arXiv subjects

Arvind Singh

Publications and source records attributed to Arvind Singh.

At least 19 recordsLinked to original sources

arXiv2026

Random sequential nearest-neighbor coloring on trees

We study a nearest-neighbor coloring process in which vertices are revealed in random order and inherit the color of the closest vertex revealed before them. This model is a discrete analogue of coloring processes previously studied by Preater (2009) and Aldous (2018) in Euclidean spaces. We focus here on regular trees and analyze the associated genealogy of color inheritance. In contrast with the Euclidean case, the genealogical graph on an infinite regular tree is not connected: it has infinitely many infinite one-ended components, each with a distinct asymptotic direction, while every vertex has only finitely many descendants. We also describe how this structure is modified in the presence of finitely many initial seeds. Finally, we study local limits of the coloring on finite regular trees as their height tends to infinity, for two natural seed configurations: two fixed seeds, and one blue seed at the root with red seeds at the leaves.

math.PR↗

arXiv2026

Time-varying System Identification of Bedform Dynamics Using Modal Decomposition

Measuring sediment transport in riverbeds has long been a challenging research problem in geomorphology and river engineering. Traditional approaches rely on direct measurements using sediment samplers. Although such measurements are often considered ground truth, they are intrusive, labor-intensive, and prone to large variability. As an alternative, sediment flux can be inferred indirectly from the kinematics of migrating bedforms and temporal changes in bathymetry. While such approaches are helpful, bedform dynamics are nonlinear and multiscale, making it difficult to determine the contributions of different scales to the overall sediment flux. Fourier decomposition has been applied to examine bedform scaling, but it treats spatial and temporal variability separately. In this work, we introduce Dynamic Mode Decomposition (DMD) as a data-driven framework for analyzing riverbed evolution. By incorporating this representation into the Exner equation, we establish a link between modal dynamics and net sediment flux. This formulation provides a surrogate measure for scale-dependent sediment transport, enabling new insights into multiscale bedform-driven sediment flux in fluvial channels.

eess.SY↗

arXiv2025

Ultrafast Terahertz Photoconductivity and Near-Field Imaging of Nanoscale Inhomogeneities in Multilayer Epitaxial Graphene Nanoribbons

We study broadband terahertz (THz) conductivity and ultrafast photoconductivity spectra in lithographically fabricated multilayer epitaxial graphene nanoribbons grown on C- face of 6H-SiC substrate. THz near-field spectroscopy reveals local conductivity variations across nanoscale structural inhomogeneities such as wrinkles and grain boundaries within the multilayer graphene. Ultrabroadband THz far-field spectroscopy (0.15-16 THz) distinguishes doped graphene layers near the substrate from quasi-neutral layers (QNLs) further from the substrate. Temperature-dependent THz conductivity spectra are dominated by intra-band transitions both in the doped and QNLs. Photoexcitation then alters mainly the response of the QNLs: these exhibit a very high carrier mobility and a large positive THz photoconductivity with picosecond lifetime. The response of QNLs strongly depends on the carrier temperature $T_c$: the scattering time drops by an order of magnitude down to ~10 fs upon an increase of $T_c$ from 50 K to $T_c >$ 1000 K, which is attributed to an enhanced electron-electron and electron-phonon scattering and to an interaction of electrons with mid-gap states.

cond-mat.mtrl-sci↗

arXiv2025

A Stochastic Differential Equation Framework for Modeling Queue Length Dynamics Inspired by Self-Similarity

This article develops a stochastic differential equation (SDE) for modeling the temporal evolution of queue length dynamics at signalized intersections. Inspired by the observed quasiperiodic and self-similar characteristics of the queue length dynamics, the proposed model incorporates three properties into the SDE: (i) mean reversion with periodic mean, (ii) multiplicative noise, and (iii) fractional Brownian motion. It replicates key statistical features observed in real data, including the probability distribution function (PDF) and PSD of queue lengths. To our knowledge, this is the first equation-based model for queue dynamics. The proposed approach offers a transparent, data-consistent framework that may help inform and enhance the design of black-box learning algorithms with underlying traffic physics.

