Wolfram Library Archive: What's New
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Thousands of pages of information on Mathematica and its applicationsen-usCopyright 2016
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8831Mathematica-based digital physics
http://library.wolfram.com/infocenter/Books/9428/
Contributed by: Junqin Jiang. The digital physics based on Mathematica' has four chapters, including electric fields, magnetic fields, numerical solution and trajectory of dynamics differential equation, and quantum mechanics. In addition, it has two appendices. The research methods and programming design ideas in many examples have important teaching and academic value. The readers can master ...BooksTue, 03 May 2016 09:51:52 -0600Toolbox for Mathematics, Mathematica Basic
http://library.wolfram.com/infocenter/Books/9427/
Contributed by: Etsuo Miyaoka. Mathematica is a very powerful software that is widely used in manufacturers, research institutes, and universities as their definitive computing system, as well as by individuals. This book illustrates how Mathematica deals with what students learned at the high school and the beginning college levels of mathematics, by comparing the mathematical expressions and ...BooksFri, 29 Apr 2016 10:51:13 -0600Income Support Benefits Law (augmented edition)
http://library.wolfram.com/infocenter/Books/9426/
Contributed by: Konosuke KIMURA. Mathematica is used to create the programs, graphs, and visualizations for: * combining income tax and social security * linear graduated tax table * Pareto index to indicate the income gap * calculating income tax revenue and annual expenditure for income support benefitsBooksFri, 29 Apr 2016 10:44:23 -0600Basic Mathematica Primer
http://library.wolfram.com/infocenter/Books/9425/
Contributed by: Seong-Deog Yang, Jang hoon Lee, Jiwon Hwang, Chae Yeong Lee, Myeong Hwan An. Fundamental Introduction to Mathematica. Rich source code that you can easily try along with friendly instructions for novices, summarized the basic knowledge of mathematics systematically.BooksFri, 29 Apr 2016 10:35:41 -0600Angular Fock coefficients: Refinement and further development
http://library.wolfram.com/infocenter/Articles/9424/
Contributed by: Evgeny Z. Liverts, Nir Barnea. The angular coefficients ψk,p(α,θ) of the Fock expansion characterizing the S-state wave function of the two-electron atomic system are calculated in hyperspherical angular coordinates α and θ. To solve the problem the Fock recurrence relations separated into the independent individual equations associated with definite power ...ArticlesTue, 26 Apr 2016 16:02:19 -0600A Simple Quantum Integro-Differential Solver (SQuIDS)
http://library.wolfram.com/infocenter/Articles/9423/
Contributed by: Carlos A. Argüelles Delgado, J. Salvador, Christopher N. Weaver. Simple Quantum Integro-Differential Solver (SQuIDS) is a C++ code designed to solve semi-analytically the evolution of a set of density matrices and scalar functions. This is done efficiently by expressing all operators in an SU(N) basis. SQuIDS provides a base class from which users can derive new classes to include ...ArticlesTue, 26 Apr 2016 16:00:40 -0600SecDec-3.0: Numerical evaluation of multi-scale integrals beyond one loop
http://library.wolfram.com/infocenter/Articles/9422/
Contributed by: Sophia Borowkaa, Gudrun Heinrich, S. P. Jones, M. Kerner, J. Schlenk, T. Zirke. SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of the finite coefficients. Here we present version 3.0 of the program, which has major improvements ...ArticlesTue, 26 Apr 2016 15:57:19 -0600Maximal noiseless code rates for collective rotation channels on qudits
http://library.wolfram.com/infocenter/Articles/9421/
Contributed by: Chi-Kwong Li, Mikio Nakahara, Yiu-Tung Poon, Nung-Sing Sze. We study noiseless subsystems on collective rotation channels of qudits, i.e., quantum channels with operators in the set E(d, n) = {U⊗n : U ∈ SU(d)}. This is done by analyzing the decomposition of the algebra A(d, n) generated by E(d, n). We summarize the results for the channels on qubits (d = 2) and obtain ...ArticlesTue, 26 Apr 2016 15:52:32 -0600Experimental and Theoretical Study of Multicomponent Batch Distillation
