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We undertake a systematic study of W*-rigidity paradigms for the embeddability relation $\hookrightarrow$ between separable II$_1$ factors and its stable version $\hookrightarrow_s$, obtaining large families of non stably isomorphic II$_1$ factors that are mutually embeddable and families of II$_1$ factors that are mutually non stably embeddable. We provide an augmentation functor $G \mapsto H_G$ from the category of groups into icc groups, so that $L(H_{G_1}) \hookrightarrow_s L(H_{G_2})$ iff $G_1 \hookrightarrow G_2$. We construct complete intervals of II$_1$ factors, including a strict chain of II$_1$ factors $(M_k)_{k\in \mathbb{Z}}$ with the property that if $N$ is any II$_1$ factor with $M_i \hookrightarrow_s N$ and $N \hookrightarrow_s M_{j}$, then $N \cong M_k^t$ for some $i \leq k \leq j$ and $t > 0$., v3: minor changes, final version, to appear in Communications in Mathematical Physics

We establish a surface order large deviation estimate for the magnetisation of low temperature $\phi^4_3$. As a byproduct, we obtain a decay of spectral gap for its Glauber dynamics given by the $\phi^4_3$ singular stochastic PDE. Our main technical contributions are contour bounds for $\phi^4_3$, which extends 2D results by Glimm, Jaffe, and Spencer (1975). We adapt an argument by Bodineau, Velenik, and Ioffe (2000) to use these contour bounds to study phase segregation. The main challenge to obtain the contour bounds is to handle the ultraviolet divergences of $\phi^4_3$ whilst preserving the structure of the low temperature potential. To do this, we build on the variational approach to ultraviolet stability for $\phi^4_3$ developed recently by Barashkov and Gubinelli (2019)., Comment: 92 pages. Version 2 fixes minor typos (incl. replacing $\beta$ by $\sqrt\beta$ in Theorem 1.2) and includes a small technical result about block averaging Wick square field (Remark 3.3 and Proposition 5.23)

Fluid dynamical simulations are often performed using cheap macroscopic models like the Euler equations. For rarefied gases under near-equilibrium conditions, however, macroscopic models are not sufficiently accurate and a simulation using more accurate microscopic models is often expensive. In this paper, we introduce a hierarchical micro-macro acceleration based on moment models that combines the speed of macroscopic models and the accuracy of microscopic models. The hierarchical micro-macro acceleration is based on a flexible four step procedure including a micro step, restriction step, macro step, and matching step. We derive several new micro-macro methods from that and compare to existing methods. In 1D and 2D test cases, the new methods achieve high accuracy and a large speedup.

Radiation of sound waves by a semi-infinite circular cylindrical pipe with non-uniform lining is analyzed by using the Jones\" method in conjunction with the mode matching technique. This mixed method of formulation gives rise to a scalar Wiener-Hopf equation. The inner surface of the duct is coated by acoustically absorbing different linings. In the present study, different linings with partial rigidity make the problem more interesting when it is compared with the uniform lining. The solution of the considered problem involves three infinite sets of coefficients satisfying three infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the radiation phenomenon are shown graphically. The solution is compared graphically with a similar study existing in the literature. A perfect agreement is observed between the both results.

In this study, the Michelson–Morley experiment and the result of this experiment (the speed of light appears to be the same in all directions) were explored. Although Lorentz gave a mathematical explanation (Lorentz transformations) for this, he did not explain the decreasing momentum with the internal motion of systems. In relation to this decreasing momentum, Einstein solved the problem mathematically by proposing that the mass of the systems increases with the movement of systems (moving mass). We will study this process in a chronological order below. Our primary purpose in this study is to open a platform for discussion by asking questions about the changes in moving systems, as suggested by Lorentz and Einstein (length contraction and mass increase of the object), and to propose a different relativity model by presenting our suggestions and opinions in relation to these discussions.

In this work, we propose an approach to generate multistability based on a class of unstable systems that have all their roots in the right complex half-plane. Multistability is the coexistence of multiple stable states for a set of system parameters. The approach is realized by using linear third order differential equations that consists of two parameters. The first bifurcation parameter transforms the unstable system with all its roots in the right complex half-plane into an unstable system with one root in the left complex half-plane and two roots remaining in the right complex half-plane. With this first transformation, the system is capable of generating attractors by means of a piecewise linear function and the system presents monostability. We then use the another bifurcation parameter to switch from a monostable multiscroll attractor to several multistable states showing a single-scroll attractor.

