Introducing a quantum kinetic model using the generalized Boltzmann equation in the complex phase space

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In the present work, the three-dimensional modified radial Schrödinger equation is analytically solved. The nonrelativistic interactions under new modified Cornell potential (NMCP, in short) at finite temperature, are extended to the symmetries of nonrelativistic noncommutative space phase (NRNSP, in short), using the generalized Bopp’s shift method in the case of perturbed nonrelativistic quantum chromodynamics (pNRQCD). W generalize this process by adding multi-variable coupling potentials , and together with the modified Cornell potential model in three-dimensional nonrelativistic quantum mechanics noncommutative phase space (3D-NCSP, in short). The new energy eigenvalues and the corresponding Hamiltonian operator are calculated in 3D-NCSP symmetries instead of solving the modified Schrödinger equation with the Weyl Moyal star product. The present results, in (3D-NCSP), are applied to the charmonium and bottomonium masses at finite temperature. The present approach successfully generalizes the energy eigenvalues at finite temperature in 3D-NCSP symmetries. It is found that the perturbative solutions of the discrete spectrum and quarkonium mass can be expressed by the Gamma function, the discreet atomic quantum numbers of the state and the potential parameters ( ), in addition to noncommutativity parameters ( and ). The total complete degeneracy of new energy levels of NMCP changed to become equals to the value instead the values in ordinary quantum mechanics. Our obtained results are in good agreement with the already existing literature in NCSP. Keywords: Schrödinger Equation, Heavy Quarkonium System, Cornell Potential, Noncommutative Space Phase, Bopp’s Shift Method. Subject Classification Numbers: 03.65.-w; 03.65.Ge; 03.65. Fd; 03.65.Ca

On the field of parallel programing has emerged a new big player in the last 10 years. The GPU's have taken a relevant importance on scientific computing because they offer a high performance computing, low cost and simplicity of implementation. However, one of the most important challenges is the program languages used for this devices. The effort for recoding algorithms designed for CPUs is a critical problem. In this paper we review three of principal frameworks for programming CUDA devices compared with the new directives introduced on the OpenMP 4 standard resolving the Jacobi iterative method.

An SOR Implicit Time-accurate Scheme in Calculating Unsteady Flows

This pioneering research on how specific molecules deep inside our brains form a dynamic information holarchy in phase space, linking mind and consciousness, is not only provocative but also revolutionary. Holonomic is a dynamic encapsulation of the holonic view that originates from the word “holon” and designates a holarchical rather than a hierarchical, dynamic brain organization to encompass multiscale effects. The unitary nature of consciousness being interconnected stems from a multiscalar organization of the brain. We aim to give a holonomic modification of the thermodynamic approach to the problem of consciousness using spatiotemporal intermittency. Starting with quasiparticles as the minimalist material composition of the dynamical brain where interferences patterns between incoherent waves of quasiparticles and their quantum-thermal fluctuations constrain the kinetic internal energy of endogenous molecules through informational channels of the negentropically-derived quantum potential. This indicates that brains are not multifractal involving avalanches but are multiscalar, suggesting that unlike the hologram, where the functional interactions occur in the spectral domain, the spatiotemporal binding is multiscalar because of self-referential amplification occurring via long-range correlative information. The associated negentropic entanglement permeates the unification of the functional information architecture across multiple scales. As such, the holonomic brain theory is suitable for active consciousness, proving that consciousness is not fundamental. The holonomic model of the brain’s internal space is nonmetric and nonfractal. It contains a multiscalar informational structure decoded by intermittency spikes in the fluctuations of the negentropically-derived quantum potential. It is therefore, a more realistic approach than the platonic models in phase space.

A second-order hybrid finite-element/volume method for viscoelastic flows

Problems involving the diffusion and transport (angular dependence considered) of neutron radiation are frequently encountered in radiation physics and nuclear engineering. Neutron diffusion problems require substantial computer storage arising from the energy and spatial dependence, while in the case of transport problems the angular dependence of the neutron flux and of the neutron scattering process gives rise to a further considerable increase in storage. In the present work, a method has been developed which greatly eases the bandwidth problem in the solution of large systems of linear equations and algorithms have been developed to assemble and solve such systems of equations in one and two dimensions. The formalism used is the variational method and, for simplicity, linear interpolating functions have been used to derive a symmetric banded system of equations. Finite element algorithms have been implemented in the codes FEED1 and FEED2, which treat one and two space dimensions, respectively. Three benchmark problems are analysed in this paper and results are compared with finite difference discrete ordinate method solutions. It is shown that the finite element method provides fast and accurate solutions to neutron diffusion and transport problems.

