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Sachin Kumar

Publications and source records attributed to Sachin Kumar.

At least 91 records · Page 5Linked to original sources
arXiv2020

On exact solutions, conservation laws and invariant analysis of the generalized Rosenau-Hyman equation

In this paper, the nonlinear Rosenau-Hyman equation with time dependent variable coefficients is considered for investigating its invariant properties, exact solutions and conservation laws. Using Lie classical method, we derive symmetries admitted by considered equation. Symmetry reductions are performed for each components of optimal set. Also nonclassical approach is employed on considered equation to find some additional supplementary symmetries and corresponding symmetry reductions are performed. Later three kinds of exact solutions of considered equation are presented graphically for different parameters. In addition, local conservation laws are constructed for considered equation by multiplier approach.

nlin.SI↗
arXiv2020

PT-symmetric potentials with imaginary asymptotic saturation

We point out that PT-symmetric potentials $V_{PT}(x)$ having imaginary asymptotic saturation: $V_{PT}(x=\pm \infty) =\pm i V_1, V_1 \in \Re$ are devoid of scattering states and spectral singularity. We show the existence of real (positive and negative) discrete spectrum both with and without complex conjugate pair(s) of eigenvalues (CCPEs). If the states are arranged in the ascending order or real part of discrete eigenvalues, the initial states have few nodes but latter ones oscillate fast. Both real and imaginary parts of $ψ(x)$ vanish asymptotically, $|ψ(x)|$ for the CCPEs are asymmetric and for real energies these are symmetric about origin. For CCPEs $E_{\pm}$ the eigenstates $ψ_{\pm}$ follow an interesting property that $|ψ_+(x)|= N |ψ_-(-x)|, N \in \Re^+$. We remark that, the fast oscillating real discrete energy states discussed are likely to be confused with: reflectionless states, one dimensional version of von Neumann states of Hermitian and spectral singularity state of complex PT-symmetric potentials.

quant-ph↗
arXiv2020

Low reflection at zero or low-energies in the well-barrier scattering potentials

Probability of reflection $R(E)$ off a finite attractive scattering potential at zero or low energies is ordinarily supposed to be 1. However, a fully attractive potential presents a paradoxical result that $R(0)=0$ or $R(0)<1$, when an effective parameter $q$ of the potential admits special discrete values. Here, we report another class of finite potentials which are well-barrier (attractive-repulsive) type and which can be made to possess much less reflection at zero and low energies for a band of low values of $q$. These well-barrier potentials have only two real turning points for $E \in(V_{min}, V_{max})$, excepting $E=0$. We present two exactly solvable and two numerically solved models to confirm this phenomenon.

quant-ph↗
arXiv2019

Symmetric Fermi-type potential

We utilize the amenability of the Fermi-type potential profile in Schr{ö}dinger equation to construct a symmetric one dimensional well as $V(x){=}{-}U_n/[1+\exp[(|x|{-}a)/b]], ~ U_n{=}V_n[1+\exp[-a/b]]$. We define $α=a/b, ~β_n {=}b\sqrt{2m U_n}/\hbar$, we find $β_n$ values for which critically the well has $n$-node half bound state at $E{=}0$. Consequently, this fixed well has $n$ number of bound states. Also we obtain a semi-classical expression ${\cal G}(α,β)$ such that the Fermi well has either $[\cal G]$ or $[{\cal G}]+1$ number of bound states. Here $[.]$ indicates the integer part. We also confirm the consistency of $\cal G$ with the number of s-wave neutron energy levels in a central ($x\in (0,\infty))$ Fermi potential well.

quant-ph↗
arXiv2019

Solvable model of bound states in the continuum (BIC) in one dimension

Historically, most of the quantum mechanical results have originated in one dimensional model potentials. However, Von-Neumann's Bound states in the Continuum (BIC) originated in specially constructed, three dimensional, oscillatory, central potentials. One dimensional version of BIC has long been attempted, where only quasi-exactly-solvable models have succeeded but not without instigating degeneracy in one dimension. Here, we present an exactly solvable bottomless exponential potential barrier $V(x)=-V_0[\exp(2|x|/a)-1]$ which for $E V_0$, there is again a continuum of complex scattering solutions $ψ(x)$ whose real and imaginary parts though solutions of Schr{ö}dinger equation yet their parities cannot be ascertained as $Cψ(x)$ is also a solution where $C$ is an arbitrary complex non-real number.

