arXiv subjects

P. K. Mishra

Publications and source records attributed to P. K. Mishra.

At least 19 recordsLinked to original sources

arXiv2026

Stability and dynamics of dark-bright solitons in spin-orbit- and Rabi-coupled binary Bose-Einstein condensates

We investigate the stability and nonlinear dynamics of dark--bright solitons in a one-dimensional binary Bose--Einstein condensate subjected to synthetic spin--orbit and Rabi couplings. In the absence of spin--orbit coupling, we map the coupled Gross--Pitaevskii equations onto the integrable Manakov model to obtain exact dark--bright soliton solutions, providing a rigorous theoretical benchmark. We demonstrate that finite spin--orbit coupling breaks integrability by inducing spin-dependent phase gradients that drive component-wise spatial separation and intrinsic density oscillations. By contrast, coherent Rabi driving enforces phase locking between spin components and supports robust breather-like excitations. Furthermore, we derive analytical continuity relations for mass and spin current densities, mapping the internal spin dynamics onto an internal Josephson-junction framework in which the gauge field acts as a continuous spatial momentum bias. Using imaginary-time propagation together with Bogoliubov--de Gennes analysis, we systematically characterise ground-state phases and excitation spectra for both symmetric and asymmetric interaction regimes in homogeneous and harmonically trapped systems. Real-time simulations further demonstrate that synthetic gauge fields and interaction quenches drive the system far from equilibrium, triggering modulational-instability-induced multi-soliton fragmentation, breathing stripe patterns, and non-equilibrium transport. Our results highlight the interplay of synthetic gauge fields, external confinement, and interaction engineering as powerful tools for controlling the stability and internal dynamics of multicomponent quantum fluids.

cond-mat.quant-gas↗

arXiv2023

On the Experimental Evidence for Possible Superconductivity in LK99

The desire to create an energy efficient world is bound to be incomplete without the discovery of a room temperature superconductor at ambient pressure. A recent report on the room-temperature ambient-pressure superconductor has inspired scientists to study the Cu doped Lead apatite named as LK-99. Here, we have synthesized Cu doped LK-99 and Ni-doped LK-99 compounds and studied their temperature dependent transport and magnetization behavior. In spite of the presence of impurity phase Cu$_2$S, the temperature dependent resistance shows an insulating nature of the sample. The radio frequency penetration depth measurement unveils the absence of diamagnetic flux expulsion in this sample. The temperature dependent ac susceptibility measurements reveal the paramagnetic nature of the Ni doped LK-99.

cond-mat.supr-con↗

arXiv2023

Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter

In this work we study the following nonlocal problem \begin{equation*} \left\{ \begin{aligned} M(\|u\|^2_X)(-Δ)^s u&= λ{f(x)}|u|^{γ-2}u+{g(x)}|u|^{p-2}u &&\mbox{in}\ \ Ω, u&=0 &&\mbox{on}\ \ \mathbb R^N\setminus Ω, \end{aligned} \right. \end{equation*} where $Ω\subset \mathbb R^N$ is open and bounded with smooth boundary, $N>2s, s\in (0, 1), M(t)=a+bt^{θ-1},\;t\geq0$ with $ θ>1, a\geq 0$ and $b>0$. The exponents satisfy $1<γ<2<{2θ<p<2^*_{s}=2N/(N-2s)}$ (when $a\neq 0$) and $2<γ<2θ<p<2^*_{s}$ (when $a=0$). The parameter $λ$ involved in the problem is real and positive. The problem under consideration has nonlocal behaviour due to the presence of nonlocal fractional Laplacian operator as well as the nonlocal Kirchhoff term $M(\|u\|^2_X)$, where $\|u\|^{2}_{X}=\iint_{\mathbb R^{2N}} \frac{|u(x)-u(y)|^2}{\left|x-y\right|^{N+2s}}dxdy$. The weight functions $f, g:Ω\to \mathbb R$ are continuous, $f$ is positive while $g$ is allowed to change sign. In this paper an extremal value of the parameter, a threshold to apply Nehari manifold method, is characterized variationally for both degenerate and non-degenerate Kirchhoff cases to show an existence of at least two positive solutions even when $λ$ crosses the extremal parameter value by executing fine analysis based on fibering maps and Nehari manifold.

