arXiv subjects

Anish Sarkar

Publications and source records attributed to Anish Sarkar.

15 recordsLinked to original sources

arXiv2026

Magnetising the quokka code with fast, second-order accurate, error-correcting schemes for magnetohydrodynamics on GPUs

We implement a second-order accurate constrained transport (CT) magnetohydrodynamics (MHD) module with first-order flux correction in the open-source, adaptive mesh refinement (AMR), GPU-accelerated code quokka, supporting both ideal and resistive (constant Ohmic) regimes. For computing and averaging the electromotive forces (EMFs) at cell edges, the basis of any CT-MHD method, we experiment with a wide range of recent, state-of-the-art schemes, together with different reconstruction schemes. Alongside these, we develop a new EMF compute scheme that requires fewer reconstruction steps than existing approaches. We evaluate these scheme combinations on the basis of accuracy, stability, and GPU throughput, and demonstrate that our new scheme achieves accuracy comparable to the best-in-class existing methods, together with greater stability in reconnection-dominated flows and roughly 25--60% higher GPU throughput. Using this scheme, quokka achieves excellent results across a wide range of MHD flow regimes, reaching >50 million cell updates per GPU per second, with >70% parallel efficiency out to >500 GPUs. Finally, we confirm that our CT implementation preserves divergence-free magnetic fields (to machine precision) under AMR.

astro-ph.IM↗

arXiv2026

Black hole-Neutron star distinction based on long-term MAXI and Swift study of 42 low mass X-ray binaries

In this study, we analysed about $\sim$13 years of publicly available data from MAXI and Swift/BAT to examine the long-term source evolution of 42 transient low-mass X-ray binaries. The sample consists of 11 confirmed black hole X-ray binaries (BHXBs), 10 black hole candidates (BHC), and 21 neutron star X-ray binaries (NSXBs). Outbursts and flaring activities studied over 13 years show that 19/21 NSXBs spend significantly longer time in the hard state (observations for which hardness ratio is $\geq$ 0.2) while 15/21 BHXB+XRC spend substantially longer time in the soft state (observations for which hardness ratio is $<$ 0.2). The frequency distribution of the hardness ratio clearly shows two distinct distributions for BHXBs and NSXBs, with their peaks separated: NSXBs prefer harder values, while BHXBs prefer softer values of hardness. Our model-independent analysis for 42 transient sources shows that statistically NSXBs do not prefer to show a canonical high soft state as observed in BHXBs. Additionally, the probability distribution of the duration of the 2-20 keV X-ray outburst is observed to peak at a significantly longer duration ($>$100 days) for BHXBs than for NSXBs (15-60 days). Our analysis shows that among candidate sources, Swift J1728.9-3613, MAXI J1535-571, MAXI J1659-152, EXO 1846-031 show a `q' diagram in the HID and prefer to align with the HID frequency distribution of BHXBs that show `q' diagram, MAXI J1305-704 and MAXI J1836-194 align with frequency distribution of black hole sources without `q' diagram while MAXI J1848-015 shows the HID distribution similar to NSXBs, indicating a neutron star accretor. Therefore, a long-term statistical study of MAXI and Swift/BAT X-ray outbursts from a large sample of transient sources may be used to distinguish BHXB from NSXB.

astro-ph.HE↗

arXiv2024

Probing the origin of the extended flaring branch of Z-type X-ray binaries GX 340+0 and GX 5-1 using AstroSat

`Z' type neutron star low-mass X-ray binaries typically show a `Z'-like three-branched track in their hardness intensity diagram. However, a few such `Z' sources show an additional branch known as the extended flaring branch (EFB). EFB has been poorly studied, and its origin is not known. It is thought to be an extension of the flaring branch (FB) or associated with Fe K$\alpha$ complex or an additional continuum due to the radiative recombination continuum (RRC) process. Using AstroSat observations, we have detected the EFB from two `Z' sources, GX 340+0 and GX 5-1, and performed a broadband spectral analysis in the 0.5-22 keV energy range. During EFB, both sources show the presence of a significant RRC component with absorption edges at $7.91^{+0.16}_{-0.15}$ keV and $8.10^{+0.16}_{-0.17}$ keV, respectively along with blackbody radiation and thermal Comptonisation. No signature of RRC was detected during the FB, which is adjoint to the EFB. No Fe K$\alpha$ complex is detected. Interestingly, inside EFB dips of GX 5-1, for the first time, we have detected flaring events of 30-60s, which can be modelled with a single blackbody radiation. During the FB to EFB transition, an increase in the blackbody radius by a factor of 1.5-2 is observed in both sources. Our analysis strongly suggests that EFB is not an extension of FB or caused by the Fe K$\alpha$ complex. Rather, it is caused by a sudden expansion of the hot, thermalised boundary layer and subsequent rapid cooling.