This paper presents computational procedures to formulate an algorithm based on the new iterative method (NIM) for the numerical solution of nonlinear convection-diffusion heat equation with constant coefficients. The newly formulated algorithm (NIA) was fully described the relationship between convection and diffusion constants. Three test cases (prototype) are consider to investigate the time distribution profiles in heat equation other study. The algorithm is easy and efficient to solve similar problems in physical sciences.

Training data-driven turbulence models with high fidelity Reynolds stress can be impractical and recently such models have been trained with velocity and pressure measurements. For gradient-based optimization, such as training deep learning models, this requires evaluating the sensitivities of the RANS equations. This paper explores the use of an ensemble approximation of the sensitivities of the RANS equations in training data-driven turbulence models with indirect observations. A deep neural network representing the turbulence model is trained using the network’s gradients obtained by backpropagation and the ensemble approximation of the RANS sensitivities. Different ensemble approximations are explored and a method based on explicit projection onto the sample space is presented. As validation, the gradient approximations from the different methods are compared to that from the continuous adjoint equations. The ensemble approximation is then used to learn different turbulence models from velocity observations. In all cases, the learned model predicts improved velocities. However, it was observed that once the sensitivity of the velocity to the underlying model becomes small, the approximate nature of the ensemble gradient hinders further optimization of the underlying model. The benefits and limitations of the ensemble gradient approximation are discussed, in particular as compared to the adjoint equations. Accepted version

In order to account for the asymmetry along the ring, the numerical analysis of a semiconductor ring laser using the basic two-mode model and a parameter mismatch in the backscattering coefficients is presented in this paper. The operation of the laser is discovered to be affected by changing the conservative backscattering parameter for a fixed value of the dissipative backscattering parameter, and the bidirectional regime with alternating oscillation can be suppressed. A good correspondence between the numerical results of this paper and the experimental results of the literature is obtained.

The dynamical modeling of romantic relationships is explained with a differential equation system designed to explain the development of love/hate feeling between two people over time. In this study, it was assumed that the individual's emotion was two-component, intimacy and passion, instead of a single-component feeling of love. As a result of this assumption, the relationship dynamics is represented by a four-dimensional system of equations. The possible results of this new 4D model were compared with the results of the classical 2D model and it was seen that they could give very different outputs from each other. In addition, situations that cannot be explained by classical models such as the end of passion in long-term relationships, relationships that turn from friendship to love, and couples reunited after separation are interpreted.

In this paper, we estabilsh a fractional-order Leslie-Gower prey-predator-parasite model with time delay. The analysis of stability and Hopf bifurcation of this model are presented. By analyzing the corresponding characteristic equations of each equilibrium points, we investigate the impact of time delay on the stability of the model. Regarding time delay as a bifurcation parameter, we obtain that Hopf bifurcation can occur as time delay passes the critical values. We also shown that the system is globally asymptotically stable at equilibria E4. Lastly, by using numerical simulations, some examples are given to support our theoretical results.

In this paper, we applied the improved Bernoulli sub-equation function method for the Klein-Gordon equation. Firstly, we reduced the equation to a nonlinear ordinary differential equation by the aid of wave transform. Then we have been obtained various new exact solutions via the method. For some solutions, we drew two and three-dimensional graphics to understand physical behaviors. Nonlinear evolution equations (NLEEs) are widely used because it finds application in many nonlinear disciplines such as plasma physics, optical fibers, fluid mechanics, fluid dynamics and so on. One of the best known of these equations is Klein-Gordon equation(KGE).

We develop a theory for drying-induced stresses in sessile, poroelastic drops undergoing evaporation on rigid surfaces. Using a lubrication-like approximation, the governing equations of three-dimensional nonlinear poroelasticity are reduced to a single thin-film equation for the drop thickness. We find that thin drops experience compressive elastic stresses but the total in-plane stresses are tensile. The mechanical response of the drop is dictated by the initial profile of the solid skeleton, which controls the in-plane deformation, the dominant components of elastic stress, and sets a limit on the depth of delamination that can potentially occur. Our theory suggests that the alignment of desiccation fractures in colloidal drops is selected by the shape of the drop at the point of gelation. We propose that the emergence of three distinct fracture patterns in dried blood drops is a consequence of a non-monotonic drop profile at gelation. We also show that depletion fronts, which separate wet and dry solid, can invade the drop from the contact line and localise the generation of mechanical stress during drying. Finally, the finite element method is used to explore the stress profiles in drops with large contact angles.

