arXiv subjects

Anirban Ghosh

Publications and source records attributed to Anirban Ghosh.

At least 37 records · Page 2Linked to original sources

arXiv2024

Diffusion dynamics of an overdamped active ellipsoidal particle in two dimensions

Shape asymmetry is the most abundant in nature and attracted great interest in recent research. The phenomenon is widely recognized: a free ellipsoidal Brownian particle displays anisotropic diffusion during short time intervals, which subsequently transitions to an isotropic diffusion pattern over longer time scales. We have further expanded this concept to incorporate active ellipsoidal particles characterized by an initial self-propelled velocity. This paper provides analytical and simulation results of diffusion dynamics of an active ellipsoidal particle. The active ellipsoidal particle manifests three distinct regimes in its diffusion dynamics over time. In the transient regime, it displays diffusive behavior followed by a super-diffusive phase, and in the longer time duration, it transitions to purely diffusive dynamics. We investigated diffusion dynamics for the free particle as well as the particle in a harmonic trap, and the particle subject to a constant field force. Moreover, we have studied the rotational diffusion dynamics and torque production resulting from an external constant force field. Furthermore, our investigation extends to the examination of the scaled average velocity of an ellipsoidal active particle, considering both a constant force field and a one-dimensional ratchet.

cond-mat.soft↗

arXiv2023

Asymmetrical post quench transport in an embedded parity time symmetric Su-Schrieffer-Heeger system

We study the effect of PT-symmetric non-hermiticity on the transport of edge state probability density arising as a result of a quench. A hybrid system involving a PT-symmetric SSH region sandwiched between two plain SSH systems is designed to study the dynamics. Geometrical arguments and numerical calculations were made to ascertain the nature of edge states. We then compute the quench dynamics numerically and demonstrate that the post-quench probability density light cones exhibit contrasting shapes as a result of asymmetrical reflections from the non-Hermitian part of the system depending on the direction of propagation of the transporting wave and, hence, on the initial localization of the edge state.

quant-ph↗

arXiv2023

Phen-DC 3 Induces Refolding of Human Telomeric DNA into a Chair-Type Antiparallel G-Quadruplex through Ligand Intercalation

Human telomeric G-quadruplex DNA structures are attractive anticancer drug targets, but the target's polymorphism complicates the drug design: different ligands prefer different folds, and very few complexes have been solved at high resolution. Here we report that Phen-DC3, one of the most prominent G-quadruplex ligands in terms of high binding affinity and selectivity, causes dTAGGG(TTAGGG)3 to completely change its fold in KCl solution from a hybrid-1 to an antiparallel chair-type structure, wherein the ligand intercalates between a two-quartet unit and a pseudo-quartet, thereby ejecting one potassium ion. This unprecedented high-resolution NMR structure shows for the first time a true ligand intercalation into an intramolecular G-quadruplex.

q-bio.BM↗

arXiv2023

Engineering an algorithm for constructing low-stretch geometric graphs with near-greedy average-degrees

We design and engineer Fast-Sparse-Spanner, a simple and practical (fast and memory-efficient) algorithm for constructing sparse low stretch-factor geometric graphs on large pointsets in the plane. To our knowledge, this is the first practical algorithm to construct fast low stretch-factor graphs on large pointsets with average-degrees (hence, the number of edges) competitive with that of greedy-spanners, the sparsest known class of Euclidean geometric spanners. To evaluate our implementation in terms of computation speed, memory usage, and quality of output, we performed extensive experiments with synthetic and real-world pointsets, and by comparing it to our closest competitor Bucketing, the fastest known greedy-spanner algorithm for pointsets in the plane, devised by Alewijnse et al. (Algorithmica, 2017). We always found that Fast-Sparse-Spanner generated near-greedy t-spanners while being fast and memory-efficient. Our experiment with constructing a 1.1-spanner on a large synthetic pointset with 128K points uniformly distributed within a square shows more than a 41-fold speedup with roughly a third of the memory usage of that of Bucketing, but with only a 3% increase in the average-degree of the resulting graph. In terms of diameter, the graphs generated by Fast-Sparse-Spanner beat greedy-spanners in most cases (have substantially lower diameter) while maintaining near-greedy average-degree. As a byproduct of our research, we design and engineer Fast-Stretch-Factor, a practical parallelizable algorithm that can measure the stretch-factor of any graph generated by Fast-Sparse-Spanner. Our experiments show that it is much faster than the naive Dijkstra-based stretch-factor measurement algorithm.

