Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

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

Neurons in the brain communicate by short electrical pulses, the so-called action potentials or spikes. How can we understand the process of spike generation? How can we understand information transmission by neurons? What happens if thousands of neurons are coupled together in a seemingly random network? How does the network connectivity determine the activity patterns? And, vice versa, how does the spike activity influence the connectivity pattern? These questions are addressed in this 2002 introduction to spiking neurons aimed at those taking courses in computational neuroscience, theoretical biology, biophysics, or neural networks. The approach will suit students of physics, mathematics, or computer science; it will also be useful for biologists who are interested in mathematical modelling. The text is enhanced by many worked examples and illustrations. There are no mathematical prerequisites beyond what the audience would meet as undergraduates: more advanced techniques are introduced in an elementary, concrete fashion when needed.

/pdf/spiking-neuron-models-single-neurons-populations-plasticity-58gzrd6ih6.pdf

Spiking Neuron Models: Single Neurons, Populations, Plasticity

Langevin equations for the relaxation of spin fluctuations in a soft-spin version of the Edwards-Anderson model are used as a starting point for the study of the dynamic and static properties of spin-glasses. An exact uniform Lagrangian for the average dynamic correlation and response functions is derived for arbitrary range of random exchange, using a functional-integral method proposed by De Dominicis. The properties of the Lagrangian are studied in the mean-field limit which is realized by considering an infinite-ranged random exchange. In this limit, the dynamics are represented by a stochastic equation of motion of a single spin with self-consistent (bare) propagator and Gaussian noise. The low-frequency and the static properties of this equation are studied both above and below ${T}_{c}$. Approaching ${T}_{c}$ from above, spin fluctuations slow down with a relaxation time proportional to ${|T\ensuremath{-}{T}_{c}|}^{\ensuremath{-}1}$ whereas at ${T}_{c}$ the damping function vanishes as ${\ensuremath{\omega}}^{\frac{1}{2}}$. We derive a criterion for dynamic stability below ${T}_{c}$. It is shown that a stable solution necessarily violates the fluctuation-dissipation theorem below ${T}_{c}$. Consequently, the spin-glass order parameters are the time-persistent terms which appear in both the spin correlations and the local response. This is shown to invalidate the treatment of the spin-glass order parameters as purely static quantities. Instead, one has to specify the manner in which they relax in a finite system, along time scales which diverge in the thermodynamic limit. We show that the finite-time correlations decay algebraically with time as ${t}^{\ensuremath{-}\ensuremath{\nu}}$ at all temperatures below ${T}_{c}$, with a temperature-dependent exponent $\ensuremath{\nu}$. Near ${T}_{c}$, $\ensuremath{\nu}$ is given (in the Ising case) as $\ensuremath{\nu}(T)\ensuremath{\sim}\frac{1}{2}\ensuremath{-}{\ensuremath{\pi}}^{\ensuremath{-}1}(\frac{1\ensuremath{-}T}{{T}_{c}})+\ensuremath{\sigma}{(\frac{1\ensuremath{-}T}{{T}_{c}})}^{2}$. A tentative calculation of $\ensuremath{\nu}$ at $T=0$ K is presented. We briefly discuss the physical origin of the violation of the fluctuation-dissipation theorem.

Relaxational dynamics of the Edwards-Anderson model and the mean-field theory of spin-glasses

Molecular dynamics simulations are used to generate an ensemble of saddles of the potential energy of a Lennard-Jones liquid. Classifying all extrema by their potential energy $u$ and number of unstable directions $k$, a well-defined relation $k(u)$ is revealed. The degree of instability of typical stationary points vanishes at a threshold potential energy ${u}_{\mathrm{th}}$, which lies above the energy of the lowest glassy minima of the system. The energies of the inherent states, as obtained by the Stillinger-Weber method, approach ${u}_{\mathrm{th}}$ at a temperature close to the mode-coupling transition temperature ${T}_{c}$.

https://arxiv.org/pdf/cond-mat/0007258.pdf

Energy Landscape of a Lennard-Jones Liquid: Statistics of Stationary Points

https://www.cell.com/biophysj/pdf/S0006-3495(07)71693-4.pdf

Mechanical Properties of Spider Dragline Silk: Humidity, Hysteresis, and Relaxation

https://www.allpsych.uni-giessen.de/julia/papers/biophys03.pdf

Heterogeneous Presynaptic Release Probabilities: Functional Relevance for Short-Term Plasticity

Amyotrophic lateral sclerosis (ALS) is a fatal neurodegenerative disorder characterized by the selective loss of motor neurons (MN) in the brain stem and spinal cord. Intracellular disruptions of cytosolic and mitochondrial calcium have been associated with selective MN degeneration, but the underlying mechanisms are not well understood. The present evidence supports a hypothesis that mitochondria are a target of mutant SOD1-mediated toxicity in familial amyotrophic lateral sclerosis (fALS) and intracellular alterations of cytosolic and mitochondrial calcium might aggravate the course of this neurodegenerative disease. In this study, we used a fluorescence charged cool device (CCD) imaging system to separate and simultaneously monitor cytosolic and mitochondrial calcium concentrations in individual cells in an established cellular model of ALS. To gain insights into the molecular mechanisms of SOD1G93A associated motor neuron disease, we simultaneously monitored cytosolic and mitochondrial calcium concentrations in individual cells. Voltage – dependent cytosolic Ca2+ elevations and mitochondria – controlled calcium release mechanisms were monitored after loading cells with fluorescent dyes fura-2 and rhod-2. Interestingly, comparable voltage-dependent cytosolic Ca2+ elevations in WT (SH-SY5YWT) and G93A (SH-SY5YG93A) expressing cells were observed. In contrast, mitochondrial intracellular Ca2+ release responses evoked by bath application of the mitochondrial toxin FCCP were significantly smaller in G93A expressing cells, suggesting impaired calcium stores. Pharmacological experiments further supported the concept that the presence of G93A severely disrupts mitochondrial Ca2+ regulation. In this study, by fluorescence measurement of cytosolic calcium and using simultaneous [Ca2+]i and [Ca2+]mito measurements, we are able to separate and simultaneously monitor cytosolic and mitochondrial calcium concentrations in individual cells an established cellular model of ALS. The primary goals of this paper are (1) method development, and (2) screening for deficits in mutant cells on the single cell level. On the technological level, our method promises to serve as a valuable tool to identify mitochondrial and Ca2+-related defects during G93A-mediated MN degeneration. In addition, our experiments support a model where a specialized interplay between cytosolic calcium profiles and mitochondrial mechanisms contribute to the selective degeneration of neurons in ALS.

https://link.springer.com/content/pdf/10.1186%2F1471-2202-10-64.pdf

Annette Zippelius

Papers

Relaxational dynamics of the Edwards-Anderson model and the mean-field theory of spin-glasses

Energy Landscape of a Lennard-Jones Liquid: Statistics of Stationary Points

Mechanical Properties of Spider Dragline Silk: Humidity, Hysteresis, and Relaxation

Heterogeneous Presynaptic Release Probabilities: Functional Relevance for Short-Term Plasticity

Impairment of mitochondrial calcium handling in a mtSOD1 cell culture model of motoneuron disease