math.AP↗

arXiv2019

RDD-Eclat: Approaches to Parallelize Eclat Algorithm on Spark RDD Framework

Initially, a number of frequent itemset mining (FIM) algorithms have been designed on the Hadoop MapReduce, a distributed big data processing framework. But, due to heavy disk I/O, MapReduce is found to be inefficient for such highly iterative algorithms. Therefore, Spark, a more efficient distributed data processing framework, has been developed with in-memory computation and resilient distributed dataset (RDD) features to support the iterative algorithms. On the Spark RDD framework, Apriori and FP-Growth based FIM algorithms have been designed, but Eclat-based algorithm has not been explored yet. In this paper, RDD-Eclat, a parallel Eclat algorithm on the Spark RDD framework is proposed with its five variants. The proposed algorithms are evaluated on the various benchmark datasets, which shows that RDD-Eclat outperforms the Spark-based Apriori by many times. Also, the experimental results show the scalability of the proposed algorithms on increasing the number of cores and size of the dataset.

cs.DC↗

arXiv2019

Reorientation of large-scale circulation of turbulent Rayleigh-Bénard convection in a cubic cell

We present a direct numerical simulation on the dynamics of large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection of air (Pr = 0.7) contained in a cubic cell for Rayleigh number range 2X10^6 < Ra < 10^9 . The strength and orientation of LSC are quantified by the amplitude and phase of the first Fourier mode of the vertical velocity. The plane containing LSC is generally aligned along one of the diagonals of the box accompanied by a four-roll structure in the other. However, an abnormal single-roll state with substructures is noted at the face planes for low Ra. In addition to the primary roll, two secondary corner-roll structures are also observed in the LSC plane which grow in size and destabilize the LSC resulting in partial and complete reversals. In addition to previously reported rotation-led reorientations, we also observe cessation events which are rare in cubic cells. The distribution of turbulent kinetic energy shows that the energy is primarily extracted from the non-LSC plane and fed to the LSC plane by the transport mechanism. We observe that the corner-rolls reduce in size and the substructures diminish at higher Ra, which leads to the reduction in the occurrence of reorientations of LSC.

physics.flu-dyn↗

arXiv2019

A Data Structure Perspective to the RDD-based Apriori Algorithm on Spark

During the recent years, a number of efficient and scalable frequent itemset mining algorithms for big data analytics have been proposed by many researchers. Initially, MapReduce-based frequent itemset mining algorithms on Hadoop cluster were proposed. Although, Hadoop has been developed as a cluster computing system for handling and processing big data, but the performance of Hadoop does not meet the expectation for the iterative algorithms of data mining, due to its high I/O, and writing and then reading intermediate results in the disk. Consequently, Spark has been developed as another cluster computing infrastructure which is much faster than Hadoop due to its in-memory computation. It is highly suitable for iterative algorithms and supports batch, interactive, iterative, and stream processing of data. Many frequent itemset mining algorithms have been re-designed on the Spark, and most of them are Apriori-based. All these Spark-based Apriori algorithms use Hash Tree as the underlying data structure. This paper investigates the efficiency of various data structures for the Spark-based Apriori. Although, the data structure perspective has been investigated previously, but for MapReduce-based Apriori, and it must be re-investigated in the distributed computing environment of Spark. The considered underlying data structures are Hash Tree, Trie, and Hash Table Trie. The experimental results on the benchmark datasets show that the performance of Spark-based Apriori with Trie and Hash Table Trie are almost similar but both perform many times better than Hash Tree in the distributed computing environment of Spark.

cs.DC↗

arXiv2019

Mining Association Rules in Various Computing Environments: A Survey

Association Rule Mining (ARM) is one of the well know and most researched technique of data mining. There are so many ARM algorithms have been designed that their counting is a large number. In this paper we have surveyed the various ARM algorithms in four computing environments. The considered computing environments are sequential computing, parallel and distributed computing, grid computing and cloud computing. With the emergence of new computing paradigm, ARM algorithms have been designed by many researchers to improve the efficiency by utilizing the new paradigm. This paper represents the journey of ARM algorithms started from sequential algorithms, and through parallel and distributed, and grid based algorithms to the current state-of-the-art, along with the motives for adopting new machinery.

