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Critical indices beta, gamma delta, nv, etc. are defined and calculated for self-organized critical phenomena. Scaling relations are derived and checked numerically. The order-parameter exponent beta describes the spontaneous current and the relaxation to the criticl point. The power spectrum has 'l/f' behavior with the exponent phi = nv x z, where z is the dynamical critical exponent.
A Lanczos technique is used to study the frustrated spin-1/2 Heisenberg model on square lattices of 16 and 20 sites. Frustration is introduced by an interaction along the diagonals of the plaquettes with coupling J2 greater than or equal to 0. For large J2, the ground state breaks (spontaneously) the lattice rotational symmetry. For intermediate values of J2, the squares of order parameters associated with spin-Peierls and 'twisted'states have a peak, while a similar quantity for a chiral state shows no interesting structure.
Deformation effects of droplet fluctuations on the dynamics in an Ising ferromagnetic state in two dimensions are studied in the case of an order-parameter-nonconserving system by investigating an equation of motion for a domain boundary. Analytic and numerical studies show that the deformation effects on the survival probability of the droplets simply result in changing the time scale or renormalizing a kinetic coefficient.
The scaling behavior of sandpile models is investigated analytically. First, it is shown that sandpile models contain a set of domain walls, referred to as troughs, which bound regions that can experience avalanches. It is further shown that the dynamics of the troughs is governed by a simple set of rules involving birth, death, and coalescence events. A simple trough model is then introduced, and it is proved that the model has a phase transition with the density of the troughs as an order parameter and that, in the thermodynamic limit, the trough density goes to zero at the transition point. Finally, it is shown that the observed scaling behavior is a consequence of finite-size effects.
Highly supersaturated electrolyte solutions can be prepared and studied employing an electrodynamic levitator trap (ELT) technique. The ELT technique involves containerless suspension of a microdroplet thus eliminating dust, dirt, and container walls which normally cause heterogeneous nucleation. This allows very high supersaturations to be achieved. A theoretical study of the experimental results obtained for the water activity in microdroplets of various electrolyte solutions is based on the development of the Cahn-Hilliard formalism for electrolyte solutions. In the approach suggested the metastable state for electrolyte solutions is described in terms of the conserved order parameter omega(r,t) associated with fluctuations of the mean solute concentration n(sub 0). Parameters of the corresponding Ginzburg-Landau free energy functional which defines the dynamics of metastable state relaxation are determined and expressed through the experimentally measured quantities. A correspondence of 96-99 % between theory and experiment for all solutions studied was achieved and allowed the determination of an analytical expression for the spinodal concentration n(sub spin), and its calculation for various electrolyte solutions at 298 K. The assumption that subcritical solute clusters consist of the electrically neutral Bjerrum pairs has allowed both analytical and numerical investigation of the number-size N(sub c) of nucleation monomers (aggregates of the Bjerrum pairs) which are elementary units of the solute critical clusters. This has also allowed estimations for the surface tension Alpha, and equilibrium bulk energy Beta per solute molecule in the nucleation monomers. The dependence of these properties on the temperature T and on the solute concentration n(sub 0) through the entire metastable zone (from saturation concentration n(sub sat) to spinodal n(sub spin) is examined. It has been demonstrated that there are the following asymptotics: N(sub c), = I at spinodal concentration and N(sub c) = infinity at saturation.
We present results of molecular dynamics simulations of a glycerol 1-monooleate bilayer in water. The total length of analyzed trajectories is 5ns. The calculated width of the bilayer agrees well with the experimentally measured value. The interior of the membrane is in a highly disordered fluid state. Atomic density profile, orientational and conformational distribution functions, and order parameters indicate that disorder increases toward the center of the bilayer. Analysis of out-of-plane thermal fluctuations of the bilayer surfaces occurring at the time scale of the present calculations reveals that the distribution of modes agrees with predictions of the capillary wave model. Fluctuations of both bilayer surfaces are uncorrelated, yielding Gaussian distribution of instantaneous widths of the membrane. Fluctuations of the width produce transient thinning defects in the bilayer which occasionally span almost half of the membrane. The leading mechanism of these fluctuations is the orientational and conformational motion of head groups rather than vertical motion of the whole molecules. Water considerably penetrates the head group region of the bilayer but not its hydrocarbon core. The total net excess dipole moment of the interfacial water points toward the aqueous phase, but the water polarization profile is non-monotonic. Both water and head groups significantly contribute to the surface potential across the interface. The calculated sign of the surface potential is in agreement with that from experimental measurements, but the value is markedly overestimated. The structural and electrical properties of the water-bilayer system are discussed in relation to membrane functions, in particular transport of ions and nonelectrolytes across membranes.