Entropy production plays a fundamental role in the study of non-equilibrium systems by offering a quantitative handle on the degree of time-reversal symmetry breaking. It depends crucially on the degree of freedom considered as well as on the scale of description. It was hitherto unknown how the entropy production at one resolution of the degrees of freedom is related to the entropy production at another resolution. This relationship is of particular relevance to coarse grained and continuum descriptions of a given phenomenon. In this work, we derive the scaling of the entropy production under iterative coarse graining on the basis of the correlations of the underlying microscopic transition rates. Our approach unveils a natural criterion to distinguish equilibrium-like and genuinely non-equilibrium macroscopic phenomena based on the sign of the scaling exponent of the entropy production per mesostate., Comment: 21 pages, 6 figures

We investigate the motility of a growing population of cells in a idealized setting: we consider a system of hard disks in which new particles are added according to prescribed growth kinetics, thereby dynamically changing the number density. As a result, the expected Brownian motion of the hard disks is modified. We compute the density-dependent friction of the hard disks and insert it in an effective Langevin equation to describe the system, assuming that the inter-collision time is smaller than the timescale of the growth. We find that the effective Langevin description captures the changes in motility in agreement with the simulation results. Our framework can be extended to other systems in which the transport coefficient varies with time., Accepted Manuscript

We consider a family of strongly-asymmetric unimodal maps $\{f_t\}_{t\in [0,1]}$ of the form $f_t=t\cdot f$ where $f\colon [0,1]\to [0,1]$ is unimodal, $f(0)=f(1)=0$, $f(c)=1$ is of the form and $$f(x)=\left\{ \begin{array}{ll} 1-K_-|x-c|+o(|x-c|)& \mbox{ for }xc, \end{array}\right. $$ where we assume that $\beta>1$. We show that such a family contains a Feigenbaum-Coullet-Tresser $2^\infty$ map, and develop a renormalization theory for these maps. The scalings of the renormalization intervals of the $2^\infty$ map turn out to be super-exponential and non-universal (i.e. to depend on the map) and the scaling-law is different for odd and even steps of the renormalization. The conjugacy between the attracting Cantor sets of two such maps is smooth if and only if some invariant is satisfied. We also show that the Feigenbaum-Coullet-Tresser map does not have wandering intervals, but surprisingly we were only able to prove this using our rather detailed scaling results., Comment: Accepted for publication in Communications in Mathematical Physics

ispartof: COMMUNICATIONS IN COMPUTATIONAL PHYSICS vol:28 issue:3 pages:1038-1084 status: published

Bu makale, Einstein'ın özel ve genel görelilik teorilerini tek başlık altında toplayan yeni bir uzay-zaman modellemesini anlatan yeni bir genelleştirilmiş teori niteliğindedir. Einstein'ın iki teorisine göre de bazı fiziksel olaylar zaman kısalmasına sebep olur fakat sadece genel görelilik teorisinde uzay-zaman değişir. Bu değişim uzay-zamanın bükülmesidir. Özel görelilik teorisine de uzay-zamanın bükülmesi uyarlansaydı gözlemcinin bulunduğu noktasal konumun bükülmesi gerekirdi. Tek bir noktanın bükülmesi uzay-zaman sürekliliğini bozardı. Bu yüzden iki teoriye de uyan yeni bir modellemeye ihtiyaç duyulur. Bu modelleme kısalmış uzay-zaman modellemesidir., This article is a new generalized theory describing a new space-time modeling that gathers Einstein's special and general relativity theories under a single title. According to both of Einstein's theories, some physical events cause time shortening, but only in the theory of general relativity, space-time changes. This change is the warping of space-time. If the bending of space-time were applied to the theory of special relativity, the point position of the observer would have to be bent. The bending of a single point would break the continuity of space-time. Therefore, a new modeling that fits both theories is needed. This modeling is a shortened space-time modeling.