cs.DC↗

arXiv2018

Super critical problems with concave and convex nonlinearities in $\mathbb R^N$

In this paper, by utilizing a newly established variational principle on convex sets, we provide an existence and multiplicity result for a class of semilinear elliptic problems defined on the whole $\mathbb R^N$ with nonlinearities involving sublinear and superlinear terms. We shall impose no growth restriction on the nonlinear term and consequently our problem can be super-critical by means of Sobolev spaces.

math.AP↗

arXiv2018

Nehari Manifold for fractional Kirchhoff system with critical nonlinearity

In this paper, we show the existence and multiplicity of positive solutions of the following fractional Kirchhoff system\\ \begin{equation} \left\{ \begin{array}{rllll} \mc L_M(u)&=λf(x)|u|^{q-2}u+ \frac{2α}{α+β}\left|u\right|^{α-2}u|v|^β& \text{in } Ω,\\ \mc L_M(v)&=μg(x)|v|^{q-2}v+ \frac{2β}{α+β}\left|u\right|^α|v|^{β-2}v & \text{in } Ω,\\ u&=v=0 &\mbox{in } \mathbb{R}^{N}\setminus Ω, \end{array} \right. \end{equation} where $\mc L_M(u)=M\left(\displaystyle \int_Ω|(-Δ)^{\frac{s}{2}}u|^2dx\right)(-Δ)^{s} u $ is a double non-local operator due to Kirchhoff term $M(t)=a+b t$ with $a, b>0$ and fractional Laplacian $(-Δ)^{s}, s\in(0, 1)$. We consider that $Ω$ is a bounded domain in $\mathbb{R}^N$, {$2s 0$ are {real} parameters, $1<q<2$, $α, β\ge 2$ {and} $α+β=2_s^*={2N}/(N-2s)$ {is a fractional critical exponent}. Using the idea of Nehari manifold technique and a compactness result based on {classical idea of Brezis-Lieb Lemma}, we prove the existence of at least two positive solutions for $(λ, μ)$ lying in a suitable subset of $\mathbb R^2_+$.

math.AP↗

arXiv2018

Solutions concentrating around the saddle points of the potential for Schrödinger equations with critical exponential growth

In this paper, we deal with the following nonlinear Schrödinger equation $$ -ε^2Δu+V(x)u=f(u),\ u\in H^1(\mathbb R^2), $$ where $f(t)$ has critical growth of Trudinger-Moser type. By using the variational techniques, we construct a positive solution $u_ε$ concentrating around the saddle points of the potential $V(x)$ as $ε\rightarrow 0$. Our results complete the analysis made in \cite{MR2900480} and \cite{MR3426106}, where the Schrödinger equation was studied in $\mathbb R^N$, $N\geq 3$ for sub-critical and critical case respectively in the sense of Sobolev embedding. Moreover, we relax the monotonicity condition on the nonlinear term $f(t)/t$ together with a compactness assumption on the potential $V(x)$, imposed in \cite{MR3503193}.

math.AP↗

arXiv2017

Fractional Kirchhoff problem with critical indefinite nonlinearity

We study the existence and multiplicity of positive solutions for a family of fractional Kirchhoff equations with critical nonlinearity of the form \begin{equation*} M\left(\int_Ω|(-Δ)^{\fracα{2}}u|^2dx\right)(-Δ)^α u= λf(x)|u|^{q-2}u+|u|^{2^*_α-2}u\;\; \text{in}\; Ω,\;u=0\;\textrm{in}\;\mathbb R^n\setminus Ω, \end{equation*} where $Ω\subset \mathbb R^n$ is a smooth bounded domain, $ M(t)=a+\varepsilon t, \; a, \; \varepsilon>0,\; 0<α<1, \; 2α<n<4α$ and $ \; 1<q<2$. Here $2^*_α={2n}/{(n-2α)}$ is the fractional critical Sobolev exponent, $λ$ is a positive parameter and the coefficient $f(x)$ is a real valued continuous function which is allowed to change sign. By using a variational approach based on the idea of Nehari manifold technique, we combine effects of a sublinear and a superlinear term to prove our main results.

