Spectral statistics of the quenched normal modes of a network-forming molecular liquid

We evaluate the density of states of the quenched normal modes of ST2 water, and their statistical fluctuations, for a range of densities spanning three regimes of behavior of a hydrogen bonded liquid: a lower-density regime of random tetrahedral network formation; in the vicinity of a liquid-liquid critical point; and in a higher-density regime of fragile glass-forming behavior. For all cases we find that the fluctuations around the mean spectral densities obey the predictions of the Gaussian orthogonal ensemble of random matrix theory. We also measure the participation ratio of the normal modes across the entire frequency range, and find behavior consistent with the majority of modes being of an extended nature, rather than localized.Comment: Accepted for publication in The Journal of Chemical Physic

Sparse random matrices and vibrational spectra of amorphous solids

A random matrix approach is used to analyze the vibrational properties of amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n independent non-zero elements in each row. The average values =0 and dispersion =V^2 for all non-zero elements. The density of vibrational states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle law with radius independent of N. We argue that for n^2 << N this model can be used to describe the interaction of atoms in amorphous solids. The level statistics of matrix M is well described by the Wigner surmise and corresponds to repulsion of eigenfrequencies. The participation ratio for the major part of vibrational modes in three dimensional system is about 0.2 - 0.3 and independent of N. Together with term repulsion it indicates clearly to the delocalization of vibrational excitations. We show that these vibrations spread in space by means of diffusion. In this respect they are similar to diffusons introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous silicon. Our results are in a qualitative and sometimes in a quantitative agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure

A Computational Model of the Ionic Currents, Ca2+ Dynamics and Action Potentials Underlying Contraction of Isolated Uterine Smooth Muscle

Uterine contractions during labor are discretely regulated by rhythmic action potentials (AP) of varying duration and form that serve to determine calcium-dependent force production. We have employed a computational biology approach to develop a fuller understanding of the complexity of excitation-contraction (E-C) coupling of uterine smooth muscle cells (USMC). Our overall aim is to establish a mathematical platform of sufficient biophysical detail to quantitatively describe known uterine E-C coupling parameters and thereby inform future empirical investigations of physiological and pathophysiological mechanisms governing normal and dysfunctional labors. From published and unpublished data we construct mathematical models for fourteen ionic currents of USMCs: currents (L- and T-type), current, an hyperpolarization-activated current, three voltage-gated currents, two -activated current, -activated current, non-specific cation current, - exchanger, - pump and background current. The magnitudes and kinetics of each current system in a spindle shaped single cell with a specified surface area∶volume ratio is described by differential equations, in terms of maximal conductances, electrochemical gradient, voltage-dependent activation/inactivation gating variables and temporal changes in intracellular computed from known fluxes. These quantifications are validated by the reconstruction of the individual experimental ionic currents obtained under voltage-clamp. Phasic contraction is modeled in relation to the time constant of changing . This integrated model is validated by its reconstruction of the different USMC AP configurations (spikes, plateau and bursts of spikes), the change from bursting to plateau type AP produced by estradiol and of simultaneous experimental recordings of spontaneous AP, and phasic force. In summary, our advanced mathematical model provides a powerful tool to investigate the physiological ionic mechanisms underlying the genesis of uterine electrical E-C coupling of labor and parturition. This will furnish the evolution of descriptive and predictive quantitative models of myometrial electrogenesis at the whole cell and tissue levels

Numerical studies on the Impact of the Last Glacial Cycle on recent borehole temperature profiles: implications for terrestrial energy balance

Reconstructions of past climatic changes from borehole temperature profiles are important independent estimates of temperature histories over the last millennium. There remain, however, multiple uncertainties in the interpretation of these data as climatic indicators and as estimates of the changes in the heat content of the continental subsurface due to long-term climatic change. One of these uncertainties is associated with the often ignored impact of the last glacial cycle (LGC) on the subsurface energy content, and on the estimate of the background quasi steady-state signal associated with the diffusion of accretionary energy from the Earth's interior. Here, we provide the first estimate of the impact of the development of the Laurentide ice sheet on the estimates of energy and temperature reconstructions from measurements of terrestrial borehole temperatures in North America. We use basal temperature values from the data-calibrated Memorial University of Newfoundland glacial systems model (MUN-GSM) to quantify the extent of the perturbation to estimated steady-state temperature profiles, and to derive spatial maps of the expected impacts on measured profiles over North America. Furthermore, we present quantitative estimates of the potential effects of temperature changes during the last glacial cycle on the borehole reconstructions over the last millennium for North America. The range of these possible impacts is estimated using synthetic basal temperatures for a period covering 120 ka to the present day that include the basal temperature history uncertainties from an ensemble of results from the calibrated numerical model. For all the locations, we find that within the depth ranges that are typical for available boreholes (≈600 m), the induced perturbations to the steady-state temperature profile are on the order of 10 mW m−2, decreasing with greater depths. Results indicate that site-specific heat content estimates over North America can differ by as much as 50%, if the energy contribution of the last glacial cycle in those areas of North America that experienced glaciation is not taken into account when estimating recent subsurface energy changes from borehole temperature data

Evidence of a two-state picture for supercooled water and its connections with glassy dynamics

The picture of liquid water as consisting of a mixture of molecules of two different structural states (structured, low-density molecules and unstructured, high-density ones) represents a belief that has been around for long time awaiting for a conclusive validation. While in the last years some indicators have indeed provided certain evidence for the existence of structurally different ``species´´, a more definite bimodality in the distribution function of a sound structural quantity would be desired. In this context, our present work combines the use of a structural parameter with a minimization technique to yield neat bimodal distributions in a temperature range within the supercooled liquid regime, thus clearly revealing the presence of two populations of differently structured water molecules. Furthermore, we elucidate the role of the inter-conversion between the identified two kinds of states for the dynamics of structural relaxation, thus linking structural information to dynamics, a longstanding issue in glass physics.Fil: Appignanesi, Gustavo Adrian. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Química del Sur. Universidad Nacional del Sur. Departamento de Química. Instituto de Química del Sur; ArgentinaFil: Rodriguez Fris, Jorge Ariel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Química del Sur. Universidad Nacional del Sur. Departamento de Química. Instituto de Química del Sur; ArgentinaFil: Sciortino, Francesco. Università di Roma; Itali