The apparent dichotomy between information-processing and dynamical approaches to complexity science forces researchers to choose between two diverging sets of tools and explanations, creating conflict and often hindering scientific progress. Nonetheless, given the shared theoretical goals between both approaches, it is reasonable to conjecture the existence of underlying common signatures that capture interesting behavior in both dynamical and information-processing systems. Here, we argue that a pragmatic use of integrated information theory (IIT), originally conceived in theoretical neuroscience, can provide a potential unifying framework to study complexity in general multivariate systems. By leveraging metrics put forward by the integrated information decomposition framework, our results reveal that integrated information can effectively capture surprisingly heterogeneous signatures of complexity—including metastability and criticality in networks of coupled oscillators as well as distributed computation and emergent stable particles in cellular automata—without relying on idiosyncratic, ad hoc criteria. These results show how an agnostic use of IIT can provide important steps toward bridging the gap between informational and dynamical approaches to complex systems. Originally conceived within theoretical neuroscience, integrated information theory (IIT) has been rarely used in other fields—such as complex systems or non-linear dynamics—despite the great value it has to offer. In this article, we inspect the basics of IIT, dissociating it from its contentious claims about the nature of consciousness. Relieved of this philosophical burden, IIT presents itself as an appealing formal framework to study complexity in biological or artificial systems, applicable in a wide range of domains. To illustrate this, we present an exploration of integrated information in complex systems and relate it to other notions of complexity commonly used in systems such as coupled oscillators and cellular automata. Through these applications, we advocate for IIT as a valuable framework capable of revealing common threads between diverging branches of complexity science.

This work aims to evaluate a parallelizable approximate solution model for the wave equation. For that, we used the temporal sweep known as the Waveform Relaxation method to guarantee the parallelization in space. However, this technique has limitations for this class of problems. Therefore, we proposed the combination of the Subdomain method in a non-conventional way in time with the Multigrid method, intending to reduce computational time and improve the convergence factors. In this work, we presented the mathematical analysis of the stability of the discretization model, which uses the Central Finite Difference method with weighting at each time step. As an application of the proposed method, in addition to a problem with a known analytical solution, we solved a wave propagation problem with reflection and phase inversion.

When a drop impacts onto a pool of another liquid, the common interface will move down at a well-defined speed for the first few milliseconds. While simple mechanistic models and experiments with the same fluid used for the drop and pool have predicted this speed to be half the impacting drop speed, this is only one small part in a rich and intricate behavior landscape. Factors such as viscosity and density ratios greatly affect the penetration speed. By using a combination of high-speed photography, high-resolution numerical simulations, and physical modeling, we disentangle the different roles that physical fluid properties play in determining the true value of the postimpact interfacial velocity.\ud \ud

We prove sharp Lieb-Thirring type inequalities for the eigenvalues of a class of one-dimensional functional difference operators associated to mirror curves. We furthermore prove that the bottom of the essential spectrum of these operators is a resonance state.

Reconnection and turbulence are two of the most commonly observed dynamical processes in plasmas, but their relationship is still not fully understood. Using 2.5D kinetic particle-in-cell simulations of both strong turbulence and reconnection, we compare the cross-scale transfer of energy in the two systems by analyzing the generalization of the von Kármán Howarth equations for Hall magnetohydrodynamics, a formulation that subsumes the third-order law for steady energy transfer rates. Even though the large scale features are quite different, the finding is that the decomposition of the energy transfer is structurally very similar in the two cases. In the reconnection case, the time evolution of the energy transfer also exhibits a correlation with the reconnection rate. These results provide explicit evidence that reconnection dynamics fundamentally involves turbulence-like energy transfer.

The prevertices of the conformal map between a generic, n-vertex, simply connected, polycircular arc domain and the upper half plane are determined by finding the zeros of an isomonodromic tau function. The accessory parameters of the associated Fuchsian equation are then found in terms of logarithmic derivatives of this tau function. Using these theoretical results a constructive approach to the determination of the conformal map is given and the particular case of five vertices is considered in detail. A computer implementation of a construction of the isomonodromic tau function described by Gavrylenko and Lisovyy (2018 Commun. Math. Phys. 363 1–58) is used to calculate some illustrative examples. A procedural guide to constructing the conformal map to a given polycircular arc domain using the method presented here is also set out.

