Logarithmic Correction Term Research Articles

Study on the dynamic mechanical properties of winding‐block axial structure considering short circuit strain rate effect

AbstractTransformers may suffer multiple short‐circuit impacts during long‐term operation, and axial instability is one of the typical types of serious accidents caused by short‐circuit faults. The axial instability form of the winding‐block structure is analysed, and the dynamic solution of the winding short‐circuit electromagnetic force is obtained by establishing the three‐dimensional magnetic‐circuit‐force multi‐physical field coupling simulation model. The influence of strain rate on the cushion block constitutive equation is corrected, and the modified model is verified by short‐circuit impact test and quasi‐static test. The research results show that for 110 kV 31.5 MVA transformers, the maximum electromagnetic axial resultant force of winding is 363.16 kN, and the ultimate tilt force is 1214.2 kN. The pre‐tightening force configuration is accordingly recommended to range from 363.16 to 608.28 kN, which is narrowed by 18.49% compared with the static calculation method; Meanwhile, adding a logarithmic strain rate correction term to the classical constitutive equation of the cushion block can achieve a good correction of the stress‐strain relationship with the coefficient of determination above 0.99, and the cushion block has a larger elastic modulus under high strain rate load. The research results provide an important theoretical reference for the axial stability structure of transformers.

Anisotropic ultra-compact object in Serrano–Liska gravity model

We implement a recent model proposed by Serrano–Liska (SL) (Alonso-Serrano and Liška, JHEP, 12:196, 2020) to study the ultra-compact star properties. The matter in the interior star is modeled by the quark model, deducted from QCD theory equipped with anisotropic pressure. Anisotropy is used to increase the compactness of the stars. We intend to see the signature of the “quantum gravity” effect through the SL model in ultra-compact stars. The SL model was motivated by quantum correction appearing in the black hole by adding a logarithmic term in gravity entropy used to derive the effective Einstein field equation. We expect this correction term in the SL model also affects ultra-compact star properties. The SL model with coupling constant {tilde{c}} in logarithmic term equipped with spherically symmetric metric yields correction terms mathscr {O}({tilde{c}}) that can be expressed by a function varXi (r). The varXi (r) function vanishes at the star’s exterior. We found that the mass-radius relation prediction by the SL model with anisotropic matter deviates from the one predicted by the standard Tolman–Oppenheimer–Volkoff (TOV) equation for {tilde{c}}ge 10^7 m^2. We also have a sufficiently deep enough effective potential to produce a quasi-normal mode. We obtain the echo frequency of 15.2 kHz using maximum anisotropic pressure contribution and {tilde{c}}= 10^7 m^2. Because the corresponding effective potential is almost indistinguishable from that of GR, this echo frequency value can be indistinguishable to one of GR, but not comparable to the result from GW170817 data analysis, i.e., 72 Hz. To circumvent this problem, we can decrease the value of echo frequency by increasing the magnitude of {tilde{c}} to orders of magnitude than {tilde{c}}= 10^7 m^2. On the other hand, too large a strength from the logarithmic correction term is not physically favored because we learn from the black hole case that the logarithmic term is expected to be smaller than that of the Bekenstein term. Therefore, more precise gravitation echo measurements are crucial to understand this issue.

Hawking radiation and stability of the canonical acoustic black holes

In this paper we determine the Hawking temperature and entropy of a modified canonical acoustic black hole. In our results we obtain an entropy-area relation that has a logarithmic correction term in leading order. We also analyze the stability condition of the noncommutative canonical acoustic black hole and also with quantum corrections implemented by the generalized Heisenberg uncertainty principle.

Thermodynamics and logarithmic corrections of symmergent black holes

In this paper, we study quantum gravity effect on the symmergent black hole which is derived from quadratic-curvature gravity. To do so, we use the Klein–Gordon equation which is modified by generalized uncertainty principle (GUP). After solving the field equations, we examine the symmergent black hole’s tunneling and Hawking temperature. We explore the graphs of the temperature through the outer horizon to check the GUP influenced conditions of symmergent black hole stability. We also explain how symmergent black holes behave physically when influenced by quantum gravity. The impacts of thermal fluctuations on the thermodynamics of a symmergent black holes spacetime are examined. We first evaluate the model under consideration’s thermodynamic properties, such as its Hawking temperature, angular velocity, entropy, and electric potential. We evaluate the logarithmic correction terms for entropy around the equilibrium state in order to examine the impacts of thermal fluctuations. In the presence of these correction terms, we also examine the viability of the first law of thermodynamics. Finally, we evaluate the system’s stability using the Hessian matrix and heat capacity. It is determined that a stable model is generated by logarithmic corrections arising from thermal fluctuations.

