Exact Solution of a (2+1)-Dimensional Anisotropic Star in Finch and Skea Spacetime

We provide a new class of interior solution of a (2+1)-dimensional anisotropic star in Finch and Skea spacetime corresponding to the BTZ black hole. We develop the model by considering the MIT bag model EOS and a particular ansatz for the metric function g_rr proposed by Finch and Skea [M.R. Finch and J.E.F. Skea, Class. Quantum. Grav. 6 (1989) 467]. Our model is free from central singularity and satisfies all the physical requirements for the acceptability of the model.     

Generalized spheroidal spacetimes in 5-D Einstein–Maxwell–Gauss–Bonnet gravity

The field equations for static EGBM gravity are obtained and transformed to an equivalent form through a coordinate redefinition. A form for one of the metric potentials that generalizes the spheroidal ansatz of Vaidya–Tikekar superdense stars and additionally prescribing the electric field intensity yields viable solutions. Some special cases of the general solution are considered and analogous classes in the Einstein framework are studied. In particular the Finch–Skea ansatz is examined in detail and found to satisfy the elementary physical requirements. These include positivity of pressure and density, the existence of a pressure free hypersurface marking the boundary, continuity with the exterior metric, a subluminal sound speed as well as the energy conditions. Moreover, the solution possesses no coordinate singularities. It is found that the impact of the Gauss–Bonnet term is to correct undesirable features in the pressure profile and sound speed index when compared to the equivalent Einstein gravity model. Furthermore graphical analyses suggest that higher densities are achievable for the same radial values when compared to the 5-dimensional Einstein case. The case of a constant gravitational potential, isothermal distribution as well as an incompressible fluid are studied. All exact solutions derived exhibit an equation of state explicitly.     

Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras–McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras–McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we obtain complete agreement with the results obtained in intrinsic coordinates. We have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.     

Buchdahl–Vaidya–Tikekar model for stellar interior in pure Lovelock gravity

In the paper (Khugaev et al. in Phys Rev D94:064065. arXiv: 1603.07118, 2016), we have shown that for perfect fluid spheres the pressure isotropy equation for Buchdahl–Vaidya–Tikekar metric ansatz continues to have the same Gauss form in higher dimensions, and hence higher dimensional solutions could be obtained by redefining the space geometry characterizing Vaidya–Tikekar parameter K. In this paper we extend this analysis to pure Lovelock gravity; i.e. a \((2N+2)\)-dimensional solution with a given \(K_{2N+2}\) can be taken over to higher n-dimensional pure Lovelock solution with \(K_n=(K_{2N+2}-n+2N+2)/(n-2N-1)\) where N is degree of Lovelock action. This ansatz includes the uniform density Schwarzshild and the Finch–Skea models, and it is interesting that the two define the two ends of compactness, the former being the densest and while the latter rarest. All other models with this ansatz lie in between these two limiting distributions.     

Probability distributions with given margins: Note on a paper by Finch and Groblicki

Recently, P. D. Finch and R. Groblicki determined all bivariate probability densities with specified margins. We point out that their result follows immediately from the complete solution to the problem of determining all n-dimensional cumulative probability distribution functions with specified one-dimensional margins, which was solved by one of us in 1959.     

Theoretical studies on the proton and electron transfer (PET) in a pseudo one-dimensional hydrogen bonded network system

We investigated singly ordered phases of the charge density were (CDW), spin density wave (SDW), and singlet superconductivity (SSC) for a pseudo one-dimensional proton and electron transfer (PET) system of quinhydrone crystal by means of the two band model. We performed band structure calculations of model systems, which are (i) the quinone and the p-hydroquinone model and (ii) two semiquinones model. We found that the model (i) exhibits an insulator and the model (ii) exhibits the SDW insulator.     