http://library.wolfram.com/infocenter/Articles/9420/
Contributed by: Housam Binous, Mamdouh A Al-Harthi, Ahmed Bellagi. We present in this pedagogical paper several important aspects of multi-component batch distillation. These later include: (1) Experimental implementation and results of a simple multi-component batch distillation; (2) Theoretical prediction of temperature and composition evolution with time; and (3) Liquid-vapor equilibrium ...ArticlesTue, 26 Apr 2016 15:50:05 -0600MBsums - A Mathematica PACKAGE FOR THE REPRESENTATION OF MELLIN-BARNES INTEGRALS BY MULTIPLE SUMS
http://library.wolfram.com/infocenter/Articles/9419/
Contributed by: Michal Ochman, Tord Riemann. Feynman integrals may be represented by the Mathematica packages AMBRE and MB as multiple Mellin-Barnes integrals. With the Mathematica package MBsums we transform these Mellin-Barnes integrals into multiple sums.ArticlesTue, 26 Apr 2016 15:47:59 -0600Pedagogical View of Model Metabolic Cycles
http://library.wolfram.com/infocenter/Articles/9418/
Contributed by: Victor Garcia-Herrero, Antonio Sillero. The main purpose of this study was to present a simplified view of model metabolic cycles. Although the models have been elaborated with the Mathematica Program, and using a system of differential equations, the main conclusions were presented in a rather intuitive way, easily understandable by students of general courses of Biochemistry, ...ArticlesTue, 26 Apr 2016 15:44:40 -0600On the collinear point L3 in the generalized relativistic R3BP
http://library.wolfram.com/infocenter/Articles/9417/
Contributed by: F.A. Abd El-Salam, S.E. Abd El-Bar. The photogravitational oblate restricted three-body problem is carried out within the post- Newtonian framework. The primaries are assumed to be oblate as well as radiant sources. The perturbed location of the collinear point L3 is computed. A series form of L3 location is obtained as a new analytical results. In order to introduce a ...ArticlesTue, 26 Apr 2016 15:43:01 -0600Computing decay rates for new physics theories with FeynRules and MadGraph 5_aMC@NLO
http://library.wolfram.com/infocenter/Articles/9416/
Contributed by: Johan Alwall, Claude Duhr, Benjamin Fuks, Olivier Mattelaer, Deniz Gizem Öztürk, Chia-Hsien Shen. We present new features of the FeynRules and MadGraph 5_aMC@NLO programs for the automatic computation of decay widths that consistently include channels of arbitrary final-state multiplicity. The implementations are generic enough so that they can be used in the framework of any ...ArticlesTue, 26 Apr 2016 15:31:37 -0600Package-X: A Mathematica package for the analytic calculation of one-loop integrals
http://library.wolfram.com/infocenter/Articles/9415/
Contributed by: Hiren H. Patel. Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators, and gives compact expressions of UV divergent, IR divergent, and finite parts for any kinematic configuration involving ...ArticlesTue, 26 Apr 2016 15:29:06 -0600Automatic evaluation of UV and R2 terms for beyond the Standard Model Lagrangians: A proof-of-principle
http://library.wolfram.com/infocenter/Articles/9414/
Contributed by: Celine Degrande. The computation of renormalized one-loop amplitudes in quantum field theory requires not only the knowledge of the Lagrangian density and the corresponding Feynman rules, but also that of the ultraviolet counterterms. More in general, and depending also on the method used in the actual computation of the one-loop amplitudes, additional interactions might be ...ArticlesTue, 26 Apr 2016 15:24:21 -0600Datum Planes Based on a Constrained L1 Norm
http://library.wolfram.com/infocenter/Articles/9412/
Contributed by: Craig M. Shakarji, Vijay Srinivasan. This paper has two major goals. First, we present an algorithm for establishing planar datums suitable for a default in tolerancing standards. The algorithm is based on a constrained minimization search based on the L1 (L1) norm after forming a convex surface from the original surface or sampled points. We prove that the problem reduces to a ...ArticlesTue, 26 Apr 2016 15:20:06 -0600NMR of 133Cs+ in stretched hydrogels: One-dimensional, z- and NOESY spectra, and probing the ion's environment in erythrocytes