Nonsingular Black Holes in 4D Einstein–Gauss–Bonnet Gravity

Recently, several methods have been proposed to regularize a D→4 limit of Einstein–Gauss–Bonnet (EGB), leading to nontrivial gravitational dynamics in 4D. We present an exact nonsingular black hole solution in the 4D EGB gravity coupled to non-linear electrodynamics and analyze their thermodynamic properties to calculate precise expressions for the black hole mass, temperature, and entropy. Because of the magnetic charge, the thermodynamic quantities are corrected, and the Hawking–Page phase transition is achievable with diverges of the heat capacity at a larger critical radius r=r+C in comparison to the 5D counterpart where the temperature is maximum. Thus, we have a black hole with Cauchy and event horizons, and its evaporation leads to a thermodynamically stable extremal black hole remnant with vanishing temperature, and its size is larger than the 5D counterpart. The entropy does not satisfy the usual exact horizon Bekenstein–Hawking area law of general relativity with a logarithmic area correction term.

On the Convergence Rate of the Chaos Game

Abstract This paper studies how long it takes the orbit of the chaos game to reach a certain density inside the attractor of a strictly contracting IFS of which we only assume that its lower dimension is positive. We show that the rate of growth of this cover time is determined by the Minkowski dimension of the push-forward of the shift invariant measure with exponential decay of correlations driving the chaos game. Moreover, we bound the expected value of the cover time from above and below with multiplicative logarithmic correction terms. As an application, for Bedford–McMullen carpets, we completely characterise the family of probability vectors that minimise the Minkowski dimension of Bernoulli measures. Interestingly, these vectors have not appeared in any other aspect of Bedford–McMullen carpets before.

Marginal triviality of the scaling limits of critical 4D Ising and $\lambda\phi_4^4$ models

We prove that the scaling limits of spin fluctuations in four-dimensional Ising-type models with nearest-neighbor ferromagnetic interaction at or near the critical point are Gaussian. A similar statement is proven for the $\lambda \phi^4$ fields over $\mathbb{R}^4$ with a lattice ultraviolet cutoff, in the limit of infinite volume and vanishing lattice spacing. The proofs are enabled by the models' random current representation, in which the correlation functions' deviation from Wick's law is expressed in terms of intersection probabilities of random currents with sources at distances which are large on the model's lattice scale. Guided by the analogy with random walk intersection amplitudes, the analysis focuses on the improvement of the so-called tree diagram bound by a logarithmic correction term, which is derived here through multi-scale analysis.

Study of thermal fluctuations in five-dimensional rotating regular black hole

In this paper, we discuss the effects of thermal fluctuations on thermodynamics of rotating regular black hole in five-dimensional spacetime. We first evaluate thermodynamic quantities such as Hawking temperature, entropy, angular velocity and electric potential of the considered model. To discuss the effects of thermal fluctuations, we compute the logarithmic correction terms to entropy around the equilibrium state. We also check the validity of the first law of thermodynamics in the presence of these correction terms. Finally, we determine stability of the system through specific heat and Hessian matrix. It is concluded that logarithmic corrections originated from thermal fluctuations yield a stable model.

Long range scattering for the complex-valued Klein-Gordon equation with quadratic nonlinearity in two dimensions

In this paper, we study large time behavior of complex-valued solutions to nonlinear Klein-Gordon equation with a gauge invariant quadratic nonlinearity in two spatial dimensions. To find a possible asymptotic behavior, we consider the final value problem. It turns out that one possible behavior is a linear solution with a logarithmic phase correction as in the real-valued case. However, the shape of the logarithmic correction term has one more parameter which is also given by the final data. In the real case the parameter is constant so one cannot see its effect. However, in the complex case it varies in general. The one dimensional case is also discussed.

Thermal fluctuations of dyadosphere of Reissner-Nordström, Janis-Newman-Winicour and f(R) global monopole black holes

In this paper, we study the effects of thermal fluctuations on Dyadosphere of Reissner-Nordström, Janis-Newman-Winicour and the fragmentation of f(R) global monopole black holes. In the presence of these fluctuations, we obtain various thermodynamic quantities like pressure, entropy, specific heat, Canonical and Grand Canonical ensembles. We discuss the stability of these black holes using the γ (the ratio of heat capacities). We also discuss the phase transition and range of local and global stability. It is demonstrated that in Dyadoshpere of Reissner-Nordström, Janis-Newman-Winicour and fragmentation of f(R) global monopole black holes become locally and globally stable due to logarithmic correction term and large horizon radius.