math.AP↗

arXiv2017

A Comparative Study of Association Rule Mining Algorithms on Grid and Cloud Platform

Association rule mining is a time consuming process due to involving both data intensive and computation intensive nature. In order to mine large volume of data and to enhance the scalability and performance of existing sequential association rule mining algorithms, parallel and distributed algorithms are developed. These traditional parallel and distributed algorithms are based on homogeneous platform and are not lucrative for heterogeneous platform such as grid and cloud. This requires design of new algorithms which address the issues of good data set partition and distribution, load balancing strategy, optimization of communication and synchronization technique among processors in such heterogeneous system. Grid and cloud are the emerging platform for distributed data processing and various association rule mining algorithms have been proposed on such platforms. This survey article integrates the brief architectural aspect of distributed system, various recent approaches of grid based and cloud based association rule mining algorithms with comparative perception. We differentiate between approaches of association rule mining algorithms developed on these architectures on the basis of data locality, programming paradigm, fault tolerance, communication cost, partition and distribution of data sets. Although it is not complete in order to cover all algorithms, yet it can be very useful for the new researchers working in the direction of distributed association rule mining algorithms.

cs.DC↗

arXiv2017

Review of Apriori Based Algorithms on MapReduce Framework

The Apriori algorithm that mines frequent itemsets is one of the most popular and widely used data mining algorithms. Now days many algorithms have been proposed on parallel and distributed platforms to enhance the performance of Apriori algorithm. They differ from each other on the basis of load balancing technique, memory system, data decomposition technique and data layout used to implement them. The problems with most of the distributed framework are overheads of managing distributed system and lack of high level parallel programming language. Also with grid computing there is always potential chances of node failures which cause multiple re-executions of tasks. These problems can be overcome by the MapReduce framework introduced by Google. MapReduce is an efficient, scalable and simplified programming model for large scale distributed data processing on a large cluster of commodity computers and also used in cloud computing. In this paper, we present the overview of parallel Apriori algorithm implemented on MapReduce framework. They are categorized on the basis of Map and Reduce functions used to implement them e.g. 1-phase vs. k-phase, I/O of Mapper, Combiner and Reducer, using functionality of Combiner inside Mapper etc. This survey discusses and analyzes the various implementations of Apriori on MapReduce framework on the basis of their distinguishing characteristics. Moreover, it also includes the advantages and limitations of MapReduce framework.

cs.DB↗

arXiv2017

Observations on Factors Affecting Performance of MapReduce based Apriori on Hadoop Cluster

Designing fast and scalable algorithm for mining frequent itemsets is always being a most eminent and promising problem of data mining. Apriori is one of the most broadly used and popular algorithm of frequent itemset mining. Designing efficient algorithms on MapReduce framework to process and analyze big datasets is contemporary research nowadays. In this paper, we have focused on the performance of MapReduce based Apriori on homogeneous as well as on heterogeneous Hadoop cluster. We have investigated a number of factors that significantly affects the execution time of MapReduce based Apriori running on homogeneous and heterogeneous Hadoop Cluster. Factors are specific to both algorithmic and non-algorithmic improvements. Considered factors specific to algorithmic improvements are filtered transactions and data structures. Experimental results show that how an appropriate data structure and filtered transactions technique drastically reduce the execution time. The non-algorithmic factors include speculative execution, nodes with poor performance, data locality & distribution of data blocks, and parallelism control with input split size. We have applied strategies against these factors and fine tuned the relevant parameters in our particular application. Experimental results show that if cluster specific parameters are taken care of then there is a significant reduction in execution time. Also we have discussed the issues regarding MapReduce implementation of Apriori which may significantly influence the performance.

cs.DB↗

arXiv2015

Performance Analysis of Apriori Algorithm with Different Data Structures on Hadoop Cluster