cs.CG↗

arXiv2023

Simple experimental realization of optical Hilbert Hotel using scalar and vector fractional vortex beams

Historically, infinity was long considered a vague concept - boundless, endless, larger than the largest - without any quantifiable mathematical foundation. This view changed in the 1800s through the pioneering work of Georg Cantor showing that infinite sets follow their own seemingly paradoxical mathematical rules. In 1924, David Hilbert highlighted the strangeness of infinity through a thought experiment now referred to as the Hilbert Hotel paradox, or simply Hilbert's Hotel. The paradox describes an "fully" occupied imaginary hotel having infinite number of single-occupancy rooms, the manager can always find a room for new guest by simply shifting current guests to the next highest room, leaving first room vacant. The investigation of wavefield singularities has uncovered the existence of a direct optical analogy to Hilbert's thought experiment. Since then, efforts have been made to investigate the properties of Hilbert's Hotel by controlling the dynamics of phase singularities in``fractional'' order optical vortex beams. Here, we have taken such proposals to the next level and experimentally demonstrated Hilbert's Hotel using both phase and polarization singularities of optical fields. Using a multi-ramped spiral-phase-plate and a supercontinuum source, we generated and controlled fractional order vortex beams for the practical implementation of Hilbert's Hotel in scalar and vector vortex beams. Using a multi-ramped spiral-phase-plate, we show the possibility for complicated transitions of the generalized Hilbert's Hotel. The generic experimental scheme illustrates the usefulness of structured beams in visualizing unusual mathematical concepts and also for fractional vector beams driven fundamental and applied research.

physics.optics↗

arXiv2023

Quench dynamics of edge states in a finite extended Su-Schrieffer-Heeger system

We examine the quench dynamics of an extended Su-Schrieffer-Heeger(SSH) model involving long-range hopping that can hold multiple topological phases. Using winding number diagrams to characterize the system's topological phases geometrically, it is shown that there can be multiple winding number transition paths for a quench between two topological phases. The dependence of the quench dynamics is studied in terms of the survival probability of the fermionic edge modes and post-quench transport. For two quench paths between two topological regimes with the same initial and final topological phase, the survival probability of edge states is shown to be strongly dependent on the winding number transition path. This dependence is explained using energy band diagrams corresponding to the paths. Following this, the effect of the winding number transition path on transport is investigated. We find that the velocities of maximum transport channels varied along the winding number transition path. This variation depends on the path we choose, i.e., it increases or decreases depending upon the path. An analysis of the coefficient maps, energy spectrum, and spatial structure of the edge states of the final quench Hamiltonian provides an understanding of the path-dependent velocity variation phenomenon.

quant-ph↗

arXiv2022

Persistence of an active asymmetric rigid Brownian particle in two dimensions

We have studied the persistence probability $p(t)$ of an active Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the the probability of a stochastic variable that has not changed it's sign in the fixed given time interval. We have investigated two cases: diffusion of a free active particle and that of harmonically trapped particle. In our earlier work, \emph{Ghosh et. al.}, Journal of Chemical Physics, \textbf{152},174901, (2020), we had shown that $p(t)$ can be used to determine translational and the rotational diffusion constant of an asymmetric shape particle. The method has the advantage that the measurement of the rotational motion of the an-isotropic particle is not required. In this paper, we extend the study to an active an-isotropic particle and show how the persistence probability of an an-isotropic particle is modified in the presence of a propulsion velocity. Further, we validate our analytical expression against the measured persistence probability from the numerical simulations of single particle Langevin dynamics and test whether the method proposed in our earlier work can distinguish between an active and a passive an-isotropic particle.

cond-mat.stat-mech↗

arXiv2022

Formulation of an equivalent GNF model as an efficient approximation for flow of polymer solutions described by FENE-P

