Predictors and predictands of linear response in spatially extended systems

The goal of response theory, in each of its many statistical mechanical formulations, is to predict the perturbed response of a system from the knowledge of the unperturbed state and of the applied perturbation. A new recent angle on the problem focuses on providing a method to perform predictions of the change in one observable of the system using the change in a second observable as a surrogate for the actual forcing. Such a viewpoint tries to address the very relevant problem of causal links within complex system when only incomplete information is available. We present here a method for quantifying and ranking the predictive ability of observables and use it to investigate the response of a paradigmatic spatially extended system, the Lorenz ’96 model. We perturb locally the system and we then study to what extent a given local observable can predict the behaviour of a separate local observable. We show that this approach can reveal insights on the way a signal propagates inside the system. We also show that the procedure becomes more efficient if one considers multiple acting forcings and, correspondingly, multiple observables as predictors of the observable of interest.

Influence of Distributed Dislocations on Stability of Hollow Nonlinearly Elastic Sphere

The phenomenon of stability loss of a hollow elastic sphere containing distributed dislocations and loaded with external hydrostatic pressure is studied. The study was carried out in the framework of the nonlinear elasticity theory and the continuum theory of continuously distributed dislocations. An exact statement and solution of the stability problem for a three-dimensional elastic body with distributed dislocations are given. The static problem of nonlinear elasticity theory for a body with distributed dislocations is reduced to a system of equations consisting of equilibrium equations, incompatibility equations with a given dislocation density tensor, and constitutive equations of the material. The unperturbed state is caused by external pressure and a spherically symmet-ric distribution of dislocations. For distributed edge dislocations in the framework of a harmonic (semi-linear) mate-rial model, the unperturbed state is defined as an exact spherically symmetric solution to a nonlinear boundary value problem. This solution is valid for any function that characterizes the density of edge dislocations. The perturbed equilibrium state is described by a boundary value problem linearized in the neighborhood of the equilibrium. The analysis of the axisymmetric buckling of the sphere was performed using the bifurcation method. It consists in determining the equilibrium positions of an elastic body, which differ little from the unperturbed state. By solving the linearized problem, the value of the external pressure at which the sphere first loses stability is found. The effect of dislocations on the buckling of thin and thick spherical shells is analyzed.

Disulfide reduction allosterically destabilizes the β-ladder sub-domain assembly within the NS1 dimer of ZIKV

The Zika virus (ZIKV) was responsible for a recent debilitating epidemic that till date has no cure. A potential way to reduce ZIKV virulence is to limit the action of the non-structural proteins involved in its viral replication. One such protein, NS1, encoded as a monomer by the viral genome, plays a major role via symmetric oligomerization. We examine the homodimeric structure of the dominant β-ladder segment of NS1 with extensive all atom molecular dynamics. We find it stably bounded by two spatially separated interaction clusters (C1 and C2) with significant differences in the nature of their interactions. Four pairs of distal, intra-monomeric disulfide bonds are found to be coupled to the stability, local structure, and wettability of the interfacial region. Symmetric reduction of the intra-monomeric disulfides triggers marked dynamical heterogeneity, interfacial wettability and asymmetric salt bridging propensity. Harnessing the model-free Lipari-Szabo based formalism for estimation of conformational entropy (Sconf), we find clear signatures of heterogeneity in the monomeric conformational entropies. The observed asymmetry, very small in the unperturbed state, expands significantly in the reduced states. This allosteric effect is most noticeable in the electrostatically bound C2 cluster that underlies the greatest stability in the unperturbed state. Allosteric induction of conformational and thermodynamic asymmetry is expected to affect the pathways leading to symmetric higher ordered oligomerization, and thereby affect crucial replication pathways.Statement of significanceControlling viral pathogenesis remains a challenge in the face of modern-day epidemics. Though cumbersome and fraught with misleads, most therapeutic endeavors lean towards the design of drug molecules targeting specific proteins involved in viral pathogenesis. This work demonstrates an alternative approach, namely the usage of allosteric intervention to disrupt the binding integrity of the primary domain of the non-structural NS1 protein dimer crucially important in ZIKV virulence. The intervention, triggered by symmetric reduction of the internal monomeric disulfide bonds, results in weakening and distortion of the distal binding interfaces. It further introduces marked structural and entropic asymmetry within the homooligomeric unit, precluding the formation of higher ordered oligomers of high symmetry. The results have important ramifications for consolidated efforts at limiting ZIKV virulence.