© 2022 by the authors.The nature of dependence between random variables has always been the subject of many statistical problems for over a century. Yet today, there is a great deal of research on this topic, especially focusing on the analysis of nonlinearity. Shannon mutual information has been considered to be the most comprehensive measure of dependence for evaluating total dependence, and several methods have been suggested for discerning the linear and nonlinear components of dependence between two variables. We, in this study, propose employing the Rényi and Tsallis mutual information measures for measuring total dependence because of their parametric nature. We first use a residual analysis in order to remove linear dependence between the variables, and then we compare the Rényi and Tsallis mutual information measures of the original data with that the lacking linear component to determine the degree of nonlinearity. A comparison against the values of the Shannon mutual information measure is also provided. Finally, we apply our method to the environmental Kuznets curve (EKC) and demonstrate the validity of the EKC hypothesis for Eastern Asian and Asia-Pacific countries.

Solitons are an important class of solutions to nonlinear differential equations which appear in different areas of physics and applied mathematics. In this study we provide a general overview of the Hirota method which is one of the most powerful tool in finding the multi-soliton solutions of nonlinear wave and evaluation equations. Bright and dark soliton solutions of nonlinear Schrödinger equation are discussed in detail

In this work, Doi–Peliti field theory is used to describe the motion of free run and tumble particles in arbitrary dimensions. After deriving action and propagators, the mean squared displacement and the corresponding entropy production at stationarity are calculated in this framework. We further derive the field theory of free active Brownian particles in two dimensions for comparison.

Bohmian mechanics is an alternative to standard quantum mechanics that does not suffer from the measurement problem. While it agrees with standard quantum mechanics concerning its experimental predictions, it offers novel types of approximations not suggested by the latter. Of particular interest are semi-classical approximations, where part of the system is treated classically. Bohmian semi-classical approximations have been explored before for systems without electromagnetic interactions. Here, the Rabi model is considered as a simple model involving light-matter interaction. This model describes a single mode electromagnetic field interacting with a two-level atom. As is well-known, the quantum treatment and the semi-classical treatment (where the field is treated classically rather than quantum mechanically) give qualitatively different results. We analyse the Rabi model using a different semi-classical approximation based on Bohmian mechanics. In this approximation, the back-reaction from the two-level atom onto the classical field is mediated by the Bohmian configuration of the two-level atom. We find that the Bohmian semi-classical approximation gives results comparable to the usual mean field one for the transition between ground and first excited state. Both semi-classical approximations tend to reproduce the collapse of the population inversion, but fail to reproduce the revival, which is characteristic of the full quantum description. Also an example of a higher excited state is presented where the Bohmian approximation does not perform so well., 21 pages, 6 figures, PDFLaTeX; v2 minor corrections

We study the low-temperature phase equilibria of a fluid confined in an open capillary slit formed by two parallel walls separated by a distance $L$ which are in contact with a reservoir of gas. The top wall of the capillary is of finite length $H$ while the bottom wall is considered of macroscopic extent. This system shows rich phase equilibria arising from the competition between two different types of capillary condensation, corner filling, and meniscus depinning transitions depending on the value of the aspect ratio $a=L/H$ and divides into three regimes: For long capillaries, with $al2/\ensuremath{\pi}$, the condensation is of type I involving menisci which are pinned at the top edges at the ends of the capillary. For intermediate capillaries, with $2/\ensuremath{\pi}lal1$, depending on the value of the contact angle the condensation may be of type I or of type II, in which the menisci overspill into the reservoir and there is no pinning. For short capillaries, with $ag1$, condensation is always of type II. In all regimes, capillary condensation is completely suppressed for sufficiently large contact angles which is determined explicitly. For long and intermediate capillaries, we show that there is an additional continuous phase transition in the condensed liquid-like phase, associated with the depinning of each meniscus as they round the upper open edges of the slit. Meniscus depinning is third-order for complete wetting and second-order for partial wetting. Detailed scaling theories are developed for these transitions and phase boundaries which connect with the theories of wedge (corner) filling and wetting encompassing interfacial fluctuation effects and the direct influence of intermolecular forces. We test several of our predictions using a fully microscopic density functional theory which allows us to study the two types of capillary condensation and its suppression at the molecular level for different aspect ratios and contact angles.

