Browsing by Author "Kumar, Rajesh"

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Advances in Computational Modeling and Simulation
(Springer, 2022) Srinivas, Rallapalli; Kumar, Rajesh
AFMT: Maintaining the safety-security of industrial control systems
(Elsevier, 2022-04) Kumar, Rajesh
Modern day industrial control systems are overwhelmingly complex. These systems feature intricate interactions between the cyber and the physical components. At the same time, they need to be trustworthy and deliver their services continuously. Underpinning, a crucial industrial activity to ensure the dependability of such critical systems is through timely maintenance, inspections and repairs. Several strategies exist here: “fix it when it breaks” (reactive maintenance), monitor and maintain a system in pre-established time intervals (preventive maintenance), preventive action based upon detected symptoms of failures condition-based maintenance (CBM), etc. In literature, the question of optimal maintenance frequency have been a subject of intense study. However, most papers, do not take information security aspects into account. This paper provides an automated tool-supported quantitative risk analysis framework, Attack-Fault-Maintenance Trees, AFMTs, that will enable practitioners to make informed choice on: (a) identifying the critical component(s) necessary for uninterrupted systems; (b) a decision support system that will provide informed choices on policy measures, countermeasures and safeguards that will reduce the disruptions; (c) run the “what-if” scenarios to find the optimal trade-offs between system attributes (safety, security, usability and maintenance). The front-end of the tool is a domain-specific language geared to represent the system architecture using graphical-constructs. The back-end of the framework remains hidden to the practitioner. It consists of a mathematical engine based on statistical model-checking techniques. A case study of oil-pipeline is used to demonstrate the efficacy of our framework.
Analysis of a prion proliferation model with polymer coagulation in the presence of chaperone
(Wiley, 2023-03) Kumar, Rajesh
In the present work, a mathematical model which consists of a nonlinear partial integro-differential equation coupled with two ordinary differential equations (ODEs) is analyzed. This model describes the relation between infectious, noninfectious prion proteins, and chaperone. The well-posedness of the system is proved for bounded kernels by using evolution operator theory in the state space . The existence of a global weak solution for unbounded kernels is also discussed by a weak compactness argument. In addition, we investigated the stability analysis results theoretically and effect of chaperone on prion proliferation numerically.
An analytic approach for nonlinear collisional fragmentation model arising in bubble column
(AIP, 2024-10) Kumar, Rajesh
The phenomenon of coagulation and breakage of particles plays a pivotal role in diverse fields. It aids in tracking the development of aerosols and granules in the pharmaceutical sector, coagulation or breakage of droplets in chemical engineering, understanding blood clotting mechanisms in biology, and facilitating cheese production through the action of enzymes within the dairy industry. A significant portion of research in this direction concentrates on coagulation or linear breakage processes. In the case of linear case, bubble particles break down due to inherent stresses or specific conditions of the breakage event. However, in many practical situations, particle division is primarily due to forces exerted during collisions between particles, necessitating an approach that accounts for nonlinear collisional breakage. Despite its critical role in a wide array of engineering and physical operations, the study of this nonlinear fragmentation phenomenon has not been extensively pursued. This article introduces an innovative semi-analytical method that leverages the beyond linear use of equation superposition function to address the nonlinear integro-partial differential model of collisional breakage population balance. This approach is versatile, allowing for the resolution of both linear/nonlinear equations while sidestepping the complexities associated with discretization of domain. To assess the precision of this method, we conduct a thorough convergence analysis. This process utilizes the principle of contractive mapping in the Banach space, a globally recognized strategy for verifying convergence. We explore a variety of kernel parameters associated with collisional kernels, alongside breakage and initial distribution functions, to derive novel iterative solutions. Comparing our findings with those obtained through the finite volume method regarding number density functions and their integral moments, we demonstrate the reliability and accuracy of our approach. The consistency and correctness of our method are further validated by depicting the errors between the exact and approximated solutions in graphical and tabular formats.
Analytical and Numerical Study of Fractured Isotropic and Composite Plates Under Mode-I Crack Extension
(Springer, 2022-04) Patel, Shuvendu Narayan; Kumar, Rajesh
This paper deals with the study of fracture characteristics through the analytical method and FE (Finite Element) based methods of isotropic and anisotropic plates containing a central crack under uniform in-plane tensile load. In this study, mode I (opening mode) of fracture is considered. A governing differential equation is established for the plates and complex theory in terms of complex variables is employed to find stress functions to satisfy the equilibrium equation, compatibility equation and boundary condition at infinite distance and crack surfaces. An analytical solution which follows the Cauchy-Riemann conditions in the form of is introduced to study the stress characteristics at different positions of the plate. The effect of the uniform in-plane tensile load on the near field and far-field crack tip stress characteristics for mode-I crack is studied. ABAQUS/Standard software is used to carry out numerical analysis. The FEM results are compared with those of the analytical results. The damage parameters for composite plate is also studied.