quant-ph↗
arXiv2019

Expectation value of $p^6$ in continuous two-piece symmetric potential wells

Earlier, potentials like square well and several other half-potential wells with discontinuous jump have been found to have the expectation value $<\! p^6 \!>$ to be divergent for all bound states. Here, we consider two-piece symmetric potential wells to prove and demonstrate that in them the expectation value of $p^6$ diverges for even states and converges for odd states. Here, $p$ denotes momentum. We also present three exactly solvable models.

quant-ph↗
arXiv2019

Von Mises-Fisher Loss for Training Sequence to Sequence Models with Continuous Outputs

The Softmax function is used in the final layer of nearly all existing sequence-to-sequence models for language generation. However, it is usually the slowest layer to compute which limits the vocabulary size to a subset of most frequent types; and it has a large memory footprint. We propose a general technique for replacing the softmax layer with a continuous embedding layer. Our primary innovations are a novel probabilistic loss, and a training and inference procedure in which we generate a probability distribution over pre-trained word embeddings, instead of a multinomial distribution over the vocabulary obtained via softmax. We evaluate this new class of sequence-to-sequence models with continuous outputs on the task of neural machine translation. We show that our models obtain upto 2.5x speed-up in training time while performing on par with the state-of-the-art models in terms of translation quality. These models are capable of handling very large vocabularies without compromising on translation quality. They also produce more meaningful errors than in the softmax-based models, as these errors typically lie in a subspace of the vector space of the reference translations.

cs.CL↗
arXiv2018

Optimization and Neural Network-Based Modelling of Surface Passivation Effectiveness by Hydrogenated Amorphous Silicon for Solar Cell Applications

Intrinsic hydrogenated amorphous silicon films can provide outstanding surface passivation of crystalline silicon wafer surfaces. This quality of Intrinsic hydrogenated amorphous silicon makes it valuable in heterojunction with intrinsic thin layer (HIT) solar cell fabrication. This paper describes the material characteristics and electronic properties of Intrinsic hydrogenated amorphous silicon that affects its passivation quality. A study of passivation quality of intrinsic hydrogenated amorphous silicon layer has been done with respect to deposition parameters in Plasma Enhanced Chemical Vapor Deposition (PECVD), the most commonly used method of its deposition. It was found that very good surface passivation with surface recombination velocity < 50 cm/s can be obtained from thickness of 30 nm of Intrinsic hydrogenated amorphous silicon (a-Si:H(i)), which is better than most other passivation techniques. A mathematical model based on Artificial Neural Network (ANN) is designed to predict the carrier lifetime for a given deposition condition and it is shown that the prediction capability of developed ANN model varies with the number of neurons in the hidden layer using Akaike Information Criterion (AIC), which is a widely accepted model selection method for measuring the validity of nonlinear models.

physics.app-ph↗
arXiv2018

Three types of discrete energy eigenvalues in complex PT-symmetric scattering potentials

For complex PT-symmetric scattering potentials (CPTSSPs) $V(x)= V_1 f_{even}(x) + iV_2 f_{odd}(x), f_{even}(\pm \infty) = 0 = f_{odd}(\pm \infty), V_1,V_2 \in \Re $, we show that complex $k$-poles of transmission amplitude $t(k)$ or zeros of $1/t(k)$ of the type $\pm k_1+ik_2, k_2\ge 0$ are physical which yield three types of discrete energy eigenvalues of the potential. These discrete energies are real negative, complex conjugate pair(s) of eigenvalues (CCPEs: ${\cal E}_n \pm i γ_n$) and real positive energy called spectral singularity (SS) at $E=E_*$ where the transmission and reflection co-efficient of $V(x)$ become infinite for a special critical value of $V_2=V_*$. Based on four analytically solvable and other numerically solved models, we conjecture that a parametrically fixed CPTSSP has at most one SS. When $V_1$ is fixed and $V_2$ is varied there may exist Kato's exceptional point(s) $(V_{EP})$ and critical values $V_{*m}, m=0,1,2,..$, so when $V_2$ crosses one of these special values a new CCPE is created. When $V_2$ equals a critical value $V_{*m}$ there exist one SS at $E=E_*$ along with $m$ or more number of CCPEs. Hence, this single positive energy $E_*$ is the upper (or rough upper) bound to the CCPEs: ${\cal E}_l \lessapprox E_*$, here ${\cal E}_l$ corresponds to the last of CCPEs. If $V(x)$ has Kato's exceptional points (EPs: $V_{EP1}<V_{EP2}<V_{EP3}<...<V_{EPl}$), the smallest of critical values $V_{*m}$ is always larger than $V_{EPl}$. Hence, in a CPTSSP, real discrete eigenvalue(s) and the SS are mutually exclusive whereas CCPEs and the SS can co-exist .

