General Computational Technique Research Articles

Computational Methods for Charge Density Waves in 2D Materials.

Two-dimensional (2D) materials that exhibit charge density waves (CDWs)—spontaneous reorganization of their electrons into a periodic modulation—have generated many research endeavors in the hopes of employing their exotic properties for various quantum-based technologies. Early investigations surrounding CDWs were mostly focused on bulk materials. However, applications for quantum devices require few-layer materials to fully utilize the emergent phenomena. The CDW field has greatly expanded over the decades, warranting a focus on the computational efforts surrounding them specifically in 2D materials. In this review, we cover ground in the following relevant theory-driven subtopics for TaS2 and TaSe2: summary of general computational techniques and methods, resulting atomic structures, the effect of electron–phonon interaction of the Raman scattering modes, the effects of confinement and dimensionality on the CDW, and we end with a future outlook. Through understanding how the computational methods have enabled incredible advancements in quantum materials, one may anticipate the ever-expanding directions available for continued pursuit as the field brings us through the 21st century.

Delay Differential Equations in Biosciences: Parameter Estimation and Sensitivity Analysis

This is a review article to show that delay differential models have a richer mathematical framework (compared with models without memory or after-effects) and a better consistency with biological phenomena such dynamical diseases and cell growth dynamics. The article provides a general computational technique to treat numerically the emerging delay differential models. It introduces the numerical algorithms for parameter estimations, using least squares approach. The article introduces a variational method to evaluate sensitivity of the state variables to small perturbations in the initial conditions and parameters appear in the model. An application to show the consistency of DDE models with cell growth dynamics is also considered.

Exploring subtle features of yield surfaces of porous, ductile solids through unit cell simulations

A general computational technique for deriving macro yield surfaces from unit cells with a given microstructure has been proposed in a companion paper (Chouksey, M., Keralavarma, S. M., Basu, S., 2019, “Computational investigation into the role of localization on yield of a porous ductile solid,” Journal of the Mechanics and Physics of Solids, 130,pp. 141–164). Using this technique, macro yield surfaces for porous ductile solids, represented by cuboidal unit cells containing ellipsoidal voids, have been generated and compared with suitable analytical yield criteria. These yield surfaces exhibit vertex-like features when the principal directions of the macro stress coincides with the axes of the ellipsoidal void. In this work, we study the effects of void spacing and orientation with respect to the principal directions nα (α∈[1,3]) of the macro stress. Subtle changes in the yield surface are revealed when its traces are plotted on octahedral or meridional section planes in stress space. Further, the possibility of utilizing the computational framework to automatically generate complete macro yield surfaces by sampling the entire macro stress space, for a given microstructure, is demonstrated with examples where the space of applied macro stress states are limited by suitable assumptions.

Spin-phonon relaxation from a universal ab initio density-matrix approach

Designing new quantum materials with long-lived electron spin states urgently requires a general theoretical formalism and computational technique to reliably predict intrinsic spin relaxation times. We present a new, accurate and universal first-principles methodology based on Lindbladian dynamics of density matrices to calculate spin-phonon relaxation time of solids with arbitrary spin mixing and crystal symmetry. This method describes contributions of Elliott-Yafet and D’yakonov-Perel’ mechanisms to spin relaxation for systems with and without inversion symmetry on an equal footing. We show that intrinsic spin and momentum relaxation times both decrease with increasing temperature; however, for the D’yakonov-Perel’ mechanism, spin relaxation time varies inversely with extrinsic scattering time. We predict large anisotropy of spin lifetime in transition metal dichalcogenides. The excellent agreement with experiments for a broad range of materials underscores the predictive capability of our method for properties critical to quantum information science.

