arXiv subjects
Publications and source records attributed to S. Kar.
In this paper we introduce a quotient structure on topological ternary semigroup by defining a congruence suitably. We have found conditions under which this quotient structure becomes a topological ternary semigroup. We have also obtained conditions that make this quotient a topological ternary group, whenever the base structure is a topological ternary group.
In this short review, we provide an overview of recent progress in deploying advanced characterization techniques to understand the effects of local inhomogeneities in moir\'e heterostructures over multiple length scales. Particular emphasis is placed on correlating the impact of twist angle misalignment, nano-scale disorder, and atomic relaxation on the moir\'e potential and its collective excitations, particularly moir\'e excitons. Finally, we discuss future technological applications leveraging based on moi\'e excitons.
Laser-driven neutron sources are routinely produced by the interaction of laser-accelerated protons with a converter. They present complementary characteristics to those of conventional accelerator-based neutron sources (e.g. short pulse durations, enabling novel applications like radiography). We present here results from an experiment aimed at performing a global characterization of the neutrons produced using the Titan laser at the Jupiter Laser Facility (Livermore, USA), where protons were accelerated from 23 $\mu m$ thick plastic targets and directed onto a LiF converter to produce neutrons. For this purpose, several diagnostics were used to measure these neutron emissions, such as CR-39, activation foils, Time-of-Flight detectors and direct measurement of $^{7}$Be residual activity in the LiF converters. The use of these different, independently operating diagnostics enables comparison of the various measurements performed to provide a robust characterization. These measurements led to a neutron yield of $2.10^{9}$ neutrons per shot with a modest angular dependence, close to that simulated.
The Quantum Materials group at Indian Institute of Technology Patna is working on a range of topics relating to nanoelectronics, spintronics, clean energy and memory design etc. The PI has past experiences of working extensively with superconducting systems like cuprates [1, 2], ruthanate [3], pnictide [4, 5], thin film heterostructures [6, 7] etc and magnetic recording media [8, 9] etc. In this report, we have summarised the ongoing works in our group. We explored a range of functional materials like two-dimensional materials, oxides. topological insulators, organic materials etc. using a combination of experimnetal and computational tools. Some of the useful highlights are as follows: (a) tuning and control of the magnetic and electronic state of 2D magentic materials with rapid enhancement in the Curie temperature, (b) Design and detection of single electron transistor based nanosensors for the detection of biological species with single molecular resolution, (c) Observation of non-volatile memory behaviour in the hybrid structures made of perovskite materials and 2D hybrids. The results offer useful insight in the design of nanoelectronic architecrures for diverse applications.
Here a real life optimal control problem under fuzzy time period using variational principle is formulated and Solved. The unit production cost is a function of production rate and also dependent on raw material cost, development cost due to durability and wear-tear cost. The holding cost is assumed to be non-linear, dependent on time. The profit function which consists of revenue, production cost and holding cost is formulated as a Fuzzy-Final Time and Fixed State System optimal control problem with fuzzy time period. Here production rate is unknown and considered as a control variable and stock level is taken as a state variable. It is formulated to optimize the production rate so that total profit is maximum. The non-linear optimization technique-Generalised Reduced Gradient Method (LINGO 11.0) is used. The optimum results are illustrated both numerically and graphically.
The response of the BAS-TR image plate (IP) was absolutely calibrated using CR-39 track detector for high linear energy transfer (LET) Au ions up to $\sim$1.6 GeV (8.2 MeV/nucleon), accelerated by high-power lasers. The calibration was carried out by employing a high-resolution Thomson parabola spectrometer, which allowed resolving Au ions with closely spaced ionization states up to 58$^+$. A response function was obtained by fitting the photo-stimulated luminescence (PSL) per Au ion for different ion energies, which is broadly in agreement with that expected from ion stopping in the active layer of the IP. This calibration would allow quantifying the ion energy spectra for high energy Au ions, which is important for further investigation of the laser-based acceleration of heavy ion beams.
High power lasers have proven being capable to produce high energy gamma rays, charged particles and neutrons to induce all kinds of nuclear reactions. At ELI, the studies with high power lasers will enter for the first time into new domains of power and intensities.