Entanglement entropy of random partitioning

We study the entanglement entropy of random partitions in one- and two-dimensional critical fermionic systems. In an infinite system we consider a finite, connected (hypercubic) domain of linear extent L, the points of which with probability p belong to the subsystem. The leading contribution to the average entanglement entropy is found to scale with the volume as a(p)LD, where a(p) is a non-universal function, to which there is a logarithmic correction term, b(p)LD−1 ln L. In 1D the prefactor is given by b(p)=c/3f(p),where c is the central charge of the model and f(p) is a universal function. In 2D the prefactor has a different functional form of p below and above the percolation threshold.Graphical abstract

Logarithmic corrections in Fisher–KPP type porous medium equations

We consider the large time behavior of solutions to the porous medium equation with a Fisher–KPP type reaction term and nonnegative, compactly supported initial function in L∞(RN)∖{0}:(⋆)ut=Δum+u−u2 in Q:=RN×R+,u(⋅,0)=u0in RN, with m>1. It is well known that the spatial support of the solution u(⋅,t) to this problem remains bounded for all time t>0 (whose boundary is called the free boundary), which is a main different feature of (⋆) to the corresponding semilinear case m=1. Similar to the corresponding semilinear case m=1, it is known that there is a minimal speed c⁎>0 such that for any c≥c⁎, the equation admits a wavefront solution Φc(r): For any ν∈SN−1, v(x,t):=Φc(x⋅ν−ct) solves vt=Δvm+v−v2. When m=1, it is well known that the long-time behavior of the solution with compact initial support can be well approximated by Φc⁎(|x|−c⁎t+N+2c⁎log⁡t+O(1)), and the term N+2c⁎log⁡t is known as the logarithmic correction term. When m>1, an analogous approximation has been an open question for N≥2. In this paper, we answer this question by showing that there exists a constant c#>0 independent of the dimension N and the initial function u0, such that for all large time, any solution of (⋆) is well approximated by Φc⁎(|x|−c⁎t+(N−1)c#log⁡t+O(1)). This is achieved by a careful analysis of the radial case, where the initial function u0 is radially symmetric, which enables us to give a formula for c# (involving integrals of Φc⁎(r)), and to replace the O(1) term by C+o(1) with C a constant depending on u0. The approximation for the general non-radial case is obtained by using the radial results and simple comparison arguments. We note that in sharp contrast to the m=1 case, when N=1, there is no logarithmic correction term for (⋆).

One-loop determinants for black holes in 4d gauged supergravity

We continue the effort of defining and evaluating the quantum entropy function for supersymmetric black holes in 4d mathcal{N} = 2 gauged supergravity, initiated in [1]. The emphasis here is on the missing steps in the previous localization analysis, mainly dealing with one-loop determinants for abelian vector multiplets and hypermultiplets on the non-compact space ℍ2× Σg with particular boundary conditions. We use several different techniques to arrive at consistent results, which have a most direct bearing on the logarithmic correction terms to the Bekenstein-Hawking entropy of said black holes.

On Non-localization of Eigenvectors of High Girth Graphs

Abstract We prove improved bounds on how localized an eigenvector of a high girth regular graph can be, and present examples showing that these bounds are close to sharp. This study was initiated by Brooks and Lindenstrauss [6] who relied on the observation that certain suitably normalized averaging operators o nhigh girth graphs are hyper-contractive and can be used to approximate projectors onto the eigenspaces of such graphs. Informally, their delocalization result in the contrapositive states that for any $\varepsilon \in (0,1)$ and positive integer $k,$ if a $(d+1)-$regular graph has an eigenvector that supports $\varepsilon $ fraction of the $\ell _2^2$ mass on a subset of $k$ vertices, then the graph must have a cycle of size $\log _{d}(k)/\varepsilon ^2)$, up to multiplicative universal constants and additive logarithmic terms in $1/\varepsilon $. In this paper, we improve the upper bound to $\log _{d}(k)/\varepsilon $ up to similar logarithmic correction terms; and present a construction showing a lower bound of $\log _d(k)/\varepsilon $ up to multiplicative constants. Our construction is probabilistic and involves gluing together a pair of trees while maintaining high girth as well as control on the eigenvectors and could be of independent interest.