A general method of computing mixed Poisson probabilities by Monte Carlo sampling

Mixed Poisson distributions form an important class of distributions in applications. However, the application of many of these mixed Poisson distributions is hampered by the complicated probability distributions. The paper examines Monte Carlo sampling as a general technique for computation of mixed Poisson probabilities which is applicable to any mixed Poisson distribution with arbitrary mixing distribution. The accuracy and computational speed of this method is illustrated with the Poisson–inverse Gaussian distribution. The proposed method is then applied to compute probabilities of the Poisson–lognormal distribution, a popular species abundance model. It is also shown that in the maximum likelihood estimation of Poisson–lognormal parameters by E–M algorithm, the application of the proposed Monte Carlo computation in the algorithm avoids numerical problems.

VISIBILITY INTERVALS BETWEEN TWO SATELLITES ORBITS UNDER J2-GRAVITY AND DRAG FORCE

The research introduces a general analytical and computational technique for satellite-to-satellite visibility. The effect of earth’s oblateness and drag force were taken into account.The Visibility function in terms of the orbital elements of the two satellites and the time were derived. The rise and set periods of the satellites are determined through the sign of the visibility function. Numerical examples were worked for some satellites.

Kinematic Design of Redundant Robotic Manipulators for Spatial Positioning that are Optimally Fault Tolerant

This work presents a method for identifying all the kinematic designs of spatial positioning manipulators that are optimally fault tolerant in a local sense. We use a common definition of fault tolerance, i.e., the post-failure Jacobian possesses the largest possible minimum singular value over all possible single locked-joint failures. The large family of physical manipulators that can achieve this optimally failure tolerant configuration is then parameterized and categorized. We develop a general computational technique to evaluate the resulting manipulators in terms of their global kinematic properties, with an emphasis on failure tolerance. Several manipulators with a range of desirable kinematic properties are presented and analyzed, with a specific example of optimizing over a given class of manipulators that possess a specified kinematic constraint.

Novel approach of estimating grounding pit optimum dimensions in high resistivity soils

Good grounding arrangement is very important for safe and reliable operation of a power system and to ensure safety of the power apparatus as well as the operating personnel. In most of the inland arid desert areas, the soil resistivity is significantly high and it is difficult to get low earth resistance with conventional methods. Therefore, an economical and efficient grounding system design of the earthing pit is necessary which can be achieved by using a low resistivity material (LRM). When such material is used, it is important to optimize the pit design. The grounding resistance for different configurations were calculated and based on the results, an optimized pit configuration is discussed. The intent of this paper is to present a simple general computational technique for finding the optimum economical size of grounding pit when filled with LRM. It was found that the use of too high volume of LRM does not reduce the earthing resistance in a corresponding manner. The suggested method can be readily used by engineers to obtain a good earthing pit configuration for efficient grounding of the power system components in high resistivity soils.

Cytokine-Induced Signaling Networks Prioritize Dynamic Range over Signal Strength

Signaling networks respond to diverse stimuli, but how the state of the signaling network is relayed to downstream cellular responses is unclear. We modeled how incremental activation of signaling molecules is transmitted to control apoptosis as a function of signal strength and dynamic range. A linear relationship between signal input and response output, with the dynamic range of signaling molecules uniformly distributed across activation states, most accurately predicted cellular responses. When nonlinearized signals with compressed dynamic range relay network activation to apoptosis, we observe catastrophic, stimulus-specific prediction failures. We develop a general computational technique, "model-breakpoint analysis," to analyze the mechanism of these failures, identifying new time- and stimulus-specific roles for Akt, ERK, and MK2 kinase activity in apoptosis, which were experimentally verified. Dynamic range is rarely measured in signal-transduction studies, but our experiments using model-breakpoint analysis suggest it may be a greater determinant of cell fate than measured signal strength.

On the Action of the Sporadic Simple Baby Monster Group on its Conjugacy Class 2B

AbstractWe determine the character table of the endomorphism ring of the permutation module associated with the multiplicity-free action of the sporadic simple Baby Monster groupBon its conjugacy class 2B, where the centraliser of a 2B-element is a maximal subgroup of shape 21+22.Co2. This is one of the first applications of a new general computational technique to enumerate big orbits.