We performed theoretical studies of liquid helium by applying state of the art simulation and finite-size scaling techniques. We calculated universal scaling functions for the specific heat and superfluid density for various confining geometries relevant for experiments such as the confined helium experiment and other ground based studies. We also studied microscopically how the substrate imposes a boundary condition on the superfluid order parameter as the superfluid film grows layer by layer. Using path-integral Monte Carlo, a quantum Monte Carlo simulation method, we investigated the rich phase diagram of helium monolayer, bilayer and multilayer on a substrate such as graphite. We find excellent agreement with the experimental results using no free parameters. Finally, we carried out preliminary calculations of transport coefficients such as the thermal conductivity for bulk or confined helium systems and of their scaling properties. All our studies provide theoretical support for various experimental studies in microgravity.
Nanoscale structures, such as nanowires and carbon nanotubes (CNTs), are often grown in gaseous or plasma environments. Successful growth of these structures is defined by achieving a specified crystallinity or chirality, size or diameter, alignment, etc., which in turn depend on gas mixture ratios. pressure, flow rate, substrate temperature, and other operating conditions. To date, there has not been a rigorous growth model that addresses the specific concerns of crystalline nanowire growth, while demonstrating the correct trends of the processing conditions on growth rates. Most crystal growth models are based on the Burton, Cabrera, and Frank (BCF) method, where adatoms are incorporated into a growing crystal at surface steps or spirals. When the supersaturation of the vapor is high, islands nucleate to form steps, and these steps subsequently spread (grow). The overall bulk growth rate is determined by solving for the evolving motion of the steps. Our approach is to use a phase field model to simulate the growth of finite sized nanowire crystals, linking the free energy equation with the diffusion equation of the adatoms. The phase field method solves for an order parameter that defines the evolving steps in a concentration field. This eliminates the need for explicit front tracking/location, or complicated shadowing routines, both of which can be computationally expensive, particularly in higher dimensions. We will present results demonstrating the effect of process conditions, such as substrate temperature, vapor supersaturation, etc. on the evolving morphologies and overall growth rates of the nanostructures.
Estimating how free energy changes with the state of a system is a central goal in applications of statistical mechanics to problems of chemical or biological interest. From these free energy changes it is possible, for example, to establish which states of the system are stable, what are their probabilities and how the equilibria between these states are influenced by external conditions. Free energies are also of great utility in determining kinetics of transitions between different states. A variety of methods have been developed to compute free energies of condensed phase systems. Here, I will focus on one class of methods - those that allow for calculating free energy changes along one or several generalized coordinates in the system, often called reaction coordinates or order parameters . Considering that in almost all cases of practical interest a significant computational effort is required to determine free energy changes along such coordinates it is hardly surprising that efficiencies of different methods are of great concern. In most cases, the main difficulty is associated with its shape along the reaction coordinate. If the free energy changes markedly along this coordinate Boltzmann sampling of its different values becomes highly non-uniform. This, in turn, may have considerable, detrimental effect on the performance of many methods for calculating free energies.
The thermodynamic theory of superfluid helium in the presence of a heat current is presented. We show that there is a thermodynamic relation between the heat capacity and the expression ps(W), which describes the depression of the superfluid density with the counterflow velocity W. Using this relation we show that the heat capacity of superfluid super4He in the presence of a heat current diverges at a depressed lambda transition temperature, suggesting the possibility of a new second order phase transition where the superfluid wave function is not the order parameter.
