arXiv subjects

Md. Kamrul Hassan

Publications and source records attributed to Md. Kamrul Hassan.

11 recordsLinked to original sources

arXiv2026

Topological Electronic States and Phonon Mediated Superconductivity in Ru Based Ternary Pnictides: ZrRuAs and HfRuP

This study investigates the structural, electronic, mechanical, optical, thermodynamic, and superconducting properties of ZrRuAs and HfRuP. Electronic band structure calculations reveal topological semimetallic behavior in both compounds with several bands crossing the Fermi level. The inclusion of spin orbit coupling lifts band degeneracies in both compounds. The Fermi surface shows both electron and hole segments. The estimated Pugh ratio, Poisson ratio and machinability index indicate that both compounds are ductile in nature and exhibit excellent machinability. Optical results show metallic reflectivity and notable absorption in the ultraviolet region. Thermodynamic analysis indicates stable behavior. The estimated superconducting transition temperatures are 9.75 K for ZrRuAs and 9.03 K for HfRuP that indicates strong coupling conventional superconductivity. The results provide a detailed view of the physical and superconducting properties of ZrRuAs and HfRuP and help to close the existing research gaps in these topological superconducting materials.

cond-mat.mtrl-sci↗

arXiv2026

Percolation on multifractal, scale-free weighted planar stochastic porous lattice

We introduce the Weighted Planar Stochastic Porous Lattice (WPSPL), a geometrically disordered substrate generated by iteratively subdividing a unit square. At each step a block is selected with probability proportional to its area, divided into four parts, and one sub-block is retained (removed) with probability $q$ ($1-q$). We show analytically that the WPSPL exhibits multifractality for each of its infinitely many nontrivial conserved quantities and demonstrate numerically that its snapshots at different times are statistically self-similar. The dual of the lattice forms a complex network with a power-law degree distribution. Motivated by these properties of this porous lattice, we study bond percolation on the WPSPL, determine the percolation threshold, and estimate the critical exponents $α$, $β$, and $γ$ associated with the specific heat, order parameter, and susceptibility, respectively. The exponents vary continuously with $q$, reflecting a family of distinct universality classes as the global dimension of the lattice depends on $q$. Remarkably, the Rushbrooke inequality, $α+ 2β+ γ\ge 2$, is satisfied in near equality. Notably, the nonporous case ($q=1$) has a global dimension $2$ but lies outside the universality class of conventional two-dimensional lattices. Our results highlight how geometric disorder, multifractality, scale-free coordination number disorder, and porosity produce unconventional critical behavior.

cond-mat.stat-mech↗

arXiv2024

Complexity measure of extreme events

Complexity is an important metric for appropriate characterization of different classes of irregular signals, observed in the laboratory or in nature. The literature is already rich in the description of such measures using a variety of entropy and disequilibrium measures, separately or in combination. Chaotic signal was given prime importance in such studies while no such measure was proposed so far, how complex were the extreme events when compared to non-extreme chaos. We address here this question of complexity in extreme events and investigate if we can distinguish them from non-extreme chaotic signal. The normalized Shannon entropy in combination with disequlibrium is used for our study and it is able to distinguish between extreme chaos and non-extreme chaos and moreover, it depicts the transition points from periodic to extremes via Pomeau-Manneville intermittency and, from small amplitude to large amplitude chaos and its transition to extremes via interior crisis. We report a general trend of complexity against a system parameter that increases during a transition to extreme events, reaches a maximum, and then starts decreasing. We employ three models, a nonautonomous Lienard system, 2-dimensional Ikeda map and a 6-dimensional coupled Hindmarh-Rose system to validate our proposition.

