2,158 research outputs found
Thermo-acoustic wave propagation and reflection near the liquid-gas critical point
We study the thermo-acoustic wave propagation and reflection near the
liquid-gas critical point. Specifically, we perform a numerical investigation
of the acoustic responses in a near-critical fluid to thermal perturbations
based on the same setup of a recent ultrasensitive interferometry measurement
in CO2 [Y. Miura et al. Phys. Rev. E 74, 010101(R) (2006)]. The numerical
results agree well with the experimental data. New features regarding the
reflection pattern of thermo-acoustic waves near the critical point under pulse
perturbations are revealed by the proper inclusion of the critically diverging
bulk viscosity.Comment: 14 pages, 4 figures, Accepted by PRE (Rapid Communication
Gaussian approximation for finitely extensible bead-spring chains with hydrodynamic interaction
The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys.,
90 (1) : 463-473, 1989] to account for the influence of fluctuations in
hydrodynamic interactions in Rouse chains, is adapted here to derive a new
mean-field approximation for the FENE spring force. This "FENE-PG" force law
approximately accounts for spring-force fluctuations, which are neglected in
the widely used FENE-P approximation. The Gaussian Approximation for
hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force
approximations to obtain approximate models for finitely-extensible bead-spring
chains with hydrodynamic interactions. The closed set of ODE's governing the
evolution of the second-moments of the configurational probability distribution
in the approximate models are used to generate predictions of rheological
properties in steady and unsteady shear and uniaxial extensional flows, which
are found to be in good agreement with the exact results obtained with Brownian
dynamics simulations. In particular, predictions of coil-stretch hysteresis are
in quantitative agreement with simulations' results. Additional simplifying
diagonalization-of-normal-modes assumptions are found to lead to considerable
savings in computation time, without significant loss in accuracy.Comment: 26 pages, 17 figures, 2 tables, 75 numbered equations, 1 appendix
with 10 numbered equations Submitted to J. Chem. Phys. on 6 February 200
Thermoacoustic effects in supercritical fluids near the critical point: Resonance, piston effect, and acoustic emission and reflection
We present a general theory of thermoacoustic phenomena in supercritical
fluids near the critical point in a one-dimensional cell. We take into account
the effects of the heat conduction in the boundary walls and the bulk viscosity
near the critical point. We introduce a coefficient characterizing
reflection of sound with frequency at the boundary. As applications,
we examine the acoustic eigenmodes in the cell, the response to time-dependent
perturbations, sound emission and reflection at the boundary. Resonance and
rapid adiabatic changes are noteworthy. In these processes, the role of the
thermal diffusion layers is enhanced near the critical point because of the
strong critical divergence of the thermal expansion.Comment: 15 pages, 7 figure
Estimation of the motor threshold for near-rectangular stimuli using the Hodgkin-Huxley model
The motor threshold measurement is a standard in preintervention probing in TMS experiments. We aim to predict the motor threshold for near-rectangular stimuli to efficiently determine the motor threshold size before any experiments take place. Estimating the behavior of large-scale networks requires dynamically accurate and efficient modeling. We utilized a Hodgkin–Huxley (HH) type model to evaluate motor threshold values and computationally validated its function with known true threshold data from 50 participants trials from state-of-the-art published datasets. For monophasic, bidirectional, and unidirectional rectangular stimuli in posterior-anterior or anterior-posterior directions as generated by the cTMS device, computational modeling of the HH model captured the experimentally measured population-averaged motor threshold values at high precision (maximum error ≤ 8%). The convergence of our biophysically based modeling study with experimental data in humans reveals that the effect of the stimulus shape is strongly correlated with the activation kinetics of the voltage-gated ion channels. The proposed method can reliably predict motor threshold size using the conductance-based neuronal models and could therefore be embedded in new generation neurostimulators. Advancements in neural modeling will make it possible to enhance treatment procedures by reducing the number of delivered magnetic stimuli to participants
Simulating the Mammalian Blastocyst - Molecular and Mechanical Interactions Pattern the Embryo
