Topology in thermodynamics of regular black strings with Kaluza-Klein reduction

We study the topological defects in the thermodynamics of regular black strings (from a four-dimensional perspective) that is symmetric under the double Wick rotation and constructed in the high-dimensional spacetime with an extra dimension compactified on a circle. We observe that the thermodynamic phases of regular black strings can be topologically classified by the positive and negative winding numbers (at the defects) which correspond to the thermodynamically stable and unstable branches. This topological classification implies a phase transition due to the decay of a thermodynamically unstable regular black string to another which is thermodynamically stable. We confirm these topological properties of the thermodynamics of regular black strings by investigating their free energy, heat capacity, and Ruppeiner scalar curvature of the state space. The Ruppeiner scalar curvature of regular black strings is found to be always negative, implying that the interactions among the microstructures of regular black strings are only attractive.Comment: 21 pages, 10 figure

Well-Rounded ideal lattices of cyclic cubic and quartic fields

In this paper, we find criteria for when cyclic cubic and cyclic quartic fields have well-rounded ideal lattices. We show that every cyclic cubic field has at least one well-rounded ideal. We also prove that there exist families of cyclic quartic fields which have well-rounded ideals and explicitly construct their minimal bases. In addition, for a given prime number $p$, if a cyclic quartic field has a unique prime ideal above $p$, then we provide the necessary and sufficient conditions for that ideal to be well-rounded. Moreover, in cyclic quartic fields, we provide the prime decomposition of all odd prime numbers and construct an explicit integral basis for every prime ideal.Comment: 26 page

Well-Rounded Twists of Ideal Lattices from Imaginary Quadratic Fields

In this paper, we investigate the properties of well-rounded twists of a given ideal lattice of an imaginary quadratic field $K$. We show that every ideal lattice $I$ of $K$ has at least one well-rounded twist lattice. Moreover, we provide an explicit algorithm to compute all well-rounded twists of $I$.Comment: 24 page

La fonction de partition de Minc et une conjecture de Segal pour certains spectres de Thom

On construit dans cet article une résolution injective minimale dans la catégorie \U des modules instables sur l'algèbre de Steenrod modulo $2$, de la cohomologie de certains spectres obtenus à partir de l'espace de Thom du fibré, associé à la représentation régulière réduite du groupe abélien élémentaire $(\Z/2)^n$, au dessus de l'espace $B(\Z/2)^n$. Les termes de la résolution sont des produits tensoriels de modules de Brown-Gitler $J(k)$ et de modules de Steinberg $L_n$ introduits par S. Mitchell et S. Priddy. Ces modules sont injectifs d'après J. Lannes et S. Zarati, de plus ils sont indécomposables. L'existence de cette résolution avait été conjecturée par Jean Lannes et le deuxième auteur. La principale indication soutenant cette conjecture était un résultat combinatoire de G. Andrews : la somme alternée des séries de Poincaré des modules considérées est nulle

Performance analysis for power-splitting energy harvesting based two-way full-duplex relaying network over nakagami-m fading channel

Energy harvesting relay network is considered as the promising solution for a wireless communication network in our time. In this research, we present and demonstrate the system performance of the energy harvesting based two-way full-duplex relaying network over Nakagami-m fading environment. Firstly, we propose the analytical expressions of the achievable throughput and outage probability of the proposed system. In the second step, the effect of various system parameters on the system performance is presented and investigated. In the final step, the analytical results are also demonstrated by Monte-Carlo simulation. The numerical results demonstrated and convinced the analytical and the simulation results are agreed with each other

EFFECT OF VISCOUS HEAT GENERATION ON TEMPERATURE OF RAREFIED GAS MICROFLOWS DRIVEN BY MOVING SURFACE

Good understanding of the gas flow under rarefied conditions is important for designing the micro-electro-mechanical systems. The Navier-Stokes-Fourier equations with the slip and jump conditions can capture the rarefied gas flows in the slip regime. In this paper, we focus on evaluating new type of the Smoluchowski jump condition that was recently proposed in our previous work by considering the viscous heat generation. It was validated for external highspeed rarefied gas flows over the stationary surface. Our investigation is undertaken for internal rarefied gas microflows past the moving surfaces. The lid driven microcavity and Couette cases are adopted for this investigation with Knudsen number ranging from 0.05 to 1, the surface velocity varying from 50 m/s to 200 m/s, and argon as working gas. All simulations are run within the OpenFOAM framework. The gas temperatures along the moving surface and those across the microchannel predicted by new type of the Smoluchowski jump condition are close to the DSMC and R13-moment data in all cases considere

Outage probability analysis of EH relay-assisted non-orthogonal multiple access (NOMA) systems over Block Rayleigh Fading Channel

Non-orthogonal multiple access (NOMA) has been identified as a promising multiple access technique for the fifth generation (5G) mobile networks due to its superior spectral efficiency. In this paper, we propose and investigate a Non-Orthogonal Multiple Access (NOMA) of energy harvesting (EH) relay assisted system over Block Rayleigh Fading Channel. In order to evaluate the performance of the proposed system, the integral expression of the outage probability is analyzed and derived. Numerical results confirm that our derived analytical results match well with the Monte Carlo simulations in connection with all possible system parameter

Half-duplex power beacon-assisted energy harvesting relaying networks: system performance analysis

In this work, the half-duplex (HF) power beacon-assisted (PB) energy harvesting (EH) relaying network, which consists of a source (S), Relay (R), destination (D) and a power beacon (PB) are introduced and investigated. Firstly, the analytical expressions of the system performance in term of outage probability (OP) and the system throughput (ST) are analyzed and derived in both amplify-and-forward (AF) and decode-and-forward (DF) modes. After that, we verify the correctness of the analytical analysis by using Monte-Carlo simulation in connection with the primary system parameters. From the numerical results, we can see that all the analytical and the simulation results are matched well with each other