nlin.CD↗

arXiv2022

Dynamic scaling and stochastic fractal in nucleation and growth processes

A class of nucleation and growth models of a stable phase (S-phase) is investigated for various different growth velocities. It is shown that for growth velocities $v\sim s(t)/t$ and $v\sim x/τ(x)$, where $s(t)$ and $τ$ are the mean domain size of the metastable phase (M-phase) and the mean nucleation time respectively, the M-phase decays following a power law. Furthermore, snapshots at different time $t$ are taken to collect data for the distribution function $c(x,t)$ of the domain size $x$ of M-phase are found to obey dynamic scaling. Using the idea of data-collapse we show that each snapshot is a self-similar fractal. However, for $v={\rm const.}$ like in the classical Kolmogorov-Johnson-Mehl-Avrami (KJMA) model and for $v\sim 1/t$ the decay of the M-phase are exponential and they are not accompanied by dynamic scaling. We find a perfect agreement between numerical simulation and analytical results.

cond-mat.stat-mech↗

arXiv2022

Recent development on fragmentation, aggregation and percolation

In this article, I have outlined how an accomplished researcher like Robert Ziff has influenced a new generation of researchers across the globe like gravity as an action-at-a-distance. In the 80s Ziff made significant contributions to the kinetics of fragmentation followed by the kinetics of aggregation. Here, I will discuss fractal and multifractal that emerges in fragmentation and aggregation processes where the dynamics is governed by non-trivial conservation laws. I have then discussed my recent works and results on percolation where I made extensive use of Newman-Ziff fast Monte Carlo algorithm. To this end, I have defined entropy which paved the way to define specific heat and show that the critical exponents of percolation obey Rushbrooke inequality. Besides, we discuss how entropy and order parameter together can help us to check whether the percolation is accompanied by order-disorder transition or not. The idea of entropy also help to explain why encouraging smaller cluster to grow faster than larger clusters makes the transition explosive.

cond-mat.stat-mech↗

arXiv2022

Multi-multifractality and dynamic scaling in stochastic porous lattice

In this article, we extend the idea of stochastic dyadic Cantor set to weighted planar stochastic lattice that leads to a stochastic porous lattice. The process starts with an initiator which we choose to be a square of unit area for convenience. We then define a generator that divides the initiator or one of the blocks, picked preferentially with respect to their areas, to divide it either horizontally or vertically into two rectangles of which one of them is removed with probability $q=1-p$. We find that the remaining number of blocks and their mass varies with time as $t^{p}$ and $t^{-q}$ respectively. Analytical solution shows that the dynamics of this process is governed by infinitely many hidden conserved quantities each of which is a multifractal measure with porous structure as it contains missing blocks of various different sizes. The support where these measures are distributed is fractal with fractal dimension $2p$ provided $0<p<1$. We find that if the remaining blocks are characterized by their respective area then the corresponding block size distribution function obeys dynamic scaling.

cond-mat.stat-mech↗

arXiv2021

A weighted planar stochastic lattice with scale-free, small-world and multifractal properties

We investigate a class of weighted planar stochastic lattice (WPSL1) created by random sequential nucleation of seed from which a crack is grown parallel to one of the sides of the chosen block and ceases to grow upon hitting another crack. It results in the partitioning of the square into contiguous and non-overlapping blocks. Interestingly, we find that the dynamics of WPSL1 is governed by infinitely many conservation laws and each of the conserved quantities, except the trivial conservation of total mass or area, is a multifractal measure. On the other hand, the dual of the lattice is a scale-free network as its degree distribution exhibits a power-law $P(k)\sim k^{-γ}$ with $γ=4.13$. The network is also a small-world network as we find that (i) the total clustering coefficient $C$ is high and independent of the network size and (ii) the mean geodesic path length grows logarithmically with $N$. Besides, the clustering coefficient $C_k$ of the nodes which have degree $k$ decreases exactly as $2/(k-1)$ revealing that it is also a nested hierarchical network.