Analytical and numerical treatments of a coagulation population balance model
(Elsevier, 2025-03) Kumar, Rajesh
The Redner–Ben-Avraham–Kahng (RBK) coagulation model, initially proposed as a discrete framework for investigating cluster growth kinetics, has recently been reformulated to encompass a continuous representation. While the existence, uniqueness, and long-term dynamics of solutions for the continuous model have been examined, both analytical and numerical solutions have yet to be thoroughly addressed. This study undertakes a comprehensive investigation of the continuous RBK coagulation model utilizing both numerical and semi-analytical methodologies, specifically the Finite Volume Method (FVM) and the Homotopy Perturbation Method (HPM). Analytical expressions for the number density function are derived for a variety of coagulation kernels, including constant, sum, product, and bilinear kernels, based on exponential and gamma initial distributions. The efficacy of the HPM is rigorously assessed through an extensive convergence analysis, which encompasses the order of convergence and error estimates pertinent to the series solutions. Furthermore, the outcomes obtained from HPM are validated against those derived from the established FVM, thereby demonstrating the reliability and effectiveness of HPM in addressing the continuous RBK model.
Analytical approach for dynamic instability analysis of functionally graded skew plate under periodic axial compression
(Elsevier, 2017-09) Kumar, Rajesh
Analytical studies on the dynamic instability analysis of a functionally graded (FG) skew plate subjected to uniform and linearly varying in-plane periodic loadings with four different types of boundary conditions are presented. The total energy functional of the FG skew plate is formulated based on Reddy's third order shear deformation theory (TSDT) and this functional is mapped from the physical domain to computational domain using transformation rule. The boundary characteristics orthonormal polynomials (BCOPs) are generated for different boundary conditions using Gram–Schmidt process, which satisfy the essential boundary conditions of skew plates in the computational domain. The energy functional is converted into a set of ordinary differential equations (Mathieu–Hill equations) using Rayleigh–Ritz method in conjunction with BCOPs. The solution of Mathieu–Hill equations describes the dynamic instability behavior of skew plate. The instability regions are traced using Bolotin method. The effect of skew angles, power-law distributions, span-to-thickness ratios, aspect ratios, boundary conditions and static load factors on the instability region of FG skew plates are presented. The result indicates that the width of instability region become narrow with the increase in skew angle. Moreover, the time history response and corresponding phase plot in the unstable and stable region is studied to identify the instability behavior such as existence of beats, bounded and unbounded response, and effect of forcing amplitude and its frequency on the response.
An analytical treatment to spatially inhomogeneous population balance model
(Elsevier, 2024-09) Kumar, Rajesh
In modern liquid–liquid contact components, there is an increasing use of droplet population balance models. These components include differential and completely mixed contractors. These models aim to explain the complex hydrodynamic processes occurring in the dispersion phase. The hydrodynamics of these interacting dispersions include droplet breaking, coalescence, axial dispersion, and both entry and exit events. The resulting equations for population balance are represented as integro-partial differential equations, which rarely have analytical solutions, especially when spatial dependency is apparent. Consequently, the pursuit predominantly lies in seeking numerical solutions to resolve these complex equations. In this study, we have devised analytical solutions for inhomogeneous breakage and coagulation by employing the population balance equation (PBEs) applicable to both batch and continuous flow systems. The innovative approaches for solving PBEs in these systems leverage the Adomian decomposition method (ADM) and the homotopy analysis method (HAM). These semi-analytical methodologies effectively tackle the significant challenges related to numerical discretization and stability, which have often plagued previous solutions of the homogeneous PBEs. Our findings across all test examples demonstrate that the approximated particle size distributions utilizing these two methods converge to the analytical solutions continuously.
Analyzing Advanced Persistent Threats Using Game Theory: A Critical Literature Review
(Springer, 2022) Kumar, Rajesh
Advanced persistent threats present significant security challenges due to their customized, stealthy and adaptive nature. Since no generic solution exists to combat advanced persistent threats, the recommended option is to employ information security best practices. While practitioner-oriented security guidelines have been published by the International Organization for Standardization and the U.S. National Institute of Standards and Technology, they cannot be employed in rigorous quantitative analyses required for objective decision making such as choosing countermeasures that balance security, cost and usability. In contrast, game-theoretic approaches, which express the behavior of rational agents that maximize their utility, provide appropriate models for objective decision making. This chapter conducts a critical analysis of several game-theoretic approaches for analyzing advanced persistent threats. Eleven highly-cited, peer-reviewed articles from the research literature are examined in terms of their objectives, features, game models and solutions. The models provide valuable insights into advanced persistent threat behavior, support resource-optimal decision making and can be mapped to the various risk management stages. However, they have some delicate modeling and analysis limitations. The critical analysis exposes the omissions in the literature and points to future research focused on integrating practitioner perspectives in game-theoretic approaches to advance information security risk management.