The molecular constitutive models, like FENE-P for polymer solutions, are known to have convergence issues at relatively larger flow rates. In this study, we investigate the possibility of a numerically efficient GNF-based approximation of FENE-P, which would closely approximate the flow field. Firstly, we compare the flow fields predicted by FENE-P and an equivalent GNF model. For these studies, we considered the flow around a sphere and selected the Carreau-Yasuda model as the representative GNF. This is made equivalent to the FENE-P by selecting parameters to equalize the viscosity-shear rate dependence. Our results show severe deficiencies of the GNF model, owing to its inability to account for chain stretching, particularly near the stagnation points. Next, the effect of extensional components on the local viscosity was added by formulating an equivalent GNF-X [Journal of Rheology 64, 493 (2020)] model. Even this failed to capture the asymmetry in the stress and flow profiles and predicted very large stresses at both stagnation points, relative to FENE-P. Hence, we proposed a novel modified formalism (denoted as GNF-XM) that was able to capture all trends successfully. The drag coefficients from GNF-XM agreed well with FENE-P predictions for all flow rates considered. Significantly, the computational times required to solve the flow field with GNF-XM is about an order of magnitude lower than that of FENE-P, especially at higher flow rates. Thus, we have successfully formulated a highly efficient GNF-based approximation to the FENE-P, whose formalism can be extended to other similarly complicated constitutive models.

physics.flu-dyn↗

arXiv2022

Bright entangled photon source without stringent crystal temperature and laser frequency stabilization

Entangled photon sources (EPS), the major building block for a variety of quantum communication protocols, are commonly developed by utilizing the spontaneous parametric down-conversion (SPDC) in $χ^{2}$ nonlinear bulk optical materials. While high nonlinearity and long interaction length have established the superiority of the periodically poled crystals for EPSs, the phase-matching condition of such crystals is very sensitive to the fluctuation of the crystal temperature and the laser wavelength. As a result, deploying such sources outside the laboratory, for example, satellite-based applications, demands a stringent mass and power budget, thus enhancing the mission complexity and cost. We report a bright, stable entangled photon source with a relaxed requirement of crystal temperature and laser wavelength stabilization. Using a periodically poled KTP crystal inside a polarization Sagnac interferometer producing degenerate, type-0 phase-matched entangled photon pairs at 810 nm in an annular ring, we have transformed the SPDC ring into a "perfect" ring with the help of two common optical elements, axicon, and lens. Despite the variation of the SPDC ring size from Gaussian to annular of different diameters due to the change of crystal temperature over $7^{o}$C, and laser wavelength over 300 GHz, we observe the size of the "perfect" ring to be constant. The new EPS, having a spectral brightness as high as 22.58 $\pm$ 0.15 kHz/mW collected using single-mode fiber with a Bell's parameter, S = 2.64 $\pm$ 0.05, and quantum state fidelity of 0.95 $\pm$ 0.02, requires a crystal temperature stability of $\pm$ $0.8^{o}$C, almost five times relaxation as compared to the previous EPS. The generic scheme can be used for non-collinear SPDC photons in all crystals to develop EPS at any wavelength and timescales for resource-constrained applications.

quant-ph↗

arXiv2022

Visualizing WSPDs and their applications

Introduced by Callahan and Kosaraju back in 1995, the concept of well-separated pair decomposition (WSPD) has occupied a special significance in computational geometry when it comes to solving distance problems in $d$-space. We present an in-browser tool that can be used to visualize WSPDs and several of their applications in $2$-space. Apart from research, it can also be used by instructors for introducing WSPDs in a classroom setting. The tool will be permanently maintained by the third author at https://wisno33.github.io/VisualizingWSPDsAndTheirApplications/.

cs.CG↗

arXiv2022

Bounded-degree plane geometric spanners in practice

The construction of bounded-degree plane geometric spanners has been a focus of interest since 2002 when Bose, Gudmundsson, and Smid proposed the first algorithm to construct such spanners. To date, eleven algorithms have been designed with various trade-offs in degree and stretch factor. We have implemented these sophisticated algorithms in C++ using the CGAL library and experimented with them using large synthetic and real-world pointsets. Our experiments have revealed their practical behavior and real-world efficacy. We share the implementations via GitHub for broader uses and future research. We present a simple practical algorithm, named AppxStretchFactor, that can estimate stretch factors (obtains lower bounds on the exact stretch factors) of geometric spanners - a challenging problem for which no practical algorithm is known yet. In our experiments with bounded-degree plane geometric spanners, we find that AppxStretchFactor estimates stretch factors almost precisely. Further, it gives linear runtime performance in practice for the pointset distributions considered in this work, making it much faster than the naive Dijkstra-based algorithm for calculating stretch factors