http://library.wolfram.com/infocenter/Articles/9411/
Contributed by: Philip W. Kuchel, Dmitry Shishmarev, Max Puckeridge, Malcolm H. Levitt, Christoph Naumann, B. E. Chapman. 133Cs nuclear magnetic resonance (NMR) spectroscopy was conducted on 133Cs+ in gelatin hydrogels that were either relaxed or stretched. Stretching generated a septet from this spin-7/2 nucleus, and its nuclear magnetic relaxation was studied via z-spectra, and two-dimensional ...ArticlesTue, 26 Apr 2016 15:15:24 -0600On the Complex and Hyperbolic Structures for the (2 + 1)-Dimensional Boussinesq Water Equation
http://library.wolfram.com/infocenter/Articles/9410/
Contributed by: Figen Özpinar, Haci Mehmet Baskonus, Hasan Bulut. In this study, we have applied the modified exppWpqq-expansion function method to the (2 + 1)-dimensional Boussinesq water equation. We have obtained some new analytical solutions such as exponential function, complex function and hyperbolic function solutions. It has been observed that all analytical solutions have been verified ...ArticlesTue, 26 Apr 2016 15:01:56 -0600On the optimal use of isotherm models for the characterization of biosorption of lead onto algae
http://library.wolfram.com/infocenter/Articles/9409/
Contributed by: F. Brouers, Tariq J. Al-Musawi. For the first time we apply a new method based on the mathematical derivation of some known isotherm from the Burr function which describes many birth-death (sorption-desorption) phenomena in ecology and economy. Therefore, in this study the experimental isotherm data of biosorption of Pb(II) onto algae was modeled to Langmuir, Hill-Sips, ...ArticlesTue, 26 Apr 2016 14:57:13 -0600Computing observables in curved multifield models of inflation | A guide (with code) to the transport method
http://library.wolfram.com/infocenter/Articles/9408/
Contributed by: Mafalda Dias, Jonathan Frazer, David Seery. We describe how to apply the transport method to compute in inflationary observables in a broad range of multiple-field models. The method is efficient and encompasses scenarios with curved field-space metrics, violations of slow-roll conditions and turns of the trajectory in field space. It can be used for an arbitrary mass spectrum, ...ArticlesTue, 26 Apr 2016 14:55:22 -0600Effect of slip on Herschel-Bulkley fluid flow through narrow tubes
http://library.wolfram.com/infocenter/Articles/9407/
Contributed by: Nallapu Santhosh, G. Radhakrishnamacharya, Ali J. Chamkha. A two-fluid model of Herschel-Bulkley fluid flow through tubes of small diameters and slip at the wall is studied. It is assumed that the core region consists of Herschel-Bulkley fluid and Newtonian fluid in the peripheral region. Following the analysis of Chaturani and Upadhya, the equations of motion have been linearized ...ArticlesTue, 26 Apr 2016 14:50:40 -0600Cyclic coordinate descent in a class of bang-singular-bang problems
http://library.wolfram.com/infocenter/Articles/9406/
Contributed by: L. Bayon, P. Fortuny Ayuso, J. A. Otero, P. M. Suarez, C. Tasis. In this paper, we study a class of optimal control problems inspired by the hydroelectric context. These problems model a continuous production process with several interrelated pre-set availability inputs in a finite time interval with production functions which are linear with respect to the consumption rate over ...ArticlesThu, 21 Apr 2016 15:59:03 -0600APart 2: A generalized Mathematica Apart function
http://library.wolfram.com/infocenter/Articles/9405/
Contributed by: Feng Feng. The Mathematica function Apart has been generalized to any dimension in APart package [1], we upgrade this package to the 2nd version, in which the core part has been completely rewritten. The new version is more efficient than the 1st version of APart, and the output is now more compact and more suitable for the input for the FIRE [2] or FIESTA [3].ArticlesThu, 21 Apr 2016 15:00:32 -0600Probability distributions for multimeric systems
http://library.wolfram.com/infocenter/Articles/9404/