APT attacks on industrial control systems: A tale of three incidents
(Springer, 2022-07) Kumar, Rajesh
Modern-day industries are complex socio-technical entities. Understanding the risks associated with the operation of such systems requires proper consideration of budget constraints, security expertise and evaluating the effects of legacy services. A relatively newer and unorthodox form of cyber-attacks against such systems are Advanced Persistent Threats (APTs). APTs are resourceful and strategic, aiming at maximum damage by stalling critical services and stealing sensitive information. In this article, we demonstrate how attack trees can be used as a common language to model APT attacks in a practitioner-friendly manner. We do so by modelling three prominent APT attacks, namely Stuxnet, Blackenergy and Triton. Each attack is described in a systematic and structured way following the attack tree modelling language. We show that, because attack trees are compositional models, one can reuse them to model other complex attack scenarios. We illustrate this compositional feature by modelling attacks on an industrial oil-pipeline.
APT: a buzzword and a reality - A bibliometric review of the literature (2010–2020)
(IEEE, 2021) Kumar, Rajesh
This paper performs a bibliometric analysis of the peer-reviewed literature on Advanced Persistent Threats (APTs) taken from 2010–2020. APTs being a complex and tactical attack, require a multi-disciplinary perspective. In this study, we reveal several emerging trends based on 1205 literature papers. We report many popular bibliometric indicators, for example, publication trends, prolific authors, citation analysis, co-author analysis, and publication forums. An important indicator reported in our study is to find common research themes. To do that, we utilize the unsupervised Louvain algorithm. We believe our work will give insights into the current development in APT work, identifying common research themes and promote collaborations between researchers.
Asymptotic behavior of solution of Whitham–Broer–Kaup type equations with negative dispersion
(De Gruyter, 2021-10) Kumar, Rajesh
In this work, we discuss the long time behavior of solutions of the Whitham–Broer–Kaup system with Lipschitz nonlinearity and negative dispersion term. We prove the global well-posedness when α+β2<0 as well as the convergence to 0 of small solutions at rate O(t−1/2) .
An attack tree template based on feature diagram hierarchy
(IEEE, 2020) Kumar, Rajesh
Attack trees (ATs) are a popular model-based formalism to perform a security risk assessment. The benefits of using AT are numerous: graphical top-down representation of multi-stage attack scenarios, several analysis frameworks, and many supporting tools. The current practice of constructing an attack tree for a given system is using the rules-of-thumb. Though this process is flexible, in the absence of a template, it is non-standardized. Hence it is tedious and may result in contention between the stakeholders due to individual idiosyncrasies. To address these limitations, in this paper, we develop an AT template. We meticulously design the template by performing a literature survey of the industry-size ATs and extract the meta-categories used to build them. The AT template is then structured into layers by the systematic question-answering methodology of Potts et al. Each successive layer in our template is a refinement of the previous layer, adding more details. We link the AT template to standard threat databases. Thus, our template guides the practitioner on narrowing to the appropriate attack vectors. An important question here is how to keep the AT template flexible, given the diversity of context and system variables. To address the question, we use a feature diagram to represent the AT categories. We used the AT template to gain practical experience over a hypothetical case study of smart meters (not part of the paper). Based on our experience, we suggest future research directions.
Buckling and free vibration analysis of randomly distributed CNT reinforced composite beam under thermomechanical loading
(Elsevier, 2022-12) Kumar, Rajesh
In this study, the buckling and free vibration characteristics of three-phase randomly distributed carbon nanotube (CNT) reinforced fiber composite (RD-CNTRFC) beams subjected to in-plane compressive loadings and thermal environment are discussed in-depth through a semi-analytical approach. Displacement-based governing equations of motion are derived using Lagrange equation considering higher-order shear deformation theory (HSDT). The effective material properties of RD-CNTRFC are determined in two stages; firstly, effective properties of hybrid matrix (CNTs + Polymer) are evaluated using the Eshelbhy-Mori-Tanaka approach. Finally, overall effective properties of CNTRFC are estimated by implementing different homogenization techniques. The influences of temperature-dependent material properties and CNT-agglomeration are included in the derived formulation. The buckling loads and natural frequencies of RD-CNTRFC beams are computed using a typical eigenvalue solution. The influence of various boundary conditions, CNT mass fraction, CNT-agglomeration, length-to-thickness ratio, and various ply sequences are also addressed.
