched disorder or stochastic noise. A continuum approximation and the corresponding coarse-grained partial differential equation provide a theoretical explanation for the observed anomalous exponents, while linear stability analysis accounts for the emergence of the zigzag ordered state. In two dimensions, geometric frustration inhibits complete ordering and gives rise to long-lived metastable domain-wall structures. An initial transient defect decay is observed before crossover and saturation. These results demonstrate how frustration and continuous phase variables can fundamentally modify coarsening dynamics and generate anomalously slow relaxation in deterministic many-body systems.

cond-mat.stat-mech↗

arXiv2025

Emergence of continuously varying critical exponents in coupled map lattice as an effect of quenched disorder

The transition to an absorbing phase in a spatiotemporal system is a well-investigated nonequilibrium dynamic transition. The absorbing phase transitions fall into a few universality classes, defined by the critical exponents observed at the critical point. We present a coupled map lattice (CML) model with quenched disorder in the couplings. In this model, spatial disorders are introduced in the form of asymmetric coupling with a larger coupling ($p$) to a neighbor on the right and a smaller coupling ($1-p$) to the neighbor on the left, for $0 \le p \le0.5$. For $p=0$, the system belongs to the directed percolation universality class. For $p>0$, we observe continuously changing critical exponents at the critical point. The order parameter is the fraction of turbulent sites $m(t)$. %sites that are not in the laminar region. We observe a power-law decay, $m(t) \sim t^{-δ}$, at the critical point $ε_c$, where $ε$ is the diffusive coupling parameter. These exponents change continuously and do not match any known universality class in any limit. This could be related to changes in the eigenvalue spectrum of the connectivity matrix as the disorder is introduced.

cond-mat.stat-mech↗

arXiv2023

Synchronization transition in space-time chaos in the presence of quenched disorder

Synchronization of two replicas of coupled map lattices for continuous maps is known to be in the multiplicative noise universality class. We study this transition in the presence of quenched disorder in coupling. The disorder is identical in both replicas. We study one-dimensional, two-dimensional, and globally coupled logistic and tent maps. We observe a clear second-order transition with new exponents. The order parameter decays as $t^{-δ}$ and $δ$ depends on the map and its parameters. The asymptotic order parameter for $Δ$ distance from a critical point grows as $Δ^β$ with $β=δ$. The quenched disorder in coupling is a relevant perturbation for the replica synchronization of coupled map lattices. The critical exponents are different from those of the multiplicative noise universality class. However, it does not depend on dimensionality if the transition is continuous for the cases studied.

cond-mat.stat-mech↗

arXiv2021

The emergence of Logarithmic-periodic oscillations in Contact process with the topological disorder

We present a model of contact process on Domany-Kinzel cellular automata with a geometrical disorder. In the 1-D model, each site is connected to two nearest neighbors which are either on the left or the right. The system is always attracted to an absorbing state with algebraic decay of average density with a continuously varying complex exponent. The log-periodic oscillations are imposed over and above the usual power law and are clearly evident as p --> 1. This effect is purely due to an underlying topology because all sites have the same infection probability p and there is no disorder in the infection rate. An extension of this model to two and three dimensions leads to similar results. We also study a model with fixed immunization rate p0 in one and two dimensions. If p0 > ps, where ps is percolation threshold, the system always tends to an absorbing state. As infection rate p --> 1, we observe a power law decay of order parameter with complex exponent. This may be a common feature in systems where quenched disorder leads to effective fragmentation of the lattice.

cond-mat.stat-mech↗

arXiv2020

Dynamic Phase Transition in the Contact Process with Spatial Disorder: Griffths Phase and Complex Persistence Exponents

We present a model which displays Griffiths phase i.e. algebraic decay of density with continuously varying exponent in the absorbing phase. In active phase, the memory of initial conditions is lost with continuously varying complex exponent in this model. This is 1-D model where fraction r of sites obey rules leading to directed percolation (DP) class and the rest evolve according to rules leading to compact directed percolation (CDP) class. For infection probability $p < p_c$, the fraction of active sites $ρ(t) = 0$ asymptotically. For $p > p_c$, $ρ(infty) > 0$. At $p = p_c$, $ρ(t)$, the survival probability from single seed and the average number of active sites starting from single seed decay logarithmically. The local persistence $P_l(\infty) > 0$ for $p < p_c$ and $P_l(\infty) = 0$ for $p > p_c$. For $p > p_s$, local persistence $P_l(t)$ decays as a power law with continuously varying exponents. The persistence exponent is clearly complex as $p\rightarrow 1$. The complex exponent implies logarithmic periodic oscillations in persistence. The wavelength and the amplitude of the logarithmic periodic oscillations increases with p. We note that underlying lattice or disorder does not have self-similar structure.

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