cs.CG↗

arXiv2022

Experiments with Unit Disk Cover Algorithms for Covering Massive Pointsets

Given a set of $n$ points in the plane, the Unit Disk Cover (UDC) problem asks to compute the minimum number of unit disks required to cover the points, along with a placement of the disks. The problem is NP-hard and several approximation algorithms have been designed over the last three decades. In this paper, we have engineered and experimentally compared practical performances of some of these algorithms on massive pointsets. The goal is to investigate which algorithms run fast and give good approximation in practice. We present a simple $7$-approximation algorithm for UDC that runs in $O(n)$ expected time and uses $O(s)$ extra space, where $s$ denotes the size of the generated cover. In our experiments, it turned out to be the speediest of all. We also present two heuristics to reduce the sizes of covers generated by it without slowing it down by much. To our knowledge, this is the first work that experimentally compares geometric covering algorithms. Experiments with them using massive pointsets (in the order of millions) throw light on their practical uses. We share the engineered algorithms via GitHub - https://github.com/ghoshanirban/UnitDiskCoverAlgorithms for broader uses and future research in the domain of geometric optimization.

cs.CG↗

arXiv2022

Single-pass, nonlinear frequency conversion of full Poincaré beams

Full Poincaré (FP) beams, a special class of fully correlated beams generated through the coaxial superposition of a Laguerre-Gauss and fundamental Gaussian modes of orthogonal polarizations, contain all possible polarization states on the surface of the Poincaré sphere in a single beam. While the presence of all unconventional polarization states makes the FP beams useful for various applications, the dependence of the refractive index on the polarization restricts the efficient generation of FP beams across the electromagnetic spectrum through nonlinear frequency processes. To avoid such difficulty, we use two contiguous BIBO crystals with orthogonal optic axes and generate an ultrafast FP beam at 405 nm with average power as high as 18.3 mW at a single-pass conversion efficiency of 2.19%. Using Stokes parameters and Stokes phases, we observed the doubling of C-points and L-lines singularities and the orbital angular momentum in the SHG process. We have also devised a new technique to estimate the polarization coverage of the pump and SHG FP beams and observed the variation in polarization coverage with the intensity weightage of the constituting beams. Interestingly, the SHG beam has the highest polarization coverage for the FP beam of equal intensity weightage of the superposed beams. We validated our experimental results in close agreement with the theoretical results.

physics.optics↗

arXiv2021

Sparse Hop Spanners for Unit Disk Graphs

A unit disk graph $G$ on a given set $P$ of points in the plane is a geometric graph where an edge exists between two points $p,q \in P$ if and only if $|pq| \leq 1$. A spanning subgraph $G'$ of $G$ is a $k$-hop spanner if and only if for every edge $pq\in G$, there is a path between $p,q$ in $G'$ with at most $k$ edges. We obtain the following results for unit disk graphs in the plane. (I) Every $n$-vertex unit disk graph has a $5$-hop spanner with at most $5.5n$ edges. We analyze the family of spanners constructed by Biniaz (2020) and improve the upper bound on the number of edges from $9n$ to $5.5n$. (II) Using a new construction, we show that every $n$-vertex unit disk graph has a $3$-hop spanner with at most $11n$ edges. (III) Every $n$-vertex unit disk graph has a $2$-hop spanner with $O(n\log n)$ edges. This is the first nontrivial construction of $2$-hop spanners. (IV) For every sufficiently large positive integer $n$, there exists a set $P$ of $n$ points on a circle, such that every plane hop spanner on $P$ has hop stretch factor at least $4$. Previously, no lower bound greater than $2$ was known. (V) For every finite point set on a circle, there exists a plane (i.e., crossing-free) $4$-hop spanner. As such, this provides a tight bound for points on a circle. (VI) The maximum degree of $k$-hop spanners cannot be bounded from above by a function of $k$ for any positive integer $k$.

cs.CG↗

arXiv2020

Persistence in Brownian motion of an ellipsoidal particle in two dimensions

We investigate the persistence probability $p(t)$ of the position of a Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability that a stochastic variable has not changed it's sign in the given time interval. We explicitly consider two cases -- diffusion of a free particle and that of harmonically trapped particle. The later is particularly relevant in experiments which uses trapping and tracking techniques to measure the displacements. We provide analytical expressions of $p(t)$ for both the scenarios and show that in the absence of the shape asymmetry the results reduce to the case of an isotropic particle. The analytical expressions of $p(t)$ are further validated against numerical simulation of the underlying overdamped dynamics. We also illustrate that $p(t)$ can be a measure to determine the shape asymmetry of a colloid and the translational and rotational diffusivities can be estimated from the measured persistence probability. The advantage of this method is that it does not require the tracking of the orientation of the particle.

