Multiscaling in superfluid turbulence: A shell-model study

We examine the multiscaling behavior of the normal- and superfluid-velocity structure functions in three-dimensional superfluid turbulence by using a shell model for the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) equations. Our 3D-HVBK shell model is based on the Gledzer-Okhitani-Yamada (GOY) shell model. We examine the dependence of the multiscaling exponents on the normal-fluid fraction and the mutual-friction coefficients. Our extensive study of the 3D-HVBK shell model shows that the multiscaling behavior of the velocity structure functions in superfluid turbulence is more complicated than it is in fluid turbulence.Comment: 12 pages, 6 figure

Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation

We undertake a systematic, direct numerical simulation (DNS) of the two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. First, there are transients that depend on the initial conditions. In the second regime, power-law scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power-laws and the extents of the scaling regions change with time and depended on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers $k > k_c$ and partial thermalization takes place for modes with $k < k_c$; the self-truncation wave number $k_c(t)$ depends on the initial conditions and it grows either as a power of $t$ or as $\log t$. Finally, in the fourth regime, complete-thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms.Comment: 30 pages, 12 figure

Particles and Fields in Superfluids: Insights from the Two-dimensional Gross-Pitaevskii Equation

We carry out extensive direct numerical simulations (DNSs) to investigate the interaction of active particles and fields in the two-dimensional (2D) Gross-Pitaevskii (GP) superfluid, in both simple and turbulent flows. The particles are active in the sense that they affect the superfluid even as they are affected by it. We tune the mass of the particles, which is an important control parameter. At the one-particle level, we show how light, neutral, and heavy particles move in the superfluid, when a constant external force acts on them; in particular, beyond a critical velocity, at which a vortex-antivortex pair is emitted, particle motion can be periodic or chaotic. We demonstrate that the interaction of a particle with vortices leads to dynamics that depends sensitively on the particle characteristics. We also demonstrate that assemblies of particles and vortices can have rich, and often turbulent spatiotemporal evolution. In particular, we consider the dynamics of the following illustrative initial configurations: (a) one particle placed in front of a translating vortex-antivortex pair; (b) two particles placed in front of a translating vortex-antivortex pair; (c) a single particle moving in the presence of counter-rotating vortex clusters; and (d) four particles in the presence of counter-rotating vortex clusters. We compare our work with earlier studies and examine its implications for recent experimental studies in superfluid Helium and Bose-Einstein condensates.Comment: 24 figure

Homogeneous Isotropic Superfluid Turbulence in Two Dimensions: Inverse and Forward Cascades in the Hall-Vinen-Bekharevich-Khalatnikov model

We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normal-fluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli. Our study leads to specific suggestions for experiments

Phase equilibrium study of methane hydrate

Gas hydrates are solid metastable ice like compounds formed when gas comes in contact with water and have the ability to form at low temperatures. In this study, methane gas hydrates were formed in a Berea sandstone core, which was saturated with brine and then pressurized with methane gas. The formation temperatures were 34°F, 36°F and 40°F and the initial pressures were in the range of 1000--1200 psi. Variation of the methane pressure was monitored with time during the formation run. Dissociation experiments were then carried out and the pressure profile along the core with time was recorded. The volume of gas produced during dissociation was recorded with time. Equilibrium pressures were found to be 540 psi, 544 psi and 620 psi for 34°F, 36°F and 40°F, respectively. From the initial rate constants for formation, the activation energy was found to be 79 kJ/mole. The formation of hydrate usually takes 45 hrs while the dissociation takes less than 2 hrs

Asynchronous Validations using Programming Contracts in Java

Design by Contract is a software development methodology based on the idea of having contracts between two software components. Programming contracts are invariants specified as pre-conditions and post-conditions. The client component must ensure that all the pre-conditions are satisfied before calling the server component. The server component must guarantee the post-conditions are met before the call returns to the client component. Current work in Design by Contract in Java focuses on writing shorthand contracts using annotations that are processed serially. Modern software systems require a lot of business rules validations on complicated domain objects. Often, such validations are in the form of a chain of independent tasks that need to be validated one after another. These tasks are computation-intensive and often involve numerous database calls and API calls over the web. This paper presents a validation rule engine framework, Rule4j to facilitate writing such business rules with the help of programming contracts in Java. The contracts are organized in a hierarchy similar to the Racket programming language. The programmer can specify the business rules in the form of a series of higher-order contracts that form a chain. These chains of contracts are validated concurrently and asynchronously to present a final validation result to the programmer. A sample scenario of trade execution is used to demonstrate the performance gain and maintainability of the framework. The experiments conducted show that validations executed using Rule4J run four times faster than the traditional approach. A clear separation of business logic and business validations for the trade execution scenario was achieved using Rule4J

The Statistical Properties of Superfluid Turbulence in 4^4He from the Hall-Vinen-Bekharevich-Khalatnikov Model

We obtain the von K\'arm\'an-Howarth relation for the stochastically forced three-dimensional Hall-Vinen-Bekharvich-Khalatnikov (3D HVBK) model of superfluid turbulence in Helium ($^4$He) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analyitcal studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) $P(\gamma)$, of the ratio $\gamma$ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as $P(\gamma) \sim \gamma^3$, for $\gamma \ll 1$, and $P(\gamma) \sim \gamma^{-3}$, for $\gamma \gg 1$. Furthermore, we show that the PDF $P(\theta)$, of the angle $\theta$ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: $P(\theta)\sim \theta$ for $\theta \ll \theta_*$ and $P(\theta)\sim \theta^{-4}$ for $\theta_* \ll \theta \ll 1$, where $\theta_*$ is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, and the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature $T$, by using the experimentally determined mutual-friction coefficients for superfluid Helium $^4$He, so our results are of direct relevance to superfluid turbulence in this system.Comment: 12 pages, 3 figure