Approximate Throughput Computation of Stochastic Weighted T-Systems

A general iterative technique for approximate throughput computation of stochastic live and bounded weighted T-systems (WTS) is presented. It generalizes a previous technique on stochastic marked graphs. The approach has two basic foundations. First, a deep understanding of the qualitative behavior of WTS leads to a general decomposition technique. Second, after the decomposition phase, an iterative response-time approximation method is applied for the throughput computation. Existence of convergence points for the iterative approximation method can be proved. Experimental results generally have an error of less than 5%. The state space is usually reduced by more than one order of magnitude; therefore, the analysis of otherwise intractable systems is possible

Monte-Carlo calculation of Boersch energy spreading

The effects of electron–electron coulomb interactions have been simulated by a general computational technique that can be applied to almost any system, independently of the shape of the beam or the regimes that might be present, provided that the ‘closest-encounter’ approximation is valid for the system. The technique has been applied to the ‘benchmark test’ of the energy spreading in a converging round beam. The results are compared with previous analytical results.

Factoring very-high-degree polynomials

In this article, we discuss the current status of polynomial factoring (root finding) algorithms with some historical and mathematical background including size limits, convergence, accuracy and speed. The methods of root approximation versus root refinement are also examined. We then focus on two improved general purpose computational techniques, and in particular the factorization algorithm by Lindsey-Fox (L-F), which makes use of the fast Fourier transform to factor polynomials with random coefficients of degrees as high as 1 million. Computer simulations give insight that result in significant improvements in traditional approaches to an ancient problem.

Fast-phase space computation of multiple arrivals.

We present a fast, general computational technique for computing the phase-space solution of static Hamilton-Jacobi equations. Starting with the Liouville formulation of the characteristic equations, we derive "Escape Equations" which are static, time-independent Eulerian PDEs. They represent all arrivals to the given boundary from all possible starting configurations. The solution is numerically constructed through a "one-pass" formulation, building on ideas from semi-Lagrangian methods, Dijkstra-like methods for the Eikonal equation, and Ordered Upwind Methods. To compute all possible trajectories corresponding to all possible boundary conditions, the technique is of computational order O(N log N), where N is the total number of points in the computational phase-space domain; any particular set of boundary conditions then is extracted through rapid post-processing. Suggestions are made for speeding up the algorithm in the case when the particular distribution of sources is provided in advance. As an application, we apply the technique to the problem of computing first, multiple, and most energetic arrivals to the Eikonal equation.

A simulation model for evaluating advanced dial-a-ride paratransit systems

This paper presents a simulation system that has been developed to model a variety of technology-oriented dial-a-ride paratransit systems operated in an urban environment. The latest advances in information technologies such as automatic vehicle location (AVL), digital telecommunication and computers have afforded a unique opportunity for public transit agencies to integrate these technologies in their paratransit systems for improved productivity and reliability. This opportunity has also prompted wide spread interest in quantifying the actual benefits that can be attained from such technological enhancement. The primary objective of the simulation model described in this paper was to facilitate the evaluation of the potential effects that these technologies may bring on a paratransit system. The paper discusses the general concepts, models and computational techniques applied in the simulation system, focusing on how various components are modeled and how they interact with each other in the overall simulation framework. The simulation system is applied to evaluate the potential operational improvement that may be attained from the application of automatic vehicle location technology.

Existence Verification for Singular Zeros of Complex Nonlinear Systems

Computational fixed point theorems can be used to automatically verify existence and uniqueness of a solution to a nonlinear system of n equations in n variables ranging within a given region of n-space. Such computations succeed, however, only when the Jacobi matrix is nonsingular everywhere in this region. However, in problems such as bifurcation problems or surface intersection problems, the Jacobi matrix can be singular, or nearly so, at the solution. For n real variables, when the Jacobi matrix is singular, tiny perturbations of the problem can result in problems either with no solution in the region, or with more than one; thus no general computational technique can prove existence and uniqueness. However, for systems of n complex variables, the multiplicity of such a solution can be verified. That is the subject of this paper. Such verification is possible by computing the topological degree, but such computations heretofore have required a global search on the (n-1)-dimensional boundary of an n-dimensional region. Here it is observed that preconditioning leads to a system of equations whose topological degree can be computed with a much lower-dimensional search. Formulas are given for this computation, and the special case of rank-defect one is studied, both theoretically and empirically. Verification is possible for certain subcases of the real case. That will be the subject of a companion paper.