Second-order decoupled energy-stable schemes for Cahn-Hilliard-Navier-Stokes equations

Previously, a gas kinetic Bhatnagar–Gross–Krook (BGK) scheme was proposed by us for incompressible flows in the continuum limits. [W. Li and W. Li, “A gas-kinetic BGK scheme for the finite volume lattice Boltzmann method for nearly incompressible flows,” Comput. Fluids 162, 126–138 (2018).] In the present work, we extend the gas kinetic BGK scheme to simulate low-speed isothermal rarefied nonequilibrium gas flows. This scheme is a gas kinetic Lax–Wendroff scheme (GKLWS) for the discrete velocity Boltzmann equation in the finite volume discretization framework with second-order accuracy in both time and space. As collision and transport of the molecular particles are coupled in the present GKLWS, the time step of the present method is not limited by the relaxation time, for which the present scheme is efficient for multiscale gas flows. Moreover, the present GKLWS holds the asymptotic preserving (AP) property, which ensures that both the Navier–Stokes solutions in the continuum limits and free-molecular flow solutions in the rarefied limits can be reliably obtained. To validate the accuracy and AP property of the GKLWS, several numerical benchmarks of isothermal low-speed rarefied gas flows are simulated by the present scheme. The numerical results show that the present scheme can be a reliable multiscale method for all Knudsen number low-speed isothermal gas flows.

In recent decades, the fluidic thrust vector control technique is one of the core strategies to redirect various aerospace vehicles, such as modern launch rockets, supersonic aircraft, and guided missiles. The fundamental theory of the shock vector control is that the gas is injected into the supersonic part of a conventional convergent–divergent nozzle from the transverse to cause interactions between the shock waves and boundary layers. Then, the deflection of the primary jet can be easily realized by the induced oblique shock waves. It was evident that the shock vector control is a very simple, low weight, low cost, and quick vectoring response technique to gain high thrust vectoring performance. In the present work, computational fluid dynamics studies were performed at different control parameters in a three-dimensional rectangular supersonic nozzle with the slot injector. For the validation of the numerical methodology, computational results were compared with experimental data referred to the NASA Langley Research Center. The static pressure distributions along the upper and lower nozzle surfaces in the symmetry plane were matched with the test data excellently. Numerical simulations were based on the well-assessed shear stress transport k–ω turbulence model. Second-order accuracy was selected to reveal more details of the flow-field as much as possible. Lots of factors were investigated, such as the momentum flux ratio, length-to-width ratio, injection location, and injection angle. The performance variations for different affecting factors were illustrated and some constructive conclusions were obtained to provide the reference for further investigations in fluidic thrust vector control field.

I will discuss the design of Ct, an API for nested data parallel programming in C++. Ct uses meta-programming and functional language ideas to essentially embed a pure functional programming language in impure and unsafe languages, like C++. I will discuss the evolution of the design into functional programming ideas, how this was received in the corporate world, and how we plan to proliferate the technology in the next year.Ct is a deterministic parallel programming model integrating the nested data parallelism ideas of Blelloch and bulk synchronous processing ideas of Valiant. That is, data races are not possible in Ct. Moreover, performance in Ct is relatively predictable. At its inception, Ct was conceived as a simple library implementation behind C++ template magic. However, performance issues quickly forced us to consider some form of compilation. Using template programming was highly undesirable for this purpose as it would have been difficult and overly specific to C++ idiosyncrasies. Moreover, once compilation for performance was considered, we began to consider a language semantics that would enable powerful optimizations like calculational fusion, synchronization barrier elimination, and so on. The end result of this deliberation is an API that exposes a value-oriented, purely functional vector processing language. Additional benefits of this approach are numerous, including the important ability to co-exist within legacy threading programming models (because of the data isolation inherent in the model). We will show how the model applies to a wide range of important (at least by cycle count) applications. Ct targets both shipping multi-core architectures from Intel as well as future announced architectures.The corporate reception to this approach has (pleasantly) surprised us. In the desktop and high-performance computing space, where C, C++, Java, and Fortran are the only programming models people talk about, we have made serious inroads into advocating advanced programming language technologies. The desperate need for productive, scalable, and safe programming languages for multi-core architectures has provided an opening for functional, type-safe languages. We will discuss the struggles of multi-core manufacturers (i.e. Intel) and their software vendors that have created this opening.For Intel, Ct heralds its first serious effort to champion a technology that borrows functional programming technologies from the research community. Though it is a compromise that accommodates the pure in the impure and safe in the unsafe, this is an important opportunity to demonstrate the power of functional programming to the unconverted. We plan to share the technology selectively with partners and collaborators, and will have a fully functional and parallelizing implementation by year's end. At CUFP, we will be prepared to discuss our long term plans in detail.