Parametric expressions are used to calculate the isothermal susceptibility, specific heat, order parameter, and correlation length along the critical isochore and coexistence curve from the asymptotic region to crossover region.
Optical design concepts for the telescope and instrumentation for NASA's New Worlds Observer program are presented. First order parameters are derived from the science requirements, and estimated performance metrics are shown using optical models. A four meter multiple channel telescope is discussed, as well as a suite of science instrument concepts. Wide field instrumentation (imager and spectrograph) would be accommodated by a three-mirror anastigmat telescope design. Planet finding and characterization would use a separate channel which is picked off after the first two mirrors (primary and secondary). Guiding concepts are also discussed.
A paper presents a theoretical study of shock waves in a trapped Bose-Einstein condensate (BEC). The mathematical model of the BEC in this study is a nonlinear Schroedinger equation (NLSE) in which (1) the role of the wave function of a single particle in the traditional Schroedinger equation is played by a space- and time-dependent complex order parameter (x,t) proportional to the square root of the density of atoms and (2) the atoms engage in a repulsive interaction characterized by a potential proportional to | (x,t)|2. Equations that describe macroscopic perturbations of the BEC at zero temperature are derived from the NLSE and simplifying assumptions are made, leading to equations for the propagation of sound waves and the transformation of sound waves into shock waves. Equations for the speeds of shock waves and the relationships between jumps of velocity and density across shock fronts are derived. Similarities and differences between this theory and the classical theory of sound waves and shocks in ordinary gases are noted. The present theory is illustrated by solving the equations for the example of a shock wave propagating in a cigar-shaped BEC.
We have recently shown that normal-metal/superconductor (N/S) bilayer TESs (superconducting Transition-Edge Sensors) exhibit weak-link behavior.l Here we extend our understanding to include TESs with added noise-mitigating normal-metal structures (N structures). We find TESs with added Au structures also exhibit weak-link behavior as evidenced by exponential temperature dependence of the critical current and Josephson-like oscillations of the critical current with applied magnetic field. We explain our results in terms of an effect converse to the longitudinal proximity effect (LoPE) 1, the lateral inverse proximity effect (LaiPE), for which the order parameter in the N/S bilayer is reduced due to the neighboring N structures. Resistance and critical current measurements are presented as a function of temperature and magnetic field taken on square Mol Au bilayer TESs with lengths ranging from 8 to 130 {\mu}m with and without added N structures. We observe the inverse proximity effect on the bilayer over in-plane distances many tens of microns and find the transition shifts to lower temperatures scale approximately as the inverse square of the in- plane N-structure separation distance, without appreciable broadening of the transition width. We also present evidence for nonequilbrium superconductivity and estimate a quasiparticle lifetime of 1.8 \times 10-10 s for the bilayer. The LoPE model is also used to explain the increased conductivity at temperatures above the bilayer's steep resistive transition.
We have made high resolution x-ray microcalorimeters using superconducting MoAu bilayers and Nb meander coils. The temperature sensor is a Magnetic Penetration Thermometer (MPT). Operation is similar to metallic magnetic calorimeters, but instead of the magnetic susceptibility of a paramagnetic alloy, we use the diamagnetic response of the superconducting MoAu to sense temperature changes in an x-ray absorber. Flux-temperature responsivtty can be large for small sensor heat capacity, with enough dynamic range for applications. We find models of observed flux-temperature curves require several effects to explain flux penetration or expulsion in the microscopic devices. The superconductor is non-local, with large coherence length and weak pinning of flux. At lowest temperatures, behavior is dominated by screening currents that vary as a result of the temperature dependence of the magnetic penetration depth, modified by the effect of the nonuniformity of the applied field occurring on a scale comparable to the coherence length. In the temperature regime where responslvity is greatest, spadal variations in the order parameter become important: both local variations as flux enters/leaves the film and an intermediate state is formed, and globally as changing stability of the electrical circuit creates a Meissner transition and flux is expelled/penetrates to minimize free energy.