astro-ph.HE↗

arXiv2024

Effect of Magnetic Field on the Formation of Radiatively Inefficient Accretion Flow around Black Holes

We study the effects of magnetic field in the formation of a radiatively inefficient accretion flow (RIAF) in the presence of Bremsstrahlung cooling, which facilitates the formation of a geometrically thin, optically thick accretion disk surrounded by a hot corona. We have performed axis-symmetric magnetohydrodynamic (MHD) simulations of an initial accretion torus with a $1/r$ dependant local poloidal field in the presence of a pseudo-Newtonian potential, taking into account optically thin cooling, resistivity and viscosity. We observe the formation of persistent jets and magnetised outflows from the corona surrounding a thin disk with an increase in the magnetic diffusivity parameter. We have defined an equivalent time scale ($\tau_{eq}$) which takes into account the heating time scales due to viscosity, resistivity, magnetic reconnection and magneto-rotational instability turbulence such that the thin disk is formed if the cooling time scale ($\tau_{cool}$) is lower than this equivalent time scale ($\tau_{cool}/\tau_{eq}<1$). Using this condition, for the first time, we found that the thin disk exists when the initial ratio of plasma pressure to magnetic pressure (plasma beta) exceeds a range of $600-800$ for the gas obeying a polytropic equation of state accreting at $10^{-5}\ M_{\odot}/year$

astro-ph.HE↗

arXiv2024

Learning models on rooted regular trees with majority update policy: convergence and phase transition

We study a learning model in which an agent is stationed at each vertex of $\mathbb{T}_{m}$, the rooted tree in which each vertex has $m$ children. At any time-step $t \in \mathbb{N}_{0}$, they are allowed to select one of two available technologies: $B$ and $R$. Let the technology chosen by the agent at vertex $v\in\mathbb{T}_{m}$, at time-step $t$, be $C_{t}(v)$. Let $\{C_{0}(v):v\in\mathbb{T}_{m}\}$ be i.i.d., where $C_{0}(v)=B$ with probability $π_{0}$. During epoch $t$, the agent at $v$ performs an experiment that results in success with probability $p_{B}$ if $C_{t}(v)=B$, and with probability $p_{R}$ if $C_{t}(v)=R$. If the children of $v$ are $v_{1},\ldots,v_{m}$, the agent at $v$ updates their technology to $C_{t+1}(v)=B$ if the number of successes among all $v_{i}$ with $C_{t}(v_{i})=B$ exceeds, strictly, the number of successes among all $v_{j}$ with $C_{t}(v_{j})=R$. If these numbers are equal, then the agent at $v$ sets $C_{t+1}(v)=B$ with probability $1/2$. Else, $C_{t+1}(v)=R$. We show that $\{C_{t}(v):v\in\mathbb{T}_{m}\}$ is i.i.d., where $C_{t}(v)=B$ with probability $π_{t}$, and $\{π_{t}\}_{t \in \mathbb{N}_{0}}$ converges to a fixed point $π$ of a function $g_{m}$. For $m \geqslant 3$, there exists a $p(m) \in (0,1)$ such that $g_{m}$ has a unique fixed point, $1/2$, when $p \leqslant p(m)$, and three distinct fixed points, of the form $α$, $1/2$ and $1-α$, when $p > p(m)$. When $m=3$, $p_{B}=1$ and $p_{R} \in [0,1)$, we show that $g_{3}$ has a unique fixed point, $1$, when $p_{R} < \sqrt{3}-1$, two distinct fixed points, one of which is $1$, when $p_{R} = \sqrt{3}-1$, and three distinct fixed points, one of which is $1$, when $p_{R} > \sqrt{3}-1$. When $g_{m}$ has multiple fixed points, we also specify which of these fixed points $π$ equals, depending on $π_{0}$. For $m=2$, we describe the behaviour of $g_{3}$ for all $p_{B}$ and $p_{R}$.