Buckling behaviour of laminated composite skew plates with various boundary conditions subjected to linearly varying in-plane edge loading
(Elsevier, 2015-09) Kumar, Rajesh
In the present study, the buckling behaviour of laminated composite skew plates with different boundary conditions subjected to linearly varying in-plane loads are presented. The skew plate is modelled based on higher order shear deformation theory, which accurately predicts the buckling behaviour for the thick plate. The in-plane stress distribution within the skew plate due to linearly varying in-plane load is equal to the applied in-plane edge load in the pre-buckling range. Using these in-plane stress distributions, the total potential energy functional is formulated. Total potential energy is a function of the total strain energy of skew plate and potential energy due to in-plane stress distributions. The total strain energy of skew plate contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total potential energy functionals mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Using a Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total potential energy functional is converted into sets of algebraic equations. Finally, these algebraic equations are rearranged as a linear eigenvalue problem, which is solved to obtain the critical buckling loads. The numerical results are presented for different skew angles, boundary conditions, length to thickness ratios, aspect ratios and in-plane loadings. It is observed that the critical buckling load increase with the increase of skew angle as well as change in the mode shape at a lower aspect ratio with the increase of skew angle.
Buckling of Laminated Composite Plate with Imperfections Subjected to In-Plane Pulse Loads
(Springer, 2021-06) Kumar, Rajesh; Patel, Shuvendu Narayan
In this article, the stability of a laminated composite plate when subjected to in-plane compressive pulse load is investigated in the finite element method framework. Convergence and validation studies are carried out using the current mathematical formulation and compared with the results from the existing literatures. The effects of loading duration, imperfection and ply orientation on the dynamic buckling behavior of the plate with irregular imperfection are studied in detail and the results are reported. It is observed that the plate having irregular imperfection of the order of 20% of the plate thickness has a lower non-linear dynamic buckling load than the plate with 15% irregular imperfection.
Characterization of Parasite Isolates and Analysis of Immune Responses in Indian Patients of Cutaneous Leishmaniasis
(BITS, Pilani, 1) Kumar, Rajesh
Co-engineering Safety-Security Using Statistical Model Checking
(Springer, 2022-06) Kumar, Rajesh
In this journal-first paper, we present an overview of our novel formalism of Attack-Fault-Maintenance Trees (AFMTs). Detailed version of work is available in [3]. AFMTs enable practitioners to quantify the disruption scenarios by answering several safety-security metrics. Alongside, it provides an informed decision on optimal maintenance policies by suggesting preventive component repairs and inspection frequencies. We answer the aforementioned metrics through “what-if” and “scenario analysis”. The models are supported by a graphical friendly tool of PASST. The tool’s front-end is a drawing canvas that provides the different syntactic elements used to design a well-formed AFMT model. The back-end of the tool is based on the statistical-model checking techniques. From the practitioner perspective, once the AFMT is designed and input parameters on component failure, detection rates, inspection rates are provided, the entire analysis can be then done as push-button technology using model-checking techniques
Collisional breakage population balance equation: An analytical approach
(Elsevier, 2025-01) Kumar, Rajesh
This work presents a unique semi-analytical approach based on the homotopy analysis method (HAM), called accelerated HAM, recently proposed in (Hussain et al., “Semi-analytical methods for solving non-linear differential equations: A review.”, JMAA, 2023), to solve the collisional breakage population balance model, which is an integro-partial differential equation. We compare our findings with those obtained using the Adomian decomposition method, a well-known technique for solving various forms of differential equations. By decomposing the non-linear operator, we investigate how to utilize the convergence control parameter to expedite the convergence of the HAM solution towards its precise value in accelerated HAM. The other objective of the article is to examine the theoretical convergence analysis of the two proposed methods. Additionally, we conduct theoretical research on the error estimates for both the techniques. To validate our schemes, several numerical examples are considered and the numerical simulations demonstrate that the suggested techniques provide accurate estimates for the solution and moments of the collisional breakage equation.
Comparison of variational iteration and Adomian decomposition methods to solve growth, aggregation and aggregation-breakage equations
(Elsevier, 2023-03) Kumar, Rajesh
In this work, semi-analytical approaches such as the Adomian decomposition method (ADM), and variational iteration method (VIM) are examined to solve the aggregation, aggregation-breakage and pure growth equations in series forms. The analytical and truncated series solutions are compared for the number density and various moments. The solutions produced using ADM and VIM are mathematically equal in the pure growth case and provide closed-form solutions for constant growth rate. Additionally, Optimal variational iteration method (OVIM) is implemented to solve the growth and aggregation equations, which reduces the error compared to ADM and VIM to some extent but increases the computational cost. Furthermore, in this work, we provide the ADM and VIM formulations for the coupled aggregation-breakage model. Various test cases of each problem are taken to justify the efficiency and accuracy of the series approximated methods. These observations are shown numerically by comparing the finite term series solutions with the exact solutions of number density and moments.