An efficient time-dependent (TD) Monte Carlo (MC) importance sampling method has recently been developed [G. Tao and W. H. Miller, J. Chem. Phys. 135, 024104 (2011)] for the evaluation of time correlation functions using the semiclassical (SC) initial value representation (IVR) methodology. In this TD-SC-IVR method, the MC sampling uses information from both time-evolved phase points as well as their initial values, and only the "important" trajectories are sampled frequently. Even though the TD-SC-IVR was shown in some benchmark examples to be much more efficient than the traditional time-independent sampling method (which uses only initial conditions), the calculation of the SC prefactor-which is computationally expensive, especially for large systems-is still required for accepted trajectories. In the present work, we present an approximate implementation of the TD-SC-IVR method that is completely prefactor-free; it gives the time correlation function as a classical-like magnitude function multiplied by a phase function. Application of this approach to flux-flux correlation functions (which yield reaction rate constants) for the benchmark H + H(2) system shows very good agreement with exact quantum results. Limitations of the approximate approach are also discussed.

A synchronised multi-axis digital holographic interferometry set-up is presented for the study of 3-D flow fields with large density gradients. This optical configuration provides instantaneous interferograms with fine spatial resolution in six directions of projection. A regularised tomographic approach taking into account the presence of possible shock waves is furthermore considered to reconstruct 3-D density fields. Applied to a screeching under-expanded supersonic jet with helical dynamics, this set-up is used to provide dense optical phase measurements in the initial region of the jet. The jet mean density field is shown to be satisfactorily estimated with sharply resolved density gradients. In addition, an approach based on azimuthal Fourier transform and snapshot proper orthogonal decomposition (POD) applied to the instantaneous flow observations is proposed to study the main coherent dynamics of the jet. Relying on a cluster analysis of the azimuthal POD mode coefficients, a reduced dynamical model in the POD mode phase space is used as an approximation of the two observed limit cycles. A clear 3-D representation of the density field of a helical instability associated with screech mode C is then evidenced, with two equally probable directions of rotation. Switching between the two directions is reported, highlighting intermittency in the feedback loop. This helical structure is particularly seen to extend to the jet core, driving its internal dynamics and inducing out-of-phase density fluctuations between the outer and inner shear layers. These out-of-phase motions are related to the non-uniform radial distribution of fluctuation phase associated with the outer-layer Kelvin–Helmholtz instability wave.

This paper introduces several nonlinear multi-model ensemble techniques for multiple chaotic models in high-dimensional phase space by means of artificial neural networks. A chaotic model is built by way of the time-delayed phase space reconstruction of the time series from observables. Several predictive global and local models, including Multi-layered Perceptron Neural Network (MLP-NN), are constructed and a number of multi-model ensemble techniques are implemented to produce more accurate hybrid models. One of these techniques is the nonlinear multi-model ensemble using one kind of dynamic neural network so-called Focused Time Delay Neural Network (FTDNN) with batch and incremental learning algorithms. The proposed techniques were used and tested for predicting storm surge dynamics in the North Sea. The results showed that the accuracy of multi-model ensemble predictions is generally improved in comparison to the one by single models. An FTDNN with incremental learning is more desirable for real-time operation, however in our experiments it was less accurate than batch learning.

Designing efficient and secure implementations of Elliptic Curve Cryptography (ECC) has attracted enormous interest from both theoreticians and practitioners. The main contenders in terms of performance are curves defined over binary extension fields or large prime characteristic fields. In addition to the efficiency requirements, security advantages such as implementation simplicity and resistance to side-channel attacks are receiving increasing attention in research and commercial applications. In this paper, we keep pushing in this direction and study efficient implementation of regular scalar multiplication algorithms for binary curves equipped with efficient endomorphisms. Our focus is on implementing the Galbraith-Lin-Scott (GLS) family of binary curves by exploring the space of different models and laddering algorithms, for their high performance, reasonable implementation simplicity, lower memory consumption and side-channel resistance. Our results demonstrate that laddering implementations can be competitive with window-based methods by obtaining a new speed record for laddering implementations of elliptic curves on high-end Intel processors.