math.PR↗

arXiv2023

Scaling limit of a drainage network model on perturbed lattice

Study of random networks generally requires the nodes to be independently and uniformly distributed such as a Poisson point process. In this work, we venture beyond this standard paradigm and investigate a stochastic forest obtained from a drainage network model constructed on a randomly perturbed subset of $\mathbb{Z}^2$, where both horizontal and vertical perturbations are given by exponentially decaying unbounded discrete random variables and vertical perturbations are allowed in the upward direction only. We show that the resultant stochastic network is a single tree a.s. We further establish that as a collection of paths, under diffusive scaling the resultant network converges to the Brownian web.

math.PR↗

arXiv2020

The 2d-directed spanning forest converges to the Brownian web

The two-dimensional directed spanning forest (DSF) introduced by Baccelli and Bordenave is a planar directed forest whose vertex set is given by a homogeneous Poisson point process $\mathcal{N}$ on $\mathbb{R}^2$. If the DSF has direction $-e_y$, the ancestor $h(u)$ of a vertex $u \in \mathcal{N}$ is the nearest Poisson point (in the $L_2$ distance) having strictly larger $y$-coordinate. This construction induces complex geometrical dependencies. In this paper we show that the collection of DSF paths, properly scaled, converges in distribution to the Brownian web (BW). This verifies a conjecture made by Baccelli and Bordenave in 2007.

math.PR↗

arXiv2019

Collision times of random walks and applications to the Brownian web

Convergence of directed forests, spanning on random subsets of lattices or on point processes, towards the Brownian web has made the subject of an abundant literature, a large part of which relies on a criterion proposed by Fontes, Isopi, Newman and Ravishankar (2004). One of their convergence condition, called (B2), states that the probability of the event that there exists three distinct paths for a time interval of length $t(>0)$, all starting within a segment of length $\varepsilon$, is of small order of $\varepsilon$. This condition is often verified by applying an FKG type correlation inequality together with a coalescing time tail estimate for two paths. For many models where paths have complex interactions, it is hard to establish FKG type inequalities. In this article, we show that for a non-crossing path model, with certain assumptions, a suitable upper bound on expected first collision time among three paths can be obtained directly using Lyapunov functions. This, in turn, provides an alternate verification of Condition (B2). We further show that in case of independent simple symmetric one dimensional random walks or in case of independent Brownian motions, the expected value can be computed explicitly. We apply this alternate method of verification of (B2) to several models in the basin of attraction of the Brownian web studied earlier in the literature ([S67], [H71], [FLT04]).

math.PR↗

arXiv2016

Hack's law in a drainage network model: A Brownian web approach

Hack [Studies of longitudinal stream profiles in Virginia and Maryland (1957). Report], while studying the drainage system in the Shenandoah valley and the adjacent mountains of Virginia, observed a power law relation $l\sim a^{0.6}$ between the length $l$ of a stream from its source to a divide and the area $a$ of the basin that collects the precipitation contributing to the stream as tributaries. We study the tributary structure of Howard's drainage network model of headward growth and branching studied by Gangopadhyay, Roy and Sarkar [Ann. Appl. Probab. 14 (2004) 1242-1266]. We show that the exponent of Hack's law is $2/3$ for Howard's model. Our study is based on a scaling of the process whereby the limit of the watershed area of a stream is area of a Brownian excursion process. To obtain this, we define a dual of the model and show that under diffusive scaling, both the original network and its dual converge jointly to the standard Brownian web and its dual.