quant-ph↗
arXiv2018

New solitary wave and Multiple soliton solutions of (3 + 1)-dimensional KdV type equation by using Lie symmetry approach

Solitary waves are localized gravity waves that preserve their consistency and henceforth their visibility through properties of nonlinear hydrodynamics. Solitary waves have finite amplitude and spread with constant speed and constant shape. In this paper, we have used Lie group of transformation method to solve (3 + 1)-dimensional KdV type equation. We have obtained the infinitesimal generators, commutator table of Lie algebra for the KdV type equation. We have achieved a number of exact solutions of KdV type equation in the explicit form through similarity reduction. All the reported results are expressed in analytic (closed form) and figured out graphically through their evolution solution profiles. We characterized the physical explanation of the obtained solutions with the free choice of the particular parameters by plotting some 3D and 2D illustrations. The geometrical analysis explains that the nature of solutions is travelling wave, kink wave, single solitons, doubly solitons and curve-shaped multisolitons.

math-ph↗
arXiv2018

Assessing the Effects of Treatment in HIV-TB Co-infection Model

We propose a population model for HIV-TB co-infection dynamics by considering treatments for HIV infection, active tuberculosis and co-infection. The HIV only and TB only models are analyzed separately, as well as full model. The basic reproduction numbers for TB ($\mathcal{R}_0^T$) and HIV ($\mathcal{R}_0^H$) and overall reproduction number for the system $\mathcal{R}_0= \max\{\mathcal{R}_0^T, \mathcal{R}_0^H\}$ are computed. The equilibria and their stability are studied. The main model undergoes supercritical transcritical bifurcation at $\mathcal{R}_0^T=1$ and $\mathcal{R}_0^H=1$ whereas the parameters $β^*=βe$ and $λ^*=λσ$ act as bifurcation parameters, respectively. Numerical simulation claims the existence of interior equilibrium when both the reproduction numbers are greater than unity. We explore the effect of early and late HIV treatment on disease-induced deaths during the TB treatment course. Mathematical analysis of our model shows that successful disease eradication requires treatment of single disease, that is, treatment for HIV only and TB only infected individuals with addition to co-infection treatment and in absence of which disease eradication is extremely difficult even for $\mathcal{R}_0<1$. When both the diseases are epidemic, the treatment for TB only infected individuals is very effective in reducing the total infected population and disease-induced deaths in comparison to the treatment for HIV infected individuals while these are minimum when both the single disease treatments are given with co-infection treatment.

q-bio.PE↗
arXiv2018

Lie symmetry analysis and new periodic solitary wave solutions of (3+1)-dimensional generalized shallow water wave equation

Many important physical situations such as fluid flows, marine environment, solid-state physics and plasma physics have been represented by shallow water wave equation. In this article, we construct new solitary wave solutions for the (3+1)-dimensional generalized shallow water wave (GSWW) equation by using Lie symmetry method. A variety of analytic (closed-form) solutions such as new periodic solitary wave, cross-kink soliton and doubly periodic breather-type solutions have been obtained by using invariance of the concerned (3+1)-dimensional GSWW equation under one-parameter Lie group of transformations. Lie symmetry transformations have applied to generate the different forms of invariant solutions of the (3+1)-dimensional GSWW equation. For different Lie algebra, Lie symmetry method reduces (3+1)-dimensional GSWW equation into various ordinary differential equations (ODEs) while one of the Lie algebra, it is transformed into the well known (2+1)-dimensional BLMP equation. It is affirmed that the proposed techniques are convenient, genuine and powerful tools to find the exact solutions of nonlinear partial differential equations (PDEs). Under the suitable choices of arbitrary functions and parameters, 2D, 3D and contour graphics to the obtained results of GSWW equation are also analyzed graphically.