Mining frequent itemsets from massive datasets is always being a most important problem of data mining. Apriori is the most popular and simplest algorithm for frequent itemset mining. To enhance the efficiency and scalability of Apriori, a number of algorithms have been proposed addressing the design of efficient data structures, minimizing database scan and parallel and distributed processing. MapReduce is the emerging parallel and distributed technology to process big datasets on Hadoop Cluster. To mine big datasets it is essential to re-design the data mining algorithm on this new paradigm. In this paper, we implement three variations of Apriori algorithm using data structures hash tree, trie and hash table trie i.e. trie with hash technique on MapReduce paradigm. We emphasize and investigate the significance of these three data structures for Apriori algorithm on Hadoop cluster, which has not been given attention yet. Experiments are carried out on both real life and synthetic datasets which shows that hash table trie data structures performs far better than trie and hash tree in terms of execution time. Moreover the performance in case of hash tree becomes worst.

cs.DC↗

arXiv2010

The Structural and Magnetic ordering in $La{}_{0.5-x}Nd_{x}Ca_{0.5}MnO_{3}$ (0.1 \ensuremath{\le} x \ensuremath{\le} 0.5) Manganites

The crystal and magnetic structure of polycrystalline $La{}_{0.5-x}Nd{}_{x}Ca_{0.5}MnO{}_{3}$ (0.0 \ensuremath{\le} x \ensuremath{\le} 0.5) samples have been investigated using magnetization, resistivity, transmission electron microscope, and neutron diffraction techniques. The samples are isostructural and possess orthorhombic structure in \textit{Pnma} space group. On lowering of temperature, the samples exhibit CE - type antiferromagnetic structure coexisting with a weak ferromagnetic ordering. The charge and orbitally ordered antiferromagnetic phase is weakened by the growth of ferromagnetic phase. The evolution of structural distortions and magnetic structure at low temperature as a function of Nd doping exhibit a strong correlation with A - site disorder ($σ^{2}$).

cond-mat.mtrl-sci↗

arXiv2008

The Influence of A-site Ionic Radii on the Magnetic Structure of Charge Ordered La0.5Ca0.5-xSrxMnO3 Manganites

The influence of the A-site ionic radii ( ) on the magnetic structure has been investigated in La0.5Ca0.5-xSrxMnO3 compounds (0 .GE. x .LE. 0.5) using neutron diffraction, magnetization, and resistivity techniques. All compounds in the composition range x .LE. 0.3 crystallize in the orthorhombic structure (Space Group Pnma). No further structural transition is observed as temperature is lowered below 300K. The compound x = 0.4, is a mixture of two orthorhombic phases crystallizing in Pnma and Fmmm space group. The x = 0.5 compound has a tetragonal structure in the space group, I4/mcm. The charge ordered (CO) state with CE-type antiferromagnetic order remains stable for x .LE. 0.3. Above x = 0.3, the CE-type antiferromagnetic state is suppressed. In x = 0.4 compound, A-type antiferromagnetic ordering is found at temperatures below 200K. Orbital ordering accompanying the spin ordering is found in all the samples with x .LE. 0.4. The system becomes ferromagnetic at x = 0.5 and no signature of orbital ordering is observed. As a function of , the charge ordered state is stable up to ~ 1.24A, and is suppressed thereafter. The magnetic structure undergoes a transformation from CE-type antiferromagnetic state to a ferromagnetic state with an intermediate A-type antiferromagnetic state.

cond-mat.str-el↗

arXiv2008

Substantial magneto-electric coupling near room temperature in Bi2Fe4O9

We report remarkable multiferroic effects in polycrystalline Bi2Fe4O9. High-resolution X-ray diffraction shows that this compound has orthorhombic structure. Magnetic measurements confirm an antiferromagnetic transition around 260 K. A pronounced inverse S-shape anomaly in the loss tangent of dielectric measurement is observed near the Neel temperature. This feature shifts with the application of magnetic field. These anomalies are indicative of substantial coupling between the electric and magnetic orders in this compound.

cond-mat.mtrl-sci↗