The production of polarized proton beams with multi-GeV energies in ultraintense laser interaction with targets is studied with three-dimensional particle-in-cell simulations. A near-critical density plasma target with prepolarized proton and tritium ions is considered for the proton acceleration. The prepolarized protons are initially accelerated by laser radiation pressure before injection and further acceleration in a bubblelike wakefield. The temporal dynamics of proton polarization is tracked via the Thomas-Bargmann-Michel-Telegdi equation and it is found that the proton polarization state can be altered by both the laser field and the magnetic component of the wakefield. The dependence of the proton acceleration and polarization on the ratio of the ion species is determined and it is found that the protons can be efficiently accelerated as long as their relative fraction is less than 20%, in which case the bubble size is large enough for the protons to obtain sufficient energy to overcome the bubble injection threshold. ispartof: PHYSICAL REVIEW E vol:104 issue:1 ispartof: location:United States status: published

The Muttalib-Borodin biorthogonal ensemble is a probability density function for $n$ particles on the positive real line that depends on a parameter $\theta$ and an external field $V$. For $\theta=\frac{1}{2}$ we find the large $n$ behavior of the associated correlation kernel with only few restrictions on $V$. The idea is to relate the ensemble to a type II multiple orthogonal polynomial ensemble that can in turn be related to a $3\times 3$ Riemann-Hilbert problem which we then solve with the Deift-Zhou steepest descent method. The main ingredient is the construction of the local parametrix at the origin, with the help of Meijer G-functions, and its matching condition with a global parametrix. We will present a new iterative technique to obtain the matching condition, which we expect to be applicable in more general situations as well., Comment: 51 pages

We develop tools to construct Lyapunov functionals on the space of probability measures in order to investigate the convergence to global equilibrium of a damped Euler system under the influence of external and interaction potential forces with respect to the 2-Wasserstein distance. We also discuss the overdamped limit to a nonlocal equation used in the modelling of granular media with respect to the 2-Wasserstein distance, and provide rigorous proofs for particular examples in one spatial dimension.

We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a physically meaningful, data-driven approach for decomposing the fluid transport velocity into its drift and stochastic parts, for a certain class of fluid flows. In the current paper, we develop new methodology to implement this velocity decomposition and then numerically integrate the resulting stochastic partial differential equation using a finite element discretisation for incompressible 2D Euler fluid flows. The new methodology tested here is found to be suitable for coarse graining in this case. Specifically, we perform uncertainty quantification tests of the velocity decomposition of Cotter et al. (2017), by comparing ensembles of coarse-grid realisations of solutions of the resulting stochastic partial differential equation with the "true solutions" of the deterministic fluid partial differential equation, computed on a refined grid. The time discretization used for approximating the solution of the stochastic partial differential equation is shown to be consistent. We include comprehensive numerical tests that confirm the non-Gaussianity of the stream function, velocity and vorticity fields in the case of incompressible 2D Euler fluid flows., 41 pages, 26 figures Minor changes -- updated figures to improve readability. Corrected typos. Shifted Remark 7 to just after Assumption A1. Added Remark 8

Modern hardware architectures such as GPUs and manycore processors are characterised by an abundance of compute capability relative to memory bandwidth. This makes them well-suited to solving temporally explicit and spatially compact discretisations of hyperbolic conservation laws. However, classical pressure-projection-based incompressible Navier–Stokes formulations do not fall into this category. One attractive formulation for solving incompressible problems on modern hardware is the method of artificial compressibility. When combined with explicit dual time stepping and a high-order Flux Reconstruction discretisation, the majority of operations can be cast as compute bound matrix–matrix multiplications that are well-suited for GPU acceleration and manycore processing. In this work, we develop a high-order cross-platform incompressible Navier–Stokes solver, via artificial compressibility and dual time stepping, in the PyFR framework. The solver runs on a range of computer architectures, from laptops to the largest supercomputers, via a platform-unified templating approach that can generate/compile CUDA, OpenCL and C/OpenMP code at runtime. The extensibility of the cross-platform templating framework defined within PyFR is clearly demonstrated, as is the utility of P -multigrid for convergence acceleration. The platform independence of the solver is verified on Nvidia Tesla P100 GPUs and Intel Xeon Phi 7210 KNL manycore processors with a 3D Taylor–Green vortex test case. Additionally, the solver is applied to a 3D turbulent jet test case at R e = 10,000 , and strong scaling is reported up to 144 GPUs. The new software constitutes the first high-order accurate cross-platform implementation of an incompressible Navier–Stokes solver via artificial compressibility and P -multigrid accelerated dual time stepping to be published in the literature. The technology has applications in a range of sectors, including the maritime and automotive industries. Moreover, due to its cross-platform nature, the technology is well placed to remain relevant in an era of rapidly evolving hardware architectures. Program summary Program Title: PyFR v1.7.5 Program Files doi: http://dx.doi.org/10.17632/65m665nt9c.1 Licensing provisions: BSD 3-clause Programming language: Python, CUDA, OpenCL and C Supplementary material: Configuration and mesh files for the Taylor–Green Vortex and Turbulent jet test cases Journal reference of previous version: Comput. Phys. Commun. 185 (2014) 3028–3040 Does the new version supersede the previous version?: Yes Reasons for the new version: Adding support for incompressible flows Summary of revisions: Introducing a new high-order cross-platform incompressible flow solver via artificial compressibility and P -multigrid accelerated dual time stepping. Nature of problem: Incompressible Euler and Navier–Stokes equations for solving unsteady turbulent flows. Solution method: Artificial compressibility formulation discretised with a high-order Flux Reconstruction approach in space and P -multigrid accelerated dual time stepping in time. Additional comments including restrictions and unusual features: The algorithm targets modern massively parallel hardware platforms. Cross-platform capability is achieved via runtime code generation.