nlin.PS↗
arXiv2018

1-Multisoliton and other invariant solutions of combined KdV - nKdV equation by using symmetry approach

Lie symmetry method is applied to investigate symmetries of the combined KdV-nKdV equation, that is a new integrable equation by combining the KdV equation and negative order KdV equation. Symmetries which are obtained in this article, are further helpful for reducing the combined KdV-nKdV equation into ordinary differential equation. Moreover, a set of eight invariant solutions for combined KdV-nKdV equation is obtained by using proposed method. Out of the eight solutions so obtained in which two solutions generate progressive wave solutions, five are singular solutions and one multisoliton solutions which is in terms of WeierstrassZeta function.

math-ph↗
arXiv2018

Novel Hard Link-Switching Scheme using Pre-Scanning for Indoor VLC Networks

VLC is attracting a lot of attention as an emerging potential technology for deployment in next generation indoor wireless networks. Use of efficient link switching scheme among VLC access points is critical in indoor environment to provide seamless connectivity to mobile users. This paper presents a novel position prediction link switching scheme for indoor visible light communication systems. The method exploits the fact that indoor scenario (light fixtures/furniture) mostly remains unchanged, therefore, this information can be stored at the coordinator end. Thus, the user is not required to search for the best transmitter when RSS is reduced to a threshold value as in conventional methods which cause substantial delay in switching process. Simulation results show that the proposed scheme for indoor VLC System achieves the dual purpose of adequate illumination and mobility to user in considered indoor scenario.

eess.SP↗
arXiv2018

Precision Sugarcane Monitoring Using SVM Classifier

India is agriculture based economy and sugarcane is one of the major crops produced in northern India. Productivity of sugarcane decreases due to inappropriate soil conditions and infections caused by various types of diseases , timely and accurate disease diagnosis, plays an important role towards optimizing crop yield. This paper presents a system model for monitoring of sugarcane crop, the proposed model continuously monitor parameters (temperature, humidity and moisture) responsible for healthy growth of the crop in addition KNN clustering along with SVM classifier is utilized for infection identification if any through images obtained at regular intervals. The data has been transmitted wirelessly from the site to the control unit. Model achieves an accuracy of 96% on a sample of 200 images, the model was tested at Lolai, near Malhaur, Gomti Nagar Extension.

cs.CV↗
arXiv2018

Pearson's correlation coefficient in the theory of networks: A comment

In statistics, the Pearson correlation coefficient $r_{x,y}$ determines the degree of linear correlation between two variables and it is known that $-1 \le r_{x,y} \le 1$. In the theory of networks, a curious expression proposed in [PRL {\bf 89} 208701 (2002)] for degree-degree correlation coefficient $r_{j_i,k_i}, i\in [1,M]$ has been in use. We realize that the suggested form is the conventional Pearson's coefficient for $\{(j_i,k_i), (k_i,j_i)\}$ for $2M$ data points and hence it is rightly dedicated to undirected networks.

cond-mat.dis-nn↗
arXiv2018

Automated Detection of Acute Leukemia using K-mean Clustering Algorithm

Leukemia is a hematologic cancer which develops in blood tissue and triggers rapid production of immature and abnormal shaped white blood cells. Based on statistics it is found that the leukemia is one of the leading causes of death in men and women alike. Microscopic examination of blood sample or bone marrow smear is the most effective technique for diagnosis of leukemia. Pathologists analyze microscopic samples to make diagnostic assessments on the basis of characteristic cell features. Recently, computerized methods for cancer detection have been explored towards minimizing human intervention and providing accurate clinical information. This paper presents an algorithm for automated image based acute leukemia detection systems. The method implemented uses basic enhancement, morphology, filtering and segmenting technique to extract region of interest using k-means clustering algorithm. The proposed algorithm achieved an accuracy of 92.8% and is tested with Nearest Neighbor (KNN) and Naive Bayes Classifier on the data-set of 60 samples.

cs.CV↗