There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

IEEE Transactions on Pattern Analysis and Machine Intelligence

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

The heterogeneous multiscale method (HMM), a general framework for designing multiscale algorithms, is reviewed. Emphasis is given to the error analysis that comes naturally with the framework. Examples of finite element and finite difference HMM are presented. Applications to dynamical systems and stochastic simulation algorithms with multiple time scales, spall fracture and heat conduction in microprocessors are discussed.

/pdf/the-heterogeneous-multiscale-method-4zoj61bb2c.pdf

The heterogeneous multiscale method

https://www.tau.ac.il/~andelman/reprints/107_PhysRep_2003_380_1.pdf

Neutral and charged polymers at interfaces

Levy walks have been found in the motion of large animals such as birds and fish in search of sparsely and randomly distributed food. Here, Ariel et al. observe, by tracking long-duration trajectories of fluorescently labelled bacteria, similar walks in bacterial swarms for the first time.

/pdf/swarming-bacteria-migrate-by-levy-walk-2btodm8slt.pdf

Swarming bacteria migrate by Lévy Walk

Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces, forming dynamic patterns of whirls and jets. This review presents a physical point of view of swarming bacteria, with an emphasis on the statistical properties of the swarm dynamics as observed in experiments. The basic physical principles underlying the swarm and their relation to contemporary theories of collective motion and active matter are reviewed and discussed in the context of the biological properties of swarming cells. We suggest a paradigm according to which bacteria have optimized some of their physical properties as a strategy for rapid surface translocation. In other words, cells take advantage of favorable physics, enabling efficient expansion that enhances survival under harsh conditions.

/pdf/a-statistical-physics-view-of-swarming-bacteria-vomgn5fxp0.pdf

A statistical physics view of swarming bacteria.

Over the past decade, technological advances in experimental and animal tracking techniques have motivated a renewed theoretical interest in animal collective motion and, in particular, locust swarming. This review offers a comprehensive biological background followed by comparative analysis of recent models of locust collective motion, in particular locust marching, their settings, and underlying assumptions. We describe a wide range of recent modeling and simulation approaches, from discrete agent-based models of self-propelled particles to continuous models of integro-differential equations, aimed at describing and analyzing the fascinating phenomenon of locust collective motion. These modeling efforts have a dual role: The first views locusts as a quintessential example of animal collective motion. As such, they aim at abstraction and coarse-graining, often utilizing the tools of statistical physics. The second, which originates from a more biological perspective, views locust swarming as a scientific problem of its own exceptional merit. The main goal should, thus, be the analysis and prediction of natural swarm dynamics. We discuss the properties of swarm dynamics using the tools of statistical physics, as well as the implications for laboratory experiments and natural swarms. Finally, we stress the importance of a combined-interdisciplinary, biological-theoretical effort in successfully confronting the challenges that locusts pose at both the theoretical and practical levels.

/pdf/locust-collective-motion-and-its-modeling-9ah1slnjkq.pdf

Locust Collective Motion and Its Modeling.

/pdf/kinetics-of-surfactant-adsorption-the-free-energy-approach-3y5mmjafua.pdf

Kinetics of surfactant adsorption: the free energy approach

http://www.people.fas.harvard.edu/~yburak/Publications_files/BurakArielAndelman03.pdf

Gil Ariel

Papers

Swarming bacteria migrate by Lévy Walk

A statistical physics view of swarming bacteria.

Locust Collective Motion and Its Modeling.

Kinetics of surfactant adsorption: the free energy approach

Onset of DNA aggregation in presence of monovalent and multivalent counterions.