Contributed by: Jaroslav Albert, Marianne Rooman. We propose a fast and accurate method of obtaining the equilibrium monomodal joint probability distributions for multimeric systems. The method necessitates only two assumptions: the copy number of all species of molecule may be treated as continuous; and, the probability density functions (pdf) are well-approximated by multivariate skewnormal ...ArticlesThu, 21 Apr 2016 14:59:16 -0600Modeling and analysis of laminated shape memory alloy composite plates
http://library.wolfram.com/infocenter/Articles/9403/
Contributed by: Mohamed Kassem Abbas, Mostafa Adnan Elshafei, Hany Mohamed Negm. In the present work, static deformation, dynamic characteristic, and time response of laminated composite plates with surface-bonded shape-memory alloy (SMA) sheets are modeled. A modified higher order shear deformation theory with Ritz method is utilized. The energy balance equations are used to formulate the ...ArticlesThu, 21 Apr 2016 14:56:34 -0600Nonlinear radiation effects on squeezing flow of a Casson fluid between parallel disks
http://library.wolfram.com/infocenter/Articles/9402/
Contributed by: Syed Tauseef Mohyud-Din, Sheikh Irfanullah Khan. In this paper, we investigate the nonlinear radiation effects in a time-dependent two-dimensional flow of a Casson fluid squeezed between two parallel disks when the upperdisk is taken to be impermeable and the lowerone is porous. Suitable similarity transforms are employed to convert governing partial differential equations into ...ArticlesThu, 21 Apr 2016 14:48:35 -0600On modifications of Runge-Kutta-Nyström methods for solving y(4)=f(x,y)
http://library.wolfram.com/infocenter/Articles/9401/
Contributed by: I. Th Famelis, Ch Tsitouras. We present Runge-Kutta-Nyström type methods for the solution of a special fourth order initial value problem. Order conditions theory is given based on rooted trees. Thus a new set of SN-trees is introduced named ⊤4 and the enumeration of its elements is studied. A Mathematica package is also listed that may furnish instantly order conditions of ...ArticlesThu, 21 Apr 2016 14:46:52 -0600Four-band Hamiltonian for fast calculations in intermediate-band solar cells
http://library.wolfram.com/infocenter/Articles/9400/
Contributed by: Antonio Luque, Aleksandr Panchak, Alexey Vlasov, Antonio Martí, Viacheslav Andreev. The 8-dimensional Luttinger-Kohn-Pikus-Bir Hamiltonian matrix may be made up of four 4-dimensional blocks. A 4-band Hamiltonian is presented, obtained from making the non-diagonal blocks zero. The parameters of the new Hamiltonian are adjusted to fit the calculated effective masses and strained QD ...ArticlesMon, 18 Apr 2016 15:19:49 -0600Limit cycles bifurcating from the periodic annulus of the weight-homogeneous polynomial centers of weight-degree 2
http://library.wolfram.com/infocenter/Articles/9399/
Contributed by: Jaume Llibre, B. D. Lopes, J. R. de Moraes. We obtain an explicit polynomial whose simple positive real roots provide the limit cycles which bifurcate from the periodic orbits of a family of cubic polynomial differential centers when it is perturbed inside the class of all cubic polynomial differential systems. The family considered is the unique family of weight-homogeneous ...ArticlesMon, 18 Apr 2016 15:11:28 -0600Modeling of wood-like cellular materials with a geometrical data extraction algorithm
http://library.wolfram.com/infocenter/Articles/9398/
Contributed by: Alp Karakoc, Johanna Sjölund, Mehedi Reza, Jouni Freund, Albert Hernandez-Estrada, Jouni Paltakari. An algorithm on geometrical data extraction, material reconstruction and numerical analysis is presented in order to reconstruct the actual wood-like cellular materials and investigate their linear elastic material behavior in the transverse plane under different loading conditions. ...ArticlesMon, 18 Apr 2016 15:08:40 -0600Mathematical modeling of a three-compartment electro-reactor process with ion-exchange membranes for recycling and resource recovery of desulfurization residuals
http://library.wolfram.com/infocenter/Articles/9397/