cond-mat.stat-mech↗

arXiv2020

Stochastic Fractal and Noether's Theorem

We consider the binary fragmentation problem in which, at any breakup event, one of the daughter segments either survives with probability $p$ or disappears with probability $1\!-\!p$. It describes a stochastic dyadic Cantor set that evolves in time, and eventually becomes a fractal. We investigate this phenomenon, through analytical methods and Monte Carlo simulation, for a generic class of models, where segment breakup points follow a symmetric beta distribution with shape parameter $α$, which also determines the fragmentation rate. For a fractal dimension $d_f$, we find that the $d_f$-th moment $M_{d_f}$ is a conserved quantity, independent of $p$ and $α$. We use the idea of data collapse -- a consequence of dynamical scaling symmetry -- to demonstrate that the system exhibits self-similarity. In an attempt to connect the symmetry with the conserved quantity, we reinterpret the fragmentation equation as the continuity equation of a Euclidean quantum-mechanical system. Surprisingly, the Noether charge corresponding to dynamical scaling is trivial, while $M_{d_f}$ relates to a purely mathematical symmetry: quantum-mechanical phase rotation in Euclidean time.

cond-mat.stat-mech↗

arXiv2020

Similarity and self-similarity in random walk with fixed, random and shrinking steps

In this article, we first give a comprehensive description of random walk (RW) problem focusing on self-similarity, dynamic scaling and its connection to diffusion phenomena. One of the main goals of our work is to check how robust the RW problem is under various different choices of the step size. We show that RW with random step size or uniformly shrinking step size is exactly the same as for RW with fixed step size. Krapivsky and Redner in 2004 showed that RW with geometric shrinking step size, such that the size of the $n$th step is given by $S_n=λ^n$ with a fixed $λ<1$ value, exhibits some interesting features which are different from the RW with fixed step size. Motivated by this, we investigate what if $λ$ is not a fixed number rather it depends on the step number $n$? To this end, we first generate $N$ random numbers for RW of $t=N$ which are then arranged in a descending order so that the size of the $n$th step is $λ_n^n$. We have shown, both numerically and analytically, that $λ_n=(1-n/N)$, the root mean square displacement increases as $t^{1/4}$ which are different from all the known results on RW problems.

cond-mat.stat-mech↗

arXiv2018

Dynamic Scaling, Data-collapse and Self-Similarity in Mediation-Driven Attachment Networks

Recently, we have shown that if the $i$th node of the Barabási-Albert (BA) network is characterized by the generalized degree $q_i(t)=k_i(t)t_i^β/m$, where $k_i(t)\sim t^β$ and $m$ are its degree at current time $t$ and at birth time $t_i$, then the corresponding distribution function $F(q,t)$ exhibits dynamic scaling. Applying the same idea to our recently proposed mediation-driven attachment (MDA) network, we find that it too exhibits dynamic scaling but, unlike the BA model, the exponent $β$ of the MDA model assumes a spectrum of value $1/2\leq β\leq 1$. Moreover, we find that the scaling curves for small $m$ are significantly different from those of the larger $m$ and the same is true for the BA networks albeit in a lesser extent. We use the idea of the distribution of inverse harmonic mean (IHM) of the neighbours of each node and show that the number of data points that follow the power-law degree distribution increases as the skewness of the IHM distribution decreases. Finally, we show that both MDA and BA models become almost identical for large $m$.

physics.soc-ph↗

arXiv2014

Growing Scale-free Networks by a Mediation-Driven Attachment Rule

We propose a model that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the Barabási-Albert (BA) model, each new node first picks an existing node at random, and connects not with this but with $m$ of its neighbors also picked at random. Counterintuitively enough, such a mediation-driven attachment rule results not only in preferential but super-preferential attachment, albeit in disguise. We show that for small $m$, the dynamics of our model is governed by winners take all phenomenon, and for higher $m$ it is governed by winners take some. Besides, we show that the mean of the inverse harmonic mean of degrees of the neighborhood of all existing nodes is a measure that can well qualify how straight the degree distribution is.

physics.soc-ph↗