eess.SY↗

arXiv2025

Dynamics of local photoconductivity in GaAs and InP investigated by THz SNOM

Terahertz scanning near-field optical microscope (THz-SNOM) is employed to measure ultrafast evolution of THz conductivity spectra after photoexcitation of GaAs and InP wafers using ultrashort laser pulses. Unlike in GaAs, the THz photoconductivity decay in InP is controlled mainly by the diffusion of electrons away from the photoexcited area, and also by the drift due to band-bending at the surface of the semiconductor. We propose and discuss several general strategies of the analysis of signals measured using THz-SNOM, and we estimate the accuracy of the obtained near-field photoconductivity spectra.

cond-mat.mes-hall↗

arXiv2024

A phase transition for the biased tree-builder random walk

We consider a recent model of random walk that recursively grows the network on which it evolves, namely the Tree Builder Random Walk (TBRW). We introduce a bias $\rho \in (0,\infty)$ towards the root, and exhibit a phase transition for transience/recurrence at a critical threshold $\rho_c =1+2\overline{\nu}$, where $\overline{\nu}$ is the (possibly infinite) expected number of new leaves attached to the walker's position at each step. This generalizes previously known results, which focused on the unbiased case $\rho=1$. The proofs rely on a recursive analysis of the local times of the walk at each vertex of the tree, after a given number of returns to the root. We moreover characterize the strength of the transience (law of large numbers and central limit theorem with positive speed) via standard arguments, establish recurrence at $\rho_c$, and show a condensation phenomenon in the non-critical recurrent case.

math.PR↗

arXiv2024

On cases where Litt's game is fair

A fair coin is flipped $n$ times, and two finite sequences of heads and tails (words) $A$ and $B$ of the same length are given. Each time the word $A$ appears in the sequence of coin flips, Alice gets a point, and each time the word $B$ appears, Bob gets a point. Who is more likely to win? This puzzle is a slight extension of Litt's game that recently set Twitter abuzz. We show that Litt's game is fair for any value of $n$ and any two words that have the same auto-correlation structure by building up a bijection that exchanges Bob and Alice scores; the fact that the inter-correlation does not come into play in this case may come up as a surprise.

math.CO↗

arXiv2024

Ultrafast terahertz conductivity in epitaxial graphene nanoribbons: an interplay between photoexcited and secondary hot carriers

Optical pump-terahertz probe spectroscopy has been used to investigate ultrafast photo-induced charge carrier transport in 3.4 $\mu$m wide graphene ribbons upon scaling the optical pump intensity. For low pump fluences, the deposited pump energy is rapidly redistributed through carrier-carrier scattering, producing secondary hot carriers: the picosecond THz photoconductivity then acquires a negative sign and scales linearly with an increasing pump fluence. At higher fluences, there are not enough equilibrium carriers able to accept the deposited energy, directly generated (excess) carriers start to contribute significantly to the photoconductivity with a positive sign leading to its saturation behavior. This leads to a non-monotonic variation of the carrier mobility and plasmonic resonance frequency as a function of the pump fluence and, at high fluences, to a balance between a decreasing carrier scattering time and an increasing Drude weight. In addition, a weak carrier localization observed for the polarization parallel to the ribbons at low pump fluences is progressively lifted upon increasing the pump fluence as a result of the rise of initial carrier temperature.

cond-mat.mtrl-sci↗

arXiv2024

Nanoscale Terahertz Conductivity and Ultrafast Dynamics of Terahertz Plasmons in Periodic Arrays of Epitaxial Graphene Nanoribbons

Dynamics of plasmons in nanoribbons of (hydrogen intercalated) quasi-free-standing single layer graphene is studied by terahertz spectroscopy both in the steady state and upon photoexcitation by an ultrashort near infrared laser pulse. The use of two-dimensional frequency domain analysis of the optical pump - THz probe signals allows us to determine the evolution of carrier temperature and plasmon characteristics with ~100 fs time resolution. Namely, we find that the carrier temperature decreases from more than 5000 K to the lattice temperature within about 7 ps and that during this evolution the carrier mobility remains practically constant. The time-resolved THz conductivity spectra suggest that graphene nanoribbons contain defects which act as low potential barriers causing a weak localization of charges; the potential barriers are overcome upon photoexcitation. Furthermore, the edges of graphene nanoribbons are found to slightly enhance the scattering of carriers. The results are supported by complementary measurements using THz scanning near-field microscopy which confirm a high uniformity of the THz conductivity across the sample and demonstrate high enough sensitivity to resolve even the impact of nanometric terrace steps on SiC substrate under the graphene monolayer.