Geometrothermodynamic analysis and P–V criticality of higher dimensional charged Gauss–Bonnet black holes with first order entropy correction

We consider a charged Gauss-Bonnet black hole in $d$-dimensional spacetime and examine the effect of thermal fluctuations on the thermodynamics of the concerned black hole. At first we take the first order logarithmic correction term in entropy and compute the thermodynamic potentials like Helmholtz free energy $F$, enthalpy $H$ and Gibbs free energy $G$ in the spherical, Ricci flat and hyperbolic topology of the black hole horizon, respectively. We also investigate the $P$-$V$ criticality and calculate the critical volume $V_c$, critical pressure $P_c$ and critical temperature $T_c$ using different equations when $P$-$V$ criticality appears. We show that there is no critical point without thermal fluctuations for this type of black hole. We find that the presence of logarithmic correction in it is necessary to have critical points and stable phases. Moreover, we study the stability of the black holes by employing the specific heat. Finally, we study the geometrothermodynamics and analyse the Ricci scalar of the Ruppeiner metric graphically for the same.

Impact of the running gravitational constant on the extensive thermodynamics of galaxies

We study the effect of the running gravitational constant on a system of particles (galaxies) interact via gravitational potential. The gravitational potential is derived based on the entropic modified Newtonian force by logarithmic and power correction terms. We derive the partition function for many-body system and the exact equations of state including the thermodynamic properties. A modified parameter B emerged from the thermodynamics derivation. Moreover, an extension of the study is done to determine the distribution function for point mass and extended mass structure galaxies. In particular, the rotation velocity of some galaxies is studied, and the results confronted the observed data which fit well only for short distance with considering the logarithmic correction effect. This leads us to conclude that the logarithmic correction effect explains the rotation velocity data for short and long distances at least qualitatively.

Maxima of branching random walks with piecewise constant variance

This article extends the results of Fang & Zeitouni (2012a) on branching random walks (BRWs) with Gaussian increments in time inhomogeneous environments. We treat the case where the variance of the increments changes a finite number of times at different scales in [0,1] under a slight restriction. We find the asymptotics of the maximum up to an OP(1) error and show how the profile of the variance influences the leading order and the logarithmic correction term. A more general result was independently obtained by Mallein (2015b) when the law of the increments is not necessarily Gaussian. However, the proof we present here generalizes the approach of Fang & Zeitouni (2012a) instead of using the spinal decomposition of the BRW. As such, the proof is easier to understand and more robust in the presence of an approximate branching structure.

Logarithmic correction of the BTZ black hole and adaptive model of graphene

It is known that almost all approaches to quantum gravity produce a logarithmic correction term to the entropy of a black hole, but the exact coefficient of such a term varies between the different approach to quantum gravity. Such logarithmic terms can also occur due to thermal fluctuations in both analogous and real black holes so that we will analyze the effects of logarithmic corrections term with variable coefficient on properties of analogous black hole. As these properties can be experimentally tested, they can be used to obtain the correct coefficient for such terms for an analogous black hole. We will argue that as even the real black holes can be considered as thermodynamical objects in Jacobson formalism, so such analogous black holes can be used to obtain the correct coefficient for the real black holes, and this in turn can be used to select the correct approach to quantum gravity. In that case, we use an adaptive model of graphene, which is still far from real graphene, to investigate some thermodynamics quantities of BTZ black hole.

Thermodynamic variables of first-order entropy corrected Lovelock-AdS black holes: $$P{-}V$$ P - V criticality analysis

We investigate the effect of thermal fluctuations on the thermodynamics of a Lovelock-AdS black hole. Taking the first order logarithmic correction term in entropy we analyze the thermodynamic potentials like Helmholtz free energy, enthalpy and Gibbs free energy. We find that all the thermodynamic potentials are decreasing functions of correction coefficient $\alpha$. We also examined this correction coefficient tmust be positive by analysing $P-V$ diagram. Further we study the P-V criticality and stability and find that presence of logarithmic correction in it is necessary to have critical points and stable phases. When P-V criticality appears, we calculate the critical volume $V_c$, critical pressure $P_c$ and critical temperature $T_c$ using different equations and show that there is no critical point for this black hole without thermal fluctuations. We also study the geometrothermodynamics of this kind of black holes. The Ricci scalar of the Ruppeiner metric is graphically analysed.

Quantum gravity effects on Hořava–Lifshitz black hole

In this paper, we would like to obtain quantum gravity effects by using Hořava–Lifshitz black hole. We consider logarithmic corrected thermodynamics quantities and investigate the effects of logarithmic correction term. Logarithmic correction comes from thermal fluctuation and may be interpreted as quantum loop corrections. As black hole is a gravitational system, hence we can investigate quantum gravity effect. We find such effects on the black hole stability and obtain domain of correction coefficient.