Contributed by: Chenglei Yang, Limei Cao, Ji Yang. A mathematical model of a three-compartment electro-reactor process with ion-exchange membranes for recycling and resource recovery of desulfurization residuals was developed. This model describes the electrochemical separation process in the bulk solution and the diffusion boundary layer close to themembrane surfaces with a multiphysics-based ...ArticlesMon, 18 Apr 2016 15:02:39 -0600Numerical Approaches for Linear Left-invariant Diffusions on SE(2), their Comparison to Exact Solutions, and their Applications in Retinal Imaging
http://library.wolfram.com/infocenter/Articles/9396/
Contributed by: Jiong Zhang, Remco Duits, Gonzalo Sanguinetti, Bart M. ter Haar Romeny. Left-invariant PDE-evolutions on the roto-translation group SE(2) (and their resolvent equations) have been widely studied in the fields of cortical modeling and image analysis. They include hypo-elliptic diffusion (for contour enhancement) proposed by Citti & Sarti, and Petitot, and they include the direction ...ArticlesMon, 18 Apr 2016 15:00:22 -0600Efficient Strategies for Calculating Blockwise Likelihoods Under the Coalescent
http://library.wolfram.com/infocenter/Articles/9395/
Contributed by: Konrad Lohse, Martin Chmelik, Simon H. Martin, Nicholas H. Barton. The inference of demographic history from genome data is hindered by a lack of efficient computational approaches. In particular, it has proved difficult to exploit the information contained in the distribution of genealogies across the genome. We have previously shown that the generating function (GF) of ...ArticlesMon, 18 Apr 2016 14:57:57 -0600On the numerical solution of the general kinetic 'K-angle' reaction system
http://library.wolfram.com/infocenter/Articles/9394/
Contributed by: Nikolay Kyurkchiev, Svetoslav Markov. In a recent paper by Tobias and Tasi in this journal the authors discuss the 'K-angle' kinetic problem and focus on its analytic solution for K ≤ 5. The authors correctly mention that the case K > 5 requires numerical treatment in the part of the procedure where the eigenvalues of the characteristic polynomial are determined by ...ArticlesMon, 18 Apr 2016 14:55:09 -0600FaRe: A Mathematica package for tensor reduction of Feynman integrals
http://library.wolfram.com/infocenter/Articles/9393/
Contributed by: Michele Re Fiorentin. In this paper, we present FaRe, a package for Mathematica that implements the decomposition of a generic tensor Feynman integral, with arbitrary loop number, into scalar integrals in higher dimension. In order for FaRe to work, the package FeynCalc is needed, so that the tensor structure of the di®erent contributions is preserved and the obtained scalar ...ArticlesMon, 18 Apr 2016 14:52:50 -0600Longitudinal impact of piezoelectric media
http://library.wolfram.com/infocenter/Articles/9392/
Contributed by: George A. Gazonas, Raymond A. Wildman, David A. Hopkins, Michael J. Scheidler. We consider the elastodynamic impact problem involving a one-dimensional finite-thickness piezoelectric flyer traveling at initial velocity V0 that collides with (and adheres to) a stationary piezoelectric target of finite thickness backed by a semi-infinite non-piezoelectric elastic half-space.We ...ArticlesMon, 18 Apr 2016 14:51:25 -0600MHD oscillatory channel flow, heat and mass transfer in a physiological fluid in presence of chemical reaction
http://library.wolfram.com/infocenter/Articles/9391/
Contributed by: J. C. MISRA, S.D. Adhikary. In the present paper, the problem of oscillatory MHD flow of blood in a porous arteriole in presence of chemical reaction and an external magnetic field has been investigated. Heat and mass transfer during arterial blood flow are also studied. A mathematical model is developed and analyzed by using appropriate mathematical techniques. Expressions for ...ArticlesMon, 18 Apr 2016 14:48:17 -0600QDENSITY/QCWAVE: A Mathematica quantum computer simulation update
http://library.wolfram.com/infocenter/Articles/9390/