cond-mat.mtrl-sci↗

arXiv2024

Freezing in the Infinite-Bin Model

The infinite-bin model is a one-dimensional particle system on $\mathbb{Z}$ introduced by Foss and Konstantopoulos in relation with last passage percolation on complete directed acyclic graphs. In this model, at each integer time, a particle is selected at random according to its rank, and produces a child at the location immediately to its right. In this article, we consider the limiting distribution of particles after an infinite number of branching events have occurred. Under mild assumptions, we prove that the event (called freezing) that a location contains only a finite number of balls satisfies a $0-1$ law and we provide various criteria to determine whether freezing occurs.

math.PR↗

arXiv2024

The local limit of rooted directed animals on the square lattice

We consider the local limit of finite uniformly distributed directed animals on the square lattice viewed from the root. Two constructions of the resulting uniform infinite directed animal are given: one as a heap of dominoes, constructed by letting gravity act on a right-continuous random walk and one as a Markov process, obtained by slicing the animal horizontally. We look at geometric properties of this local limit and prove, in particular, that it consists of a single vertex at infinitely many (random) levels. Several martingales are found in connection with the confinement of the infinite directed animal on the non-negative coordinates.

math.PR↗

arXiv2023

Fractal properties of the frontier in Poissonian coloring

We study a model of random partitioning by nearest-neighbor coloring from Poisson rain, introduced independently by Aldous and Preater. Given two initial points in $[0,1]^d$ respectively colored in red and blue, we let independent uniformly random points fall in $[0,1]^d$, and upon arrival, each point takes the color of the nearest point fallen so far. We prove that the colored regions converge in the Hausdorff sense towards two random closed subsets whose intersection, the frontier, has Hausdorff dimension strictly between $d-1$ and $d$, thus answering a conjecture raised by Aldous. However, several topological properties of the frontier remain elusive.

math.PR↗

arXiv2021

Optical and Terahertz Response of Carbon Nanostructures

In the last three decades or so, we have witnessed an extraordinary progress in the research and technology of carbon-based nanomaterials. Among the peculiar highlights are the discoveries of fullerene, the carbon nanotubes and the magnificent simple scotch tape exfoliated graphene. The unique photophysical properties of these different allotropic forms of the nanocarbon have opened up vast application possibilities in many fields of science and technology, with particular emphasis on optoelectronics and photonics. A prerequisite for many of these applications is a thorough understanding of the nature of the elementary and coupled excitations and also various dynamical processes involving them. Here, we present an overview of the recent excitement with the carbon nanostructures, in particular, the quantum dots, nanotubes and graphene. We discuss some of their very interesting properties investigated through optical and THz spectroscopic tools. At optical frequencies, the light emitting properties, the nonlinearities and ultrafast response have been presented, while, the low-energy response has been considered in terms of studies obtained by using THz time-domain spectroscopy. Finally, we conclude with some of the future prospects on the photophysics of carbon nanosystems in realistic applications.

physics.app-ph↗

arXiv2021

Optical Damage Threshold and THz Generation Efficiency of (Fe,CoFeB)/(Ta,Pt) Spintronic Emitters

THz pulses are generated from femtosecond pulse-excited ferromagnetic/nonmagnetic spintronic heterostructures via inverse spin Hall effect. The contribution from ultrafast demagnetization/remagnetization is extremely weak, in the comparison. The highest possible THz signal strength from spintronic THz emitters is limited by the optical damage threshold of the corresponding heterostructures. The THz generation efficiency does not saturate with the excitation fluence even up till the damage threshold. Bilayer (Fe, CoFeB)/(Pt, Ta) based FM/NM spintronic heterostructures have been studied for an optimized performance for THz generation when pumped by sub-50 fs amplified laser pulses at 800 nm. Among them, CoFeB/Pt is the best combination for an efficient THz source. The optimized FM/NM spintronic heterostructure on a quartz substrate, having alpha-phase Ta as the nonmagnetic layer, show the highest damage threshold as compared to those with Pt, irrespective of their generation efficiency. The damage threshold of the Fe/Ta heterostructure on quartz substrate is ~85 GW/cm2.