Mammalian embryogenesis is a dynamic process involving gene expression and mechanical forces between proliferating cells. The exact nature of these interactions, which determine the lineage patterning of the trophectoderm and endoderm tissues occurring in a highly regulated manner at precise periods during the embryonic development, is an area of debate. We have developed a computational modeling framework for studying this process, by which the combined effects of mechanical and genetic interactions are analyzed within the context of proliferating cells. At a purely mechanical level, we demonstrate that the perpendicular alignment of the animal-vegetal (a-v) and embryonic-abembryonic (eb-ab) axes is a result of minimizing the total elastic conformational energy of the entire collection of cells, which are constrained by the zona pellucida. The coupling of gene expression with the mechanics of cell movement is important for formation of both the trophectoderm and the endoderm. In studying the formation of the trophectoderm, we contrast and compare quantitatively two hypotheses: (1) The position determines gene expression, and (2) the gene expression determines the position. Our model, which couples gene expression with mechanics, suggests that differential adhesion between different cell types is a critical determinant in the robust endoderm formation. In addition to differential adhesion, two different testable hypotheses emerge when considering endoderm formation: (1) A directional force acts on certain cells and moves them into forming the endoderm layer, which separates the blastocoel and the cells of the inner cell mass (ICM). In this case the blastocoel simply acts as a static boundary. (2) The blastocoel dynamically applies pressure upon the cells in contact with it, such that cell segregation in the presence of differential adhesion leads to the endoderm formation. To our knowledge, this is the first attempt to combine cell-based spatial mechanical simulations with genetic networks to explain mammalian embryogenesis. Such a framework provides the means to test hypotheses in a controlled in silico environment
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Neptunium(V) and neptunium(VI) solubilities in synthetic brines of interest to the Waste Isolation Pilot Plant (WIPP)
The solubility of Np(V) and Np(VI) has been measured in three synthetic Na-K-Mg-Cl brines in the presence of CO{sub 2}(g). Experiments were prepared from oversaturation by adding an excess of NpO{sub 2}{sup +} or NpO{sub 2}{sup 2+} to the brines and allowing the neptunium solids to precipitate. Vessels were maintained in contact with fixed CO{sub 2}(g) partial pressures at constant pH and 24 {+-} 1 C. Dissolved Np(V) concentrations decreased several orders of magnitude within the first 100 days of the experiment, while dissolved Np(VI) concentrations decreased initially but then remained relatively constant for more than 400 days. The solid phases formed in all experiments were identified by X-ray powder diffraction as KNpO{sub 2}CO{sub 3}{center_dot}xH{sub 2}O(s). Steady state concentrations for Np(V) are similar to those observed for Pu(V) in the same brines under the same conditions, where Pu occurs predominantly as Pu(V). Similarly, steady state concentrations for Np(VI), which was not reduced over a two year period, compare well with measured Pu(VI) concentrations in the same brines before the Pu(VI) was reduced to Pu(V)
Mappings of least Dirichlet energy and their Hopf differentials
The paper is concerned with mappings between planar domains having least
Dirichlet energy. The existence and uniqueness (up to a conformal change of
variables in the domain) of the energy-minimal mappings is established within
the class of strong limits of homeomorphisms in the
Sobolev space , a result of considerable interest in the
mathematical models of Nonlinear Elasticity. The inner variation leads to the
Hopf differential and its trajectories.
For a pair of doubly connected domains, in which has finite conformal
modulus, we establish the following principle:
A mapping is energy-minimal if and only if
its Hopf-differential is analytic in and real along the boundary of .
In general, the energy-minimal mappings may not be injective, in which case
one observes the occurrence of cracks in . Nevertheless, cracks are
triggered only by the points in the boundary of where fails to be
convex. The general law of formation of cracks reads as follows:
Cracks propagate along vertical trajectories of the Hopf differential from
the boundary of toward the interior of where they eventually terminate
before making a crosscut.Comment: 51 pages, 4 figure
Sorption Behaviour of W, Hf, Lu, U, and Th on Ion Exchangers from HCI/H2O2 Solutions. Model Experiments for Chemical Studies of Seaborgium (Sg)
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