Metric affine gauge theory of gravity: Field equations, Noether identities, world spinors, and breaking of dilation invariance

Physics of inhomogeneous inorganic materials

Algorithmic algebra

In fibre networks, mechanical stability relies on the fibres’ bending resistance—in contrast to rubbers, where entropic stretching is the key. The extent to which the mechanics of fibre networks is controlled by bending is, however, an open question. The study of a general lattice-based model of fibrous networks now reveals two rigidity critical points, one of which controls a rich crossover from stretching-dominated to bending-dominated behaviour.

Criticality and isostaticity in fibre networks

The Rise of Gauge Theory of Gravity Up to 1961: From Special to General Relativity Theory Analyzing General Relativity Theory A Fresh Start by Yang - Mills and Utiyama Poincare Gauge Theory: Einstein - Cartan( - Sciama - Kibble) Theory as a Viable Gravitational Theory General Structure of Poincare Gauge Theory (Including Quadratic Lagrangians) Translational Gauge Theory Fallacies About Torsion Extending the Gauge Group of Gravity: Poincare Group Plus Scale Transformations: Weyl - Cartan Gauge Theory of Gravity From the Poincare to the Affine Group: Metric-Affine Gravity Conformal Gauge Theory of Gravity (Anti-)de Sitter Gauge Theory of Gravity From the Square Root of Translations to the Super-Poincare Group Specific Subjects of Metric-Affine Gravity and Poincare Gauge Theory: Hamiltonian Structure Equations of Motion for Matter Cosmological Models Exact Solutions Poincare Gauge Theory in Three Dimensions Dislocations and Torsion The Yang Episode: A Historical Case Study.

Gauge Theories Of Gravitation: A Reader With Commentaries

Monte Carlo transfer matrix evaluation of the elastic constants at the percolation threshold of the random-bond honeycomb lattice, with widths of up to 96 and lengths of about two million lattice constants (roughly 200 hours CDC Cyber 205 vector computer time) gave a critical exponentT=3.96±0.04 with a logarithmic correction term. This exponent agrees well with the scaling hypothesisT=t+2v=3.97, relatingT to the two-dimensional conductivity exponent.

Precision calculation of elasticity for percolation

Computer Simulation and Computer Algebra

I Computational Methods in Classical Physics.- 1 Motion of a Classical Point-Like Particle.- 2 Short Course in FORTRAN Programming Methodology.- 3 Methods of Higher Accuracy (and Efficiency).- 4 Finding Extremal Points of Motion.- 5 Statics and Dynamics of Strings.- 6 Dynamics of Strings.- 7 Literature.- II Monte Carlo Simulations in Statistical Physics.- 1 Random Numbers.- 2 Ising Model.- 3 Cellular Automata (Q2R and Creutz).- 4 Diffusion and Percolation.- 5 Eden Clusters.- 6 Kauffman Model.- 7 Summary.- 8 Appendix: A Short Introduction to FORTRAN.- 9 Literature.- III Principles of Vector and Parallel Computing.- 1 Basic Idea.- 2 An Example - Q2R.- 3 More About Vector Processing.- 3.1 IF-Statement.- 3.2 Initial Cost for the Vector-Processing.- 3.3 Bank Conflict.- 3.4 Library Routines.- 4 Before and After the Vectorization.- 5 Parallel Computing.- 5.1 Basic Ideas.- 5.2 Types of Parallel Computers and Algorithms.- IV REDUCE for Beginners - Seven Lectures on the Application of Computer-Algebra (CA).- First Lecture.- 1.1 A First Interactive Reduce Session.- 1.2 What Can CA Do for You?.- 1.3 The Reduce Character Set.- 1.4 Integers, Rational and Real Numbers.- 1.5 Variables Named by Identifiers.- 1.6 A Reduce Program, a Follow-up of Commands.- 1.7 Assigning Values to Variables.- 1.8 Access to Previous Input and Output.- 1.9 Homework.- Second Lecture.- 2.1 Built-in Operators.- 2.2 Reduce Expressions.- 2.3 The Process of Evaluation in Reduce.- 2.4 Repeatedly Doing Something: Loops.- 2.5 Loops and Lists.- 2.6 Multidimensional Objects: Arrays.- 2.7 Homework.- Third Lecture.- 3.1 The Conditional Statement.- 3.2 Combining Several Statements: I. The Group Statement.- 3.3 Combining Several Statements: II. The Compound Statement.- 3.4 Some Elementary Mathematical Functions.- 3.5 Differentiation with DF.- 3.6 Integration with INT.- 3.7 Substitution with SUB and Rule Lists.- 3.8 Homework.- Fourth Lecture.- 4.1 Operators That Act on Lists.- 4.2 Right- and Left-hand-side of an Equation.- 4.3 Solving (Non-)linear Equations.- 4.4 Retrieving Parts of Polynomials and Rational Functions.- 4.5 To Make Decisions with Boolean Operators.- 4.6 Writing Messages.- 4.7 How to Define Your Own Operators.- 4.8 Rule Lists and the LET-statement.- 4.9 Homework.- Fifth Lecture.- 5.1 Activate and Deactivate Rule Lists.- 5.2 More About Rule Lists.- 5.3 Examples: Factorials and Binomial Coefficients.- 5.4 Deactivating User-defined Rules.- 5.5 Non-commutative Algebras, Symmetric and Antisymmetric Operators.- 5.6 Procedures for Repeated Use of Commands.- 5.7 A Procedure for PHospitaPs Rule and a Caveat.- 5.8 Homework.- Sixth Lecture.- 6.1 Linear Algebra Package: Matrices.- 6.2 Turning Switches On and Off.- 6.3 Reordering Expressions.- 6.4 On Reduce Input and Output.- 6.5 Generating Fortran Programs.- 6.6 Concluding Remarks.- 6.7 Homework.- Seventh Lecture.- 7.1 Vector and Tensor Calculus.- 7.2 Packages for Three-dimensional Vector Calculus.- 7.3 Tensor Analysis, Christoffel Symbols, General Relativity.- 7.4 The EXCALC Package for Exterior Differential Forms.- 7.5 Graphics with GNUPLOT.- 7.6 Homework.- A Some Additional Exercises.- B Changes From Reduce 3.3 to Reduce 3.4.1.- C Further Information on Reduce.- C.1 Where Can You Buy Reduce?.- C.2 Execution Times for the Reduce Standard Test.- D Literature.- Joint Index.

Computer Simulation and Computer Algebra: Lectures for Beginners

Multitasking case study on the Cray-2: the Q2R cellular automaton

The one-dimensional elementary cellular automaton “Rule 22” is studied by means of Monte Carlo simulation on the dedicated K2 high-speed computer. If one considers random initialization with probability p for “one”-initialization per site, it is shown that the system behaves like a normal one-dimensional statistical ensemble with critical points atp=0 andp=1. Critical slowing down is exhibited, with a dynamical exponent of 1.0. The standard initialization ofp=0.5 is too far away from the critical point to allow similar observations.

John G. Zabolitzky

Papers

Precision calculation of elasticity for percolation

Computer Simulation and Computer Algebra

Computer Simulation and Computer Algebra: Lectures for Beginners

Multitasking case study on the Cray-2: the Q2R cellular automaton

Critical Properties of Rule 22 Elementary Cellular Automata