cond-mat.soft↗

arXiv2019

Single-pass, second harmonic generation of ultrafast, higher order vector vortex beams at blue

We report a novel experimental scheme for single-pass second harmonic generation (SHG) of vector vortex beam in the blue. Using an ultrafast Ti:Sapphire laser of pulse width ~17 fs and a set of spiral phase plates in polarization based Mach-Zehnder interferometer (MZI) we have generated vector vortex beams of order as high as lp = 12 at an average power of 860 mW. Given the space-variant polarization of the vector vortex beam, and the dependence of nonlinear frequency conversion processes on the polarization of the interacting beams, using two contiguous bismuth borate crystals with optic axis orthogonal to each other, we have frequency-doubled the near-IR vector vortex beam into visible vector vortex beams with order as high as lsh=24. The maximum output power of the vector vortex beam of order, lsh =2 is measured be as high as 20.5 mW at a single-pass SHG efficiency of 2.4 %. Controlling the temporal delay in the MZI, we have preserved the vector vortex nature of the beams at both pump and frequency-doubled beams at ultrafast timescales. The measurement on mode purity confirms the generation of high quality vector vortex beams at pump and SHG wavelengths. The generic experimental scheme can be used to generate vector vortex beams across the electromagnetic spectrum.

physics.optics↗

arXiv2018

Online Unit Covering in Euclidean Space

We revisit the online Unit Covering problem in higher dimensions: Given a set of $n$ points in $\mathbb{R}^d$, that arrive one by one, cover the points by balls of unit radius, so as to minimize the number of balls used. In this paper, we work in $\mathbb{R}^d$ using Euclidean distance. The current best competitive ratio of an online algorithm, $O(2^d d \log{d})$, is due to Charikar et al. (2004); their algorithm is deterministic. (I) We give an online deterministic algorithm with competitive ratio $O(1.321^d)$, thereby sharply improving on the earlier record by a large exponential factor. In particular, the competitive ratios are $5$ for the plane and $12$ for $3$-space (the previous ratios were $7$ and $21$, respectively). For $d=3$, the ratio of our online algorithm matches the ratio of the current best offline algorithm for the same problem due to Biniaz et al. (2017), which is remarkable (and rather unusual). (II) We show that the competitive ratio of every deterministic online algorithm (with an adaptive deterministic adversary) for Unit Covering in $\mathbb{R}^d$ under the $L_{2}$ norm is at least $d+1$ for every $d \geq 1$. This greatly improves upon the previous best lower bound, $Ω(\log{d} / \log{\log{\log{d}}})$, due to Charikar et al. (2004). (III) We obtain lower bounds of $4$ and $5$ for the competitive ratio of any deterministic algorithm for online Unit Covering in $\mathbb{R}^2$ and respectively $\mathbb{R}^3$; the previous best lower bounds were both $3$. (IV) When the input points are taken from the square or hexagonal lattices in $\mathbb{R}^2$, we give deterministic online algorithms for Unit Covering with an optimal competitive ratio of $3$.

cs.CG↗

arXiv2018

Simultaneous generation of high power, ultrafast 1D and 2D Airy beams and their frequency doubling characteristics

We report on a simple experimental scheme based on a pair of cylindrical lenses (convex and concave) of same focal length and common optical elements producing high power optical beams in 1D and/or 2D Airy intensity profiles with laser polarization as control parameter. Using an ultrafast Yb-fiber laser at 1064 nm of average power of 5 W in Gaussian spatial profile and pulse-width of ~180 fs, we have generated 1D and 2D Airy beams at an efficiency of 80% and 70%, respectively, and pulse width of ~188 fs and ~190 fs, respectively. We have measured the transverse deflection rate of 1D and 2D beams to be ~5.0 (10^-5) 1/mm and ~2.0 (10^-5) 1/mm, respectively. Simply rotating the polarization state of the 1D cubic phase modulated beam in the experiment we can produce 1D and 2D Airy beams on demand. Using a 5 mm long bismuth borate (BiB3O6) we have also studied frequency-doubling characteristics of both 1D and 2D Airy beams. Like 2D Airy beam, the 1D Airy beam also produce frequency-doubled 1D Airy and an additional 1D spatial cubic structure. Like the Gaussian beams, we have observed the focusing dependent conversion efficiency for both 1D and 2D Airy beams producing green 1D and 2D Airy beams of output powers in excess of 110 mW and 150 mW for 3.4 W and 2.8 W of fundamental power respectively.

physics.optics↗