Line Vortices and the Vacillation of Langmuir Circulation

Three types of breakdown of Langmuir circulation (Lc) are observed, two of which are represented in large-eddy simulation (LES) models, but the third, vacillation, is not. The stability of Lc can be examined by representing the downwind-aligned vortices by line vortices that are subjected to perturbations. Earlier conclusions relating to stability in homogeneous water of infinite depth are found to be in error because no stationary unperturbed state exists. The motion of vortices is examined and shown to be consistent with an explanation of Lc devised by Csanady. Motion of line vortices in water of limited depth or bounded below by a thermocline is examined. The motion replicates some of the features of vacillation observed by Smith in deep water bounded by a thermocline, including its periodicity and fluctuations in the formation of bubble bands. Vortices describe closed orbits within the Langmuir cells. Particle motions in the vacillating Lc pattern exhibit trapping close to the line vortices or near the cell boundaries. Vacillation appears not to have been observed in water of limited depth. Here, the vacillation period is predicted to be longer than the deep-water equivalent and may be too long for vacillations to be detected.

Unperturbed state and solitary structures in an electron-positron plasma having dust impurity and density inhomogeneity

An electron–positron pair plasma having dust impurity and density non-uniformity is studied for its unperturbed state and evolution of solitary structures under the effect of either positively charged or negatively charged dust grains. Zeroth-order equations are solved to examine the unperturbed state of the plasma via unperturbed potential φ0, drift velocities of the electrons and positrons (ve0 and vp0), and plasma (positron) density gradient np0η. It is observed that the dust distribution affects the gradient np0η significantly, which increases very sharply with a small increment in the dust density gradient nd0η. With relation to the solitary structures, a modified form of Korteweg–deVries equation (mKdV equation) is realized in the said plasma, which reveals that a tailing structure is associated with the soliton (sech2 structure). This tail is less prominent in the present pair plasma, contrary to the observation made in ordinary plasmas having only ions and electrons. The dust impurity is found to influence the solitary structure much significantly and its presence suppresses the rarefactive solitons, which are generally observed in multi-component species plasmas.

Note on magneto-hydrodynamic gravitational stability of a double fluids interface

The magneto–gravitational stability of double-fluid interface is discussed. The pressure in the unperturbed state is not constant because the self-gravitating force is a long-range force. The dispersion relation is derived and discussed. The self-gravitating model is unstable in the symmetric mode m = 0 (m is the transverse wave number), while it is stable in all other states. The effects of the densities, the liquid-fluid radii ratios, and the electromagnetic force on the stability of the present model are identified for all wavelengths.PACS Nos.: 47.35.Tv, 47.65.–d, 04.40.–b

ULF hydromagnetic oscillations with the discrete spectrum as eigenmodes of MHD-resonator in the near-Earth part of the plasma sheet

A new concept is proposed for the emergence of ULF geomagnetic oscillations with a discrete spectrum of frequencies (0.8, 1.3, 1.9, 2.6 ...mHz) registered in the magnetosphere's midnight-morning sector. The concept relies on the assumption that these oscillations are MHD-resonator eigenmodes in the near-Earth plasma sheet. This magnetospheric area is where conditions are met for fast magnetosonic waves to be confined. The confinement is a result of the velocity values of fast magnetosonic waves in the near-Earth plasma sheet which differ greatly from those in the magnetotail lobes, leading to turning points forming in the tailward direction for the waves under study. To compute the eigenfrequency spectrum of such a resonator, we used a model magnetosphere with parabolic geometry. The fundamental harmonics of this resonator's eigenfrequencies are shown to be capable of being clustered into groups with average frequencies matching, with good accuracy, the frequencies of the observed oscillations. A possible explanation for the stability of the observed oscillation frequencies is that such a resonator might only form when the magnetosphere is in a certain unperturbed state.