math.PR↗

arXiv2015

Random directed forest and the Brownian web

Consider the $d$ dimensional lattice $\mathbb{Z}^d$ where each vertex is open or closed with probability $p$ or $1-p$ respectively. An open vertex $\mathbb{u} := (\mathbb{u}(1), \mathbb{u}(2),...,\mathbb{u}(d))$ is connected by an edge to another open vertex which has the minimum $L_1$ distance among all the open vertices with $\mathbb{x}(d)>\mathbb{u}(d)$. It is shown that this random graph is a tree almost surely for $d=2$ and 3 and it is an infinite collection of disjoint trees for $d\geq 4$. In addition for $d=2$, we show that when properly scaled, family of its paths converges in distribution to the Brownian web.

math.PR↗

arXiv2013

Brownian Web in the Scaling Limit of Supercritical Oriented Percolation in Dimension 1+1

We prove that, after centering and diffusively rescaling space and time, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2_{even}:={(x,i) in Z^2: x+i is even} converges in distribution to the Brownian web. This proves a conjecture of Wu and Zhang. Our key observation is that each rightmost infinite open path can be approximated by a percolation exploration cluster, and different exploration clusters evolve independently before they intersect.

math.PR↗

arXiv2011

Brownian Web and Oriented Percolation: Density Bounds

In a recent work, we proved that under diffusive scaling, the collection of rightmost infinite open paths in a supercritical oriented percolation configuration on the space-time lattice Z^2 converges in distribution to the Brownian web. In that proof, the FKG inequality played an important role in establishing a density bound, which is a part of the convergence criterion for the Brownian web formulated by Fontes et al (2004). In this note, we illustrate how an alternative convergence criterion formulated by Newman et al (2005) can be verified in this case, which involves a dual density bound that can be established without using the FKG inequality. This alternative approach is in some sense more robust. We will also show that the spatial density of the collection of rightmost infinite open paths starting at time 0 decays asymptotically in time as c/\sqrt{t} for some c>0.

math.PR↗

arXiv2009

On the One Dimensional Critical "Learning from Neighbours" Model

We consider a model of a discrete time "interacting particle system" on the integer line where infinitely many changes are allowed at each instance of time. We describe the model using chameleons of two different colours, {\it viz}., red ($R$) and blue ($B$). At each instance of time each chameleon performs an independent but identical coin toss experiment with probability $α$ to decide whether to change its colour or not. If the coin lands head then the creature retains its colour (this is to be interpreted as a "success"), otherwise it observes the colours and coin tosses of its two nearest neighbours and changes its colour only if, among its neighbors and including itself, the proportion of successes of the other colour is larger than the proportion of successes of its own colour. This produces a Markov chain with infinite state space ${R, B}^{\Zbold}$. This model was first studied by Chatterjee and Xu (2004) where different colours had different success probabilities. In this work we consider the "critical" case where the success probability, $α$, is the same irrespective of the colour of the chameleon. We show that starting from any initial translation invariant distribution of colours the Markov chain converges to a limit of a single colour, i.e., even at the critical case there is no "coexistence" of the two colours at the limit. Moreover we show that starting with an i.i.d. colour distribution the limiting distribution gives some advantage to the "underdog".

math.PR↗

arXiv2005

Rigorous results on the threshold network model

We analyze the threshold network model in which a pair of vertices with random weights are connected by an edge when the summation of the weights exceeds a threshold. We prove some convergence theorems and central limit theorems on the vertex degree, degree correlation, and the number of prescribed subgraphs. We also generalize some results in the spatially extended cases.

math.PR↗

arXiv2004

Random oriented Trees: a Model of drainage networks

Consider the d-dimensional lattice Z^d where each vertex is ``open'' or ``closed'' with probability p or 1-p, respectively. An open vertex v is connected by an edge to the closest open vertex w such that the dth co-ordinates of v and w satisfy w(d)=v(d)-1. In case of nonuniqueness of such a vertex w, we choose any one of the closest vertices with equal probability and independently of the other random mechanisms. It is shown that this random graph is a tree almost surely for d=2 and 3 and it is an infinite collection of distinct trees for d\geq4. In addition, for any dimension, we show that there is no bi-infinite path in the tree and we also obtain central limit theorems of (a) the number of vertices of a fixed degree νand (b) the number of edges of a fixed length l.

math.PR↗