N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

A survey of models, analysis tools and compensation methods for the control of machines with friction

The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

The properties of mechanical systems of rigid bodies subject to unilateral constraints are investigated. In particular, properties of interest for the digital simulation of the motion of such systems are studied. The constraints give rise to discontinuities in the solution. Under general assumptions on the system a unique solution is constructed using the linear complementarily theory of mathematical programming. A numerical method for solution of these problems and generalizations of the constraints studied in this paper are briefly discussed.

/pdf/mechanical-systems-of-rigid-bodies-subject-to-unilateral-39vwhhwsd8.pdf

Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints

Die Losungen des Coulombschen Reibungsproblems fur starre Korper in zwei Dimensionen werden analysiert. Das bestimmende System von gewohnlichen Differentialgleichungen und Ungleichungen wird aufgestellt. Beispiele werden vorgelegt, die einige ungewunschte Eigenschaften dieses speziellen Reibungsgesetzes nachweisen. Hinreichende Bedingungen fur Existenz und Eindeutigkeit werden mit Hilfe der Theorie der linearen Komplementaritat hergeleitet.



The solutions to the Coulomb friction problem for rigid bodies in two dimensions are analyzed. The governing system of ordinary differential equations and inequalities is derived. Examples are presented demonstrating undesirable properties of this particular law of friction. Sufficient conditions for existence and uniqueness are given using the theory of linear complementarity.

Coulomb Friction in Two-Dimensional Rigid Body Systems

In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints. Systems of this form arise frequently in the modelling of problems from physics and engineering; we study some particular examples from electrical networks, fluid dynamics and constrained mechanical systems. We show that backward differentiation formulas converge with the expected order of accuracy for these systems.

/pdf/numerical-solution-of-nonlinear-differential-equations-with-le8pp196n7.pdf

Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas

A numerical method is given for the solution of a system of ordinary differential equations and algebraic, unilateral constraints. The equations govern the motion of a mechanical system of rigid bodies, where contacts between the bodies are created and disappear in the time interval of interest. The ordinary differential equations are discretized by linear multistep methods. In order to satisfy the constraints, a quadratic programming problem is solved at each time step. The fact that the variation of the objective function is small from step to step is utilized to save computing time. A discrete friction model, based on Coulomb’s law of friction and suitable for efficient computation, is proposed for planar problems where dry friction cannot be neglected. The normal forces and the friction forces are the optimal solution to a quadratic programming problem. The methods are tested on four model problems. A data structure and possible generalizations are discussed.

/pdf/numerical-simulation-of-time-dependent-contact-and-friction-568koybl2m.pdf

Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics

We model stochastic chemical systems with diffusion by a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with a discretized Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered in our method by an unstructured mesh, and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the Laplace operator on the macroscale. The resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level. The accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology.

https://www.it.uu.se/research/publications/reports/2008-012/2008-012-nc.pdf

Per Lötstedt

Papers

Mechanical Systems of Rigid Bodies Subject to Unilateral Constraints

Coulomb Friction in Two-Dimensional Rigid Body Systems

Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas

Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics

Simulation of Stochastic Reaction-Diffusion Processes on Unstructured Meshes