On‐Line and Off‐Line Routing and Scheduling of Dial‐a‐Ride Paratransit Vehicles

This article presents the general concepts, models, and computational techniques applied in a new dial‐a‐ride vehicle routing and scheduling system. The objective of this system is to improve the responsiveness, reliability, and productivity of dial‐a‐ride paratransit services. The developed software integrates dial‐a‐ride routing and scheduling principles and practical experience and explicitly considers travel time variability in urban roadway networks. Such extensive and complex integration has been made possible by improved data acquisition and processing capabilities of computer, telecommunications, and vehicle location technologies. Advanced computational methods applied in the system, such as the artificial neural network technique, which allows heuristic estimation of origin‐destination travel times in a dynamic and stochastic fashion, contribute to the processing speed required to respond expeditiously and efficiently to paratransit user requests. A real scheduling problem from the city of Edmonton, Alberta, where the system was tested, is used to illustrate the positive computational experience and the capability of the developed software to handle both off‐line and on‐line operations.

Computational neural networks and the rational design of polymeric materials: the next generation polycarbonates

We present an atomistic approach to computer aided molecular design that incorporates computational neural networks as the tools for determining accurate structure–property relationships. A general computational technique, called PropNet (where Prop represents the type of relaxation, transition, physical, or mechanical property) is developed and applied to the elucidation of transition (glass; Tg, and degradation; Td) and relaxation (Tγ) temperatures, as well as to various other physical and mechanical properties of polymeric materials. TgNet is a general purpose neural network system that rapidly formulates structure–property relationships for the glass transition temperature of amorphous and semicrystalline polymers. Up to 320 different polymers (Tg ranging from 50–700 K, including tactic and crosslinked polymers) were used to test TgNet for robustness and accuracy. The results demonstrate that TgNet is capable of predicting the glass transition temperature to within 10 K of experimentally reported values. The overall approach can easily be extended to any property for which quality data are available. Individual expert networks: TgNet (glass transition temperature), TdNet (degradation temperature), TγNet (secondary, Tγ relaxation temperatures), RiNet (refractive index), TenNet (tensile strength), ElongNet (maximum % elongation), CompNet (compressive strength), HardNet (hardness), and IzodNet (Izod notch strength) were developed and tested. Based on these neural network techniques a number of next-generation polycarbonates for increased impact resistance were rationally designed.

A General Technique for Computing Evolutionarily Stable Strategies Based on Errors in Decision-making

Realistic models of contests between animals will often involve a series of state-dependent decisions by the contestants. Computation of evolutionarily stable strategies for such state-dependent dynamic games are usually based on damped iterations of the best response map. Typically this map is discontinuous so that iterations may not converge and even if they do converge it may not be clear if the limiting strategy is a Nash equilibrium. We present a general computational technique based on errors in decision making that removes these computational difficulties. We show that the computational technique works for a simple example (the Hawk–Dove game) where an analytic solution is known, and prove general results about the technique for more complex games. It is also argued that there is biological justification for inclusion of the types of errors we have introduced.

Approximate throughput computation of stochastic marked graphs

A general iterative technique for approximate throughput computation of stochastic strongly connected marked graphs is presented. It generalizes a previous technique based on net decomposition through a single input-single output cut, allowing the split of the model through any cut. The approach has two basic foundations. First, a deep understanding of the qualitative behavior of marked graphs leads to a general decomposition technique. Second, after the decomposition phase, an iterative response time approximation method is applied for the computation of the throughput. Experimental results on several examples generally have an error of less than 3%. The state space is usually reduced by more than one order of magnitude; therefore, the analysis of otherwise intractable systems is possible. >