In this study, the generalized (3+1)-dimensional Shallow Water-Like (SWL) equation, which is one of the evolution equations, is taken into consideration. With the help of this evolution equation discussed, the modified Kudryashov method, traveling wave solutions are successfully obtained. In these solutions, graphs of solitary waves to be obtained by giving special values to arbitrary parameters are presented. At the same time, the effect of change of velocity parameter on the behavior on the solitary wave is examined in the solution obtained. The breaking of the wave is discussed. In this study, complex operations and graphic presentations are presented with the use of a ready-made package program.

In the present study, we firstly investigated the spatial properties of event horizon of a two- dimensional black hole. Then we solve Duffin-Kemmer-Petiau (DKP) equation for such a black hole metric depending on the signs of spatial variable. After obtaining the exact solutions, we determine thermal parameters related to this metric. Finally, the harmonic oscillation behavior of the system is evaluated.

We study the moduli space of Yang--Mills connections on bundles over a conformally compact manifold $\overline{M}$. We prove that, for every Yang--Mills connection $A$ that satisfies an appropriate nondegeneracy condition, and for every small deformation $\gamma$ of $A_{|\partial\overline{M}}$, there is a Yang--Mills connection in the interior that extends $A_{|\partial\overline{M}}+\gamma$. As a corollary, we confirm an expectation of Witten mentioned in his foundational paper about holography [arXiv:hep-th/9802150]., Comment: Replaced with fully revised version. The preliminary sections containing preliminary material have been reduced, and now contain only the background tools needed to prove the main theorem; the main theorem (Theorem 63) and its proof are essentially unchanged; Theorem 65 has been removed for the sake of brevity; Theorem 75 has been removed while I try and fix a gap in the proof

In this study we consider a qubit (quantum bit) as the spin degree of freedom of a spin-1/2 particle. Since the 2D plane and the 2-sphere minus the north pole are topologically equivalent, one can represent motion on the 2D plane on the 2-sphere. We use inverse stereographic projection to map the 2D plane to the 2-sphere minus the north pole. Because the 2-sphere can be thought of as the Bloch sphere where any point represents a qubit, the time evolution of a particle on the 2D plane corresponds to the time evolution of the corresponding qubit on the Bloch sphere. We use the property of magnetic field to rotate spins to provide exact time dependent magnetic field to simulate, using a single qubit, the path followed by a particle on the 2D plane., Bu çalışmada bir spin-1/2 parçacığın spin serbesti derecesi olarak bir kübiti (kuantum bit) ele alıyoruz. İki boyutlu düzlem ve kuzey kutbu çıkartılmış 2-küre topolojik olarak eşdeğer olduklarından, iki boyutlu düzlemdeki hareket 2-küre üzerinde temsil edilebilir. Ters stereografik fonksiyonu kullanarak iki boyutlu düzlemi 2-küre üzerine aktarıyoruz. Öte yandan 2-küre, üzerindeki her noktanın bir kübiti temsil ettiği Bloch küresi olarak düşünülebildiğinden, bir parçacığın iki boyutlu düzlem üzerindeki zaman içindeki evrimi, buna karşılık gelen kübitin Bloch küresi üzerinde zaman içindeki evrimine karşılık gelir. Manyetik alanın spini döndürebilme özelliğini kullanarak iki boyutlu bir düzlemdeki parçacığın hareketinin tek bir kübit kullanılarak simüle edilmesini sağlayacak zamana bağımlı manyetik alanın tam formunu veriyoruz.