The flight software (FSW) math library is a collection of reusable math components that provides typical math utilities required by spacecraft flight software. These utilities are intended to increase flight software quality reusability and maintainability by providing a set of consistent, well-documented, and tested math utilities. This library only has dependencies on ANSI C, so it is easily ported. Prior to this library, each mission typically created its own math utilities using ideas/code from previous missions. Part of the reason for this is that math libraries can be written with different strategies in areas like error handling, parameters orders, naming conventions, etc. Changing the utilities for each mission introduces risks and costs. The obvious risks and costs are that the utilities must be coded and revalidated. The hidden risks and costs arise in miscommunication between engineers. These utilities must be understood by both the flight software engineers and other subsystem engineers (primarily guidance navigation and control). The FSW math library is part of a larger goal to produce a library of reusable Guidance Navigation and Control (GN&C) FSW components. A GN&C FSW library cannot be created unless a standardized math basis is created. This library solves the standardization problem by defining a common feature set and establishing policies for the library s design. This allows the libraries to be maintained with the same strategy used in its initial development, which supports a library of reusable GN&C FSW components. The FSW math library is written for an embedded software environment in C. This places restrictions on the language features that can be used by the library. Another advantage of the FSW math library is that it can be used in the FSW as well as other environments like the GN&C analyst s simulators. This helps communication between the teams because they can use the same utilities with the same feature set and syntax.
We have recently shown that normal-metal/superconductor (N /S) bilayer TESs (superconducting Transition-Edge Sensors) exhibit weak-link behavior. Our measurements were explained in terms of a longitudinal proximity effect model in which superconducting order from the higher transition temperature leads is induced into the TES bilayer plane over remarkably long distances (up to 290 micron). Here we extend our understanding to include TESs with added noise-mitigating normal-metal structures (N structures). We explain our results in terms of an effect converse to the longitudinal proximity effect (LoPE), the lateral inverse proximity effect (LaiPE), for which the order parameter in the N /S bilayer is reduced due to the neighboring N structures. We present resistance and critical current measurements as a function of temperature and magnetic field taken on square Mo/Au bilayer TESs with lengths ranging from 8 to 130 micron with and without added N structures. We observe the inverse proximity effect on the bilayer over in-plane distances many tens of microns and find the transition shifts to lower temperatures scale approximately as the inverse square of the in-plane N-structure separation distance, without appreciable broadening of the transition width. We find TESs with added Au structures exhibit weak-link behavior as evidenced by exponential temperature dependence of the critical current and Josephson-like oscillations of the critical current with applied magnetic field. We also present evidence for nonequilbrium superconductivity and estimate a quasiparticle lifetime of 1.8 x 10(exp -10) s for the bilayer. The LoPE model is also used to explain the increased conductivity at temperatures above the bilayer's steep resistive transition.
We have recently shown that normal-metal/superconductor (N/S) bilayer TESs (superconducting Transition-Edge Sensors) exhibit weak-link behavior. Our measurements were explained in terms of a longitudinal proximity effect model in which superconducting order from the higher transition temperature leads is induced into the TES bilayer plane over remarkably long distances (up to 290 micron). Here we extend our understanding to include TESs with added noise-mitigating normal-metal structures (N structures). We explain our results of an effect converse to the longitudinal proximity effect (LoPE), the lateral inverse proximity effect (LaiPE), for which the order parameter in the N/S bilayer is reduced due to the neighboring N structures. We present resistance and critical current measurements as a function of temperature and magnetic field taken on square Mo/Au bilayer TESs with lengths ranging from 8 to 130 micron with and without added N structures. We observe the inverse proximity effect on the bilayer over in-plane distances many tens of microns and find the transition shifts to lower temperature scale approximately as the inverse square of the in-plane N-structure separation distance, without appreciable broadening of the transition width. We find TESs with added Au structures exhibit weak-link behavior as evidenced by exponential temperature dependence of the critical current and Josephson-like oscillations of the critical current with applied magnetic field. We also present evidence for nonequilbrium superconductivity and estimate a quasiparticle lifetime of 1.8 x 10(exp -10) s for the bilayer. The LoPE model is also used to explain the increased conductivity at temperatures above the bilayer's steep resistive transition