Nonuniformity of the constitutive law parameters for shear rupture and quasistatic nucleation to dynamic rupture: a physical model of earthquake generation processes.

Based on the recent high-resolution laboratory experiments on propagating shear rupture, the constitutive law that governs shear rupture processes is discussed in view of the physical principles and constraints, and a specific constitutive law is proposed for shear rupture. It is demonstrated that nonuniform distributions of the constitutive law parameters on the fault are necessary for creating the nucleation process, which consists of two phases: (i) a stable, quasistatic phase, and (ii) the subsequent accelerating phase. Physical models of the breakdown zone and the nucleation zone are presented for shear rupture in the brittle regime. The constitutive law for shear rupture explicitly includes a scaling parameter Dc that enables one to give a common interpretation to both small scale rupture in the laboratory and large scale rupture as earthquake source in the Earth. Both the breakdown zone size Xc and the nucleation zone size L are prescribed and scaled by Dc, which in turn is prescribed by a characteristic length lambda c representing geometrical irregularities of the fault. The models presented here make it possible to understand the earthquake generation process from nucleation to unstable, dynamic rupture propagation in terms of physics. Since the nucleation process itself is an immediate earthquake precursor, deep understanding of the nucleation process in terms of physics is crucial for the short-term (or immediate) earthquake prediction.

Pitch perception: A dynamical-systems perspective

Two and a half millennia ago Pythagoras initiated the scientific study of the pitch of sounds; yet our understanding of the mechanisms of pitch perception remains incomplete. Physical models of pitch perception try to explain from elementary principles why certain physical characteristics of the stimulus lead to particular pitch sensations. There are two broad categories of pitch-perception models: place or spectral models consider that pitch is mainly related to the Fourier spectrum of the stimulus, whereas for periodicity or temporal models its characteristics in the time domain are more important. Current models from either class are usually computationally intensive, implementing a series of steps more or less supported by auditory physiology. However, the brain has to analyze and react in real time to an enormous amount of information from the ear and other senses. How is all this information efficiently represented and processed in the nervous system? A proposal of nonlinear and complex systems research is that dynamical attractors may form the basis of neural information processing. Because the auditory system is a complex and highly nonlinear dynamical system, it is natural to suppose that dynamical attractors may carry perceptual and functional meaning. Here we show that this idea, scarcely developed in current pitch models, can be successfully applied to pitch perception.

Models for stochastic climate prediction

There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate prediction. Here several idealized models for stochastic climate modeling are introduced and analyzed through unambiguous mathematical theory. This analysis demonstrates the potential need for more sophisticated models beyond stable linear Langevin equations. The new phenomena include the emergence of both unstable linear Langevin stochastic models for the climate mean and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances. The strategy for stochastic climate modeling that emerges from this analysis is illustrated on an idealized example involving truncated barotropic flow on a beta-plane with topography and a mean flow. In this example, the effect of the original 57 degrees of freedom is well represented by a theoretically predicted stochastic model with only 3 degrees of freedom.

Polymer Models of Meiotic and Mitotic Chromosomes

Polymers tied together by constraints exhibit an internal pressure; this idea is used to analyze physical properties of the bottle-brush–like chromosomes of meiotic prophase that consist of polymer-like flexible chromatin loops, attached to a central axis. Using a minimal number of experimental parameters, semiquantitative predictions are made for the bending rigidity, radius, and axial tension of such brushes, and the repulsion acting between brushes whose bristles are forced to overlap. The retraction of lampbrush loops when the nascent transcripts are stripped away, the oval shape of diplotene bivalents between chiasmata, and the rigidity of pachytene chromosomes are all manifestations of chromatin pressure. This two-phase (chromatin plus buffer) picture that suffices for meiotic chromosomes has to be supplemented by a third constituent, a chromatin glue to understand mitotic chromosomes, and explain how condensation can drive the resolution of entanglements. This process resembles a thermal annealing in that a parameter (the affinity of the glue for chromatin and/or the affinity of the chromatin for buffer) has to be tuned to achieve optimal results. Mechanical measurements to characterize this protein–chromatin matrix are proposed. Finally, the propensity for even slightly chemically dissimilar polymers to phase separate (cluster like with like) can explain the apparent segregation of the chromatin into A+T- and G+C-rich regions revealed by chromosome banding.

The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

Large vortex-like structure of dipole field in computer models of liquid water and dipole-bridge between biomolecules

We propose a framework to describe the cooperative orientational motions of water molecules in liquid water and around solute molecules in water solutions. From molecular dynamics (MD) simulation a new quantity “site-dipole field” is defined as the averaged orientation of water molecules that pass through each spatial position. In the site-dipole field of bulk water we found large vortex-like structures of more than 10 Å in size. Such coherent patterns persist more than 300 ps although the orientational memory of individual molecules is quickly lost. A 1-ns MD simulation of systems consisting of two amino acids shows that the fluctuations of site-dipole field of solvent are pinned around the amino acids, resulting in a stable dipole-bridge between side-chains of amino acids. The dipole-bridge is significantly formed even for the side-chain separation of 14 Å, which corresponds to five layers of water. The way that dipole-bridge forms sensitively depends on the side-chain orientations and thereby explains the specificity in the solvent-mediated interactions between biomolecules.