Contributed by: Frank Tabakin. The Mathematica quantum computer simulation packages QDENSITY and QCWAVE are updated for Mathematica 9-10.3. An overview is given of the new QDensity, QCWave, BTSystem and Circuits packages, which includes: (1) improved treatment of tensor products of states and density matrices, (2) major extension to include qutrit (triplet), as well as qubit (binary) and hybrid ...ArticlesMon, 18 Apr 2016 14:45:41 -0600MassToMI-A Mathematica package for an automatic Mass Insertion expansion
http://library.wolfram.com/infocenter/Articles/9389/
Contributed by: Janusz Rosiek. We present a Mathematica package designed to automatize the expansion of transition amplitudes calculated in the mass eigenstates basis (i.e. expressed in terms of physical masses and mixing matrices) into series of ''mass insertions'', defined as off-diagonal entries of mass matrices in Lagrangian before diagonalization and identification of the physical states. ...ArticlesMon, 18 Apr 2016 14:43:33 -0600Study of the Theta Pinch Plasma Numerically by Varying b Parameter and Applied Current
http://library.wolfram.com/infocenter/Articles/9388/
Contributed by: H. U. Khan, Anees-ur- Rehman, M. Shafiq, Muhammad Asad khan, Shahzad Hashim. The implosion dynamics of theta pinch is studied by simulation technique through snow plow model with the help of MATHEMATICA software. The differential equation of motion for plasma implosion is derived and solved numerically by using this software. The variation effects of b parameter (plasma kinetic ...ArticlesMon, 18 Apr 2016 14:41:58 -0600Algorithms for computing symbolic representations of basic e-sums and their application to composites
http://library.wolfram.com/infocenter/Articles/9387/
Contributed by: Wojciech Nawalaniec. The main goal of the paper is to present an algorithm to realize the theoretical method by Berlyand and Mityushev (2001,2005)for computations of the effective conductivity of fibrous composites expressed in therms of the linear combinations of the basic e-sums. Algorithms are presented in Mathematical Pseudo-language with examples in Mathematica®. A method for ...ArticlesMon, 18 Apr 2016 14:38:36 -0600Exact distribution of the product and the quotient of two stable Lévy random variables
http://library.wolfram.com/infocenter/Articles/9386/
Contributed by: P. N. Rathie, L. C. de S. M. Ozelim, C. E. G. Otiniano. In the present paper, the exact probability density function and cumulative distribution function of the product and the quotient of two independent stable Lévy random variables are derived in terms of the H-function. For practical applications, a routine in the Mathematica software has been developed for the evaluation of ...ArticlesMon, 18 Apr 2016 14:37:07 -0600Graph Theory Applications in Network Security
http://library.wolfram.com/infocenter/Articles/9385/
Contributed by: Fernando Docemmilli, Jonathan Webb, Mikhail Bonin. Graph theory has become a very critical component in many applications in the computing field including networking and security. Unfortunately, it is also amongst the most complex topics to understand and apply. In this paper, we review some of the key applications of graph theory in network security. We first cover some ...ArticlesMon, 18 Apr 2016 09:13:47 -0600Visualizing Gene Expression Patterns: A Computational Approach with CAS Software
http://library.wolfram.com/infocenter/Articles/9384/
Contributed by: Kyriaki D. Tsilika, Menelaos Kavouras, Athanasios Exadactylos. Gene expression as a biological response to environmental stimulus and as a physiological process of development, is crucial for the study of life. Visualization is an important means to identify complex gene networks. The primary purpose of this study is to provide immediate connection to analytics of biological ...ArticlesMon, 11 Apr 2016 09:29:52 -0600Early retirement for mothers in Greece
http://library.wolfram.com/infocenter/Articles/9383/
Contributed by: Ioannis A. Kaskarelis, Kyriaki D. Tsilika. Purpose - Greek social security system has a provision, under which women who have children are entitled to exit the labour force and claim pension benefits after completing 20 years of work and at a fully productive age. The critical issue arising from this regime is that it seems that mothers are rewarded for their nature of being able ...ArticlesFri, 08 Apr 2016 11:27:36 -0600