We report the signatures of dynamic spin fluctuations in the layered honeycomb Li$_3$Cu$_2$SbO$_6$ compound, with a 3$d$ S = 1/2 $d^9$ Cu$^{2+}$ configuration, through muon spin rotation and relaxation ($\mu$SR) and neutron scattering studies. Our zero-field (ZF) and longitudinal-field (LF)-$\mu$SR results demonstrate the slowing down of the Cu$^{2+}$ spin fluctuations below 4.0 K. The saturation of the ZF relaxation rate at low temperature, together with its weak dependence on the longitudinal field between 0 and 3.2 kG, indicates the presence of dynamic spin fluctuations persisting even at 80 mK without static order. Neutron scattering study reveals the gaped magnetic excitations with three modes at 7.7, 13.5 and 33 meV. Our DFT calculations reveal that the next nearest neighbors (NNN) AFM exchange ($J_{AFM}$ = 31 meV) is stronger than the NN FM exchange ($J_{FM}$ = -21 meV) indicating the importance of the orbital degrees of freedom. Our results suggest that the physics of Li$_3$Cu$_2$SbO$_6$ can be explained by an alternating AFM chain rather than the honeycomb lattice.
Magnetized plasma interactions are ubiquitous in astrophysical and laboratory plasmas. Various physical effects have been shown to be important within colliding plasma flows influenced by opposing magnetic fields, however, experimental verification of the mechanisms within the interaction region has remained elusive. Here we discuss a laser-plasma experiment whereby experimental results verify that Biermann battery generated magnetic fields are advected by Nernst flows and anisotropic pressure effects dominate these flows in a reconnection region. These fields are mapped using time-resolved proton probing in multiple directions. Various experimental, modelling and analytical techniques demonstrate the importance of anisotropic pressure in semi-collisional, high-$β$ plasmas, causing a reduction in the magnitude of the reconnecting fields when compared to resistive processes. Anisotropic pressure dynamics are crucial in collisionless plasmas, but are often neglected in collisional plasmas. We show pressure anisotropy to be essential in maintaining the interaction layer, redistributing magnetic fields even for semi-collisional, high energy density physics (HEDP) regimes
Breakability rate of fragile item depends on the accumulated stress of heaped stock level. So breakablility rate can be considered as dependent parameter of stock variable. The unit production cost is a function of production rate and also dependent on raw material cost, development cost and wear-tear cost. The holding cost is assumed to be non-linear, dependent on time. Here optimal control problem for a fragile item under finite time horizon is considered. The profit function which consists of revenue, production and holding costs is formulated as a Fixed-Final Time and Fixed State System(cf. Naidu (2000)) optimal control problem with finite time horizon. Here production rate is unknown and considered as a control variable and stock level is taken as a state variable. It is formulated to optimize the production rate so that total profit is maximum. As particular cases, models are evaluated with and without breakability. The models are solved by using conventional Variational Principle along with the non-linear optimization technique-Generalised Reduced Gradient Method (LINGO 12.0). The optimum results are illustrated both numerically and graphically. Some sensitivity analysis on breakability coefficient are presented.
The Time-of-Flight (ToF) technique coupled with semiconductor-like detectors, as silicon carbide and diamond, is one of the most promising diagnostic methods for high-energy, high repetition rate, laser-accelerated ions allowing a full on-line beam spectral characterization. A new analysis method for reconstructing the energy spectrum of high-energy laser-driven ion beams from TOF signals is hereby presented and discussed. The proposed method takes into account the detector's working principle, through the accurate calculation of the energy loss in the detector active layer, using Monte Carlo simulations. The analysis method was validated against well-established diagnostics, such as the Thomson Parabola Spectrometer, during an experimental campaign carried out at the Rutherford Appleton Laboratory (RAL, UK) with the high-energy laser-driven protons accelerated by the VULCAN Petawatt laser.
We establish the primary decomposition and uniqueness of primary decomposition for k-ideals in commutative Noetherian semirings.
We derive an effective Hamiltonian for the two-dimensional Hubbard-Holstein model in the regimes of strong electron-electron and strong electron-phonon interactions by using a nonperturbative approach. In the parameter region where the system manifests the existence of a correlated singlet phase, the effective Hamiltonian transforms to a $t_1-V_1-V_2-V_3$ Hamiltonian for hard-core-bosons on a checkerboard lattice. We employ quantum Monte Carlo simulations, involving stochastic-series-expansion technique, to obtain the ground state phase diagram. At filling $1/8$, as the strength of off-site repulsion increases, the system undergoes a first-order transition from a superfluid to a diagonal striped solid with ordering wavevector $\vec{Q}=(π/4,3π/4)$ or $(π/4,5π/4)$. Unlike the one-dimensional situation, our results in the two-dimensional case reveal a supersolid phase (corresponding to the diagonal striped solid) around filling $1/8$ and at large off-site repulsions. Furthermore, for small off-site repulsions, we witness a valence bond solid at one-fourth filling and tiny phase-separated regions at slightly higher fillings.