physics.app-ph↗

arXiv2021

Reversible Poisson-Kirchhoff Systems

We define a general class of random systems of horizontal and vertical weighted broken lines on the quarter plane whose distribution are proved to be translation invariant. This invariance stems from a reversibility property of the model. This class of systems generalizes several classical processes of the same kind, such as Hammersley's broken line processes involved in Last Passage Percolation theory or such as the six-vertex model for some special sets of parameters. The novelty comes here from the introduction of a weight associated with each line. The lines are initially generated by spatially homogeneous weighted Poisson Point Process and their evolution (turn, split, crossing) are ruled by a Markovian dynamics which preserves Kirchhoff's node law for the line weights at each intersection. Among others, we derive some new explicit invariant measures for some bullet models as well as new reversible properties for some six-vertex models with an external electromagnetic field.

math.PR↗

arXiv2021

Sub-bandgap activated charges transfer in a graphene-MoS2-graphene heterostructure

Monolayers of transition metal dichalcogenides are semiconducting materials which offer many prospects in optoelectronics. A monolayer of molybdenum disulfide (MoS2) has a direct bandgap of 1.88 eV. Hence, when excited with optical photon energies below its bandgap, no photocarriers are generated and a monolayer of MoS2 is not of much use in either photovoltaics or photodetection. Here, we demonstrate that large size MoS2 monolayer sandwiched between two graphene layers makes this heterostructure optically active well below the band gap of MoS2. An ultrafast optical pump-THz probe experiment reveals in real-time, transfer of carriers between graphene and MoS2 monolayer upon photoexcitation with photon energies down to 0.5 eV. It also helps to unravel an unprecedented enhancement in the broadband transient THz response of this tri-layer material system. We propose possible mechanism which can account for this phenomenon. Such specially designed heterostructures, which can be easily built around different transition metal dichalcogenide monolayers, will considerably broaden the scope for modern optoelectronic applications at THz bandwidth.

cond-mat.mes-hall↗

arXiv2021

THz pulses from optically excited Fe, Pt and Ta based Spintronic Heterostructures

Spintronic heterostructures are considered to be the new generation THz sources for their capability in producing high power and broadband THz radiation. Here, we provide a brief review on the state-of-the-art in this field. The optically excited bi- and tri-layer combinations of ferromagnetic and nonmagnetic thin films have become increasingly popular. Towards optimizing the THz conversion efficiency and broadband gapless spectrum from these THz emitters, various control parameters need to be taken into consideration. The inverse spin Hall effect in the heavy metal layer of the heterostructure is primarily responsible for the generation of THz pulses. A few new results on iron, platinum and tantalum based heterostructures have also been reported here. It is observed that the Ta(2nm)/Fe(2nm)/Pt(2nm) tri-layer heterostructure generates ~40(250)% stronger THz signal as compared to the counterpart Fe(2nm)/Pt(2nm) (Fe(3nm)/Ta(2nm)) bi-layer heterostructure.

physics.app-ph↗

arXiv2020

Enhancement in optically induced ultrafast THz response of MoSe2MoS2 heterobilayer

THz conductivity of large area MoS2 and MoSe2 monolayers as well as their vertical heterostructure, MoSe2MoS2 is measured in the 0.3-5 THz frequency range. Compared to the monolayers, the ultrafast THz reflectivity of the MoSe2MoS2 heterobilayer is enhanced many folds when optically excited above the direct band gap energies of the constituting monolayers. The free carriers generated in the heterobilayer evolve with the characteristic times found in each of the two monolayers. Surprisingly, the same enhancement is recorded in the ultrafst THz reflectivity of the heterobilayer when excited below the MoS2 bandgap energy. A mechanism accounting for these observations is proposed.

physics.app-ph↗