We study M1-transitions involving mesons: $B_c(1s)$, $B_c^*(1s)$, $B_c(2s)$, $B_c^*(2s)$, $B_c(3s)$ and $B_c^*(3s)$ in the relativistic independent quark (RIQ) model based on a flavor independent average potential in the scalar-vector harmonic form. The transition form factor for $B_c^*\to B_cγ$ is found to have analytical continuation from spacelike to physical timelike region. Our predicted coupling constant $g_{B_c^* B_c}$ = 0.34 Ge$V^{-1}$ and decay width $Γ(B_c^*\to B_cγ)$ = 23 eV agree with other model predictions. In view of possible observation of $B_c$ and $B_c^*$ s-wave states at LHC and Z-factory and potential use of theoretical estimate on M1-transitions, we investigate the allowed as well as hindered transitions of orbitally excited $B_c$-meson states and predict their decay widths in overall agreement with other model predictions. We consider the typical case of $B_c^*(1s)\to B_c(1s)γ$, where our predicted decay width which is found quite sensitive to the mass difference between $B_c^*$ and $B_c$ mesons may help in determining the mass of $B_c^*$ experimentally.
Millions of surveillance cameras operate at 24x7 generating huge amount of visual data for processing. However, retrieval of important activities from such a large data can be time consuming. Thus, researchers are working on finding solutions to present hours of visual data in a compressed, but meaningful way. Video synopsis is one of the ways to represent activities using relatively shorter duration clips. So far, two main approaches have been used by researchers to address this problem, namely synopsis by tracking moving objects and synopsis by clustering moving objects. Synopses outputs, mainly depend on tracking, segmenting, and shifting of moving objects temporally as well as spatially. In many situations, tracking fails, thus produces multiple trajectories of the same object. Due to this, the object may appear and disappear multiple times within the same synopsis output, which is misleading. This also leads to discontinuity and often can be confusing to the viewer of the synopsis. In this paper, we present a new approach for generating compressed video synopsis by grouping tracklets of moving objects. Grouping helps to generate a synopsis where chronologically related objects appear together with meaningful spatio-temporal relation. Our proposed method produces continuous, but a less confusing synopses when tested on publicly available dataset videos as well as in-house dataset videos.
We report on the experimental observation of beam-like neutron emission with peak flux of the order of 10^9 n/sr, from light nuclei reactions in a pitcher-catcher scenario, by employing MeV ions driven by high power laser. The spatial profile of the neutron beam, fully captured for the first time by employing a CR39 nuclear track detector, shows a FWHM divergence angle of 70 degrees, with a peak flux nearly an order of magnitude higher than the isotropic component elsewhere. The observed beamed flux of neutrons is highly favourable for a wide range of applications, and indeed for further transport and moderation to thermal energies. A systematic study employing various combinations of pitcher-catcher materials indicates the dominant reactions being d(p, n+p)^1H and d(d,n)^3He. Albeit insufficient cross-section data are available for modelling, the observed anisotropy in the neutrons' spatial and spectral profiles are most likely related to the directionality and high energy of the projectile ions.
Calibration of three scintillators (EJ232Q, BC422Q and EJ410) in a time-of-flight (TOF) arrangement using a laser drive-neutron source is presented. The three plastic scintillator detectors were calibrated with gamma insensitive bubble detector spectrometers, which were absolutely calibrated over a wide range of neutron energies ranging from sub MeV to 20 MeV. A typical set of data obtained simultaneously by the detectors are shown, measuring the neutron spectrum emitted from a petawatt laser irradiated thin foil.
The paper is concerned with distributed learning and optimization in large-scale settings. The well-known Fictitious Play (FP) algorithm has been shown to achieve Nash equilibrium learning in certain classes of multi-agent games. However, FP can be computationally difficult to implement when the number of players is large. Sampled FP is a variant of FP that mitigates the computational difficulties arising in FP by using a Monte-Carlo (i.e., sampling-based) approach. The Sampled FP algorithm has been studied both as a tool for distributed learning and as an optimization heuristic for large-scale problems. Despite its computational advantages, a shortcoming of Sampled FP is that the number of samples that must be drawn in each round of the algorithm grows without bound (on the order of $\sqrt{t}$, where $t$ is the round of the repeated play). In this paper we propose Computationally Efficient Sampled FP (CESFP)---a variant of Sampled FP in which only one sample need be drawn each round of the algorithm (a substantial reduction from $O(\sqrt{t})$ samples per round, as required in Sampled FP). CESFP operates using a stochastic-approximation type rule to estimate the expected utility from round to round. It is proven that the CESFP algorithm achieves Nash equilibrium learning in the same sense as classical FP and Sampled FP. Simulation results suggest that the convergence rate of CESFP (in terms of repeated-play iterations) is similar to that of Sampled FP.