A sharp-interface interpretation of a continuous density model for homogenization of gravity-driven flow in porous media

We examine homogenization methods applied to sharp-interface and diffuse-interface models for gravity-driven flow in heterogeneous porous media. Our work specifically examines a matrix of models that includes (1) a variable media, diffuse-interface model, (2) a variable media, sharp-interface model, (3) a homogenized media, diffuse-interface model and (4) a homogenized media, sharp-interface model. We connect all four of these models via homogenization theory and sharp-interface limits. We show that existing results based on homogenization methods applied to sharp-interface models can be recovered by a less direct but more rigorous approach involving well-established homogenization theory and sharp-interface limits.     

Coloring random triangulations

We introduce and solve a two-matrix model for the tri-coloring problem of the vertices of a random triangulation. We present three different solutions: (i) by orthogonal polynomial techniques, (ii) by use of a discrete Hirota bilinear equation, (iii) by direct expansion. The model is found to lie in the universality class of pure two-dimensional quantum gravity, despite the non-polynomiality of its potential.     

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi (LTB) cosmology supported by a perfect fluid source. This model is the natural generalization of the flat Friedmann-Robertson-Walker (FRW) universe, and describes an inhomogeneous universe with spherical symmetry. After reviewing some basic equations in the parabolic LTB cosmology, we obtain a relation for the deceleration parameter in this model. We also obtain a condition for which the universe undergoes an accelerating phase at the present time. We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology. We find out that in LTB model of cosmology, the apparent horizon's entropy could be feeded by a term, which incorporates the effects of the inhomogeneity. We consider this result and get a relation for the total entropy evolution, which is used to examine the generalized second law of thermodynamics for an accelerating universe. We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence

We primarily deal with homogeneous isotropic turbulence and use a closure model for the von Kármán-Howarth equation to study several geometric properties of turbulent fluid dynamics. We focus our attention on the application of Riemannian geometry methods in turbulence. Some advantage of this approach consists in exploring the specific form of a closure model for the von Kármán-Howarth equation that enables to equip a model manifold (a cylindrical domain in the correlation space) by a family of inner metrics (length scales of turbulent motion) which depends on time. We show that for large Reynolds numbers (in the limit of large Reynolds numbers) the radius of this manifold can be evaluated in terms of the second-order structure function and the correlation distance. This model manifold presents a shrinking cylindrical domain as time evolves. This result is derived by using a selfsimilar solution of the closure model for the von Kármán-Howarth equation under consideration. We demonstrate that in the new variables the selfsimilar solution obtained coincides with the element of Beltrami surface (or pseudo-sphere): a canonical surface of the constant sectional curvature equals − 1.      

Generalized Second Law of Thermodynamics in Parabolic LTB Inhomogeneous Cosmology

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi(LTB) cosmology supported by a perfect Suid source.This model is the natural generalization of the Sat Friedmann-Robertson-Walker(FRW) universe,and describes an inhomogeneous universe with spherical symmetry.After reviewing some basic equations in the parabolic LTB cosmology,we obtain a relation for the deceleration parameter in this model.We also obtain a condition for which the universe undergoes an accelerating phase at the present time.We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology.We find out that in LTB model of cosmology,the apparent horizon's entropy could be feeded by a term,which incorporates the effects of the inhomogeneity.We consider this result and get a relation for the total entropy evolution,which is used to examine the generalized second law of thermodynamics for an accelerating universe.We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model.     

Application of the short and long consecutive pairs model to the triplet-doublet interaction in molecular crystals

We have adapted the model of two consecutive pairs to the study of the triplet-doublet (T-D) interaction in molecular crystals. We have applied this model to the modulation of the photoconductivity in crystalline anthracene by a static magnetic field (MFE) and a microwave field (PDMR). We were able to reproduce, for the first time, quite perfectly two types of experiments with the same set of kinetic constants.     

Search for excited and exotic muons in the mugamma decay channel in p-p collisions at sqrt s =1.96 TeV

We search for excited and exotic muon states mu* using an integrated luminosity of 371 pb(-1) of p[over]p collision data at sqrt[s]=1.96 TeV. We search for associated production of mumu* followed by the decay mu*-->mugamma. We compare the data to model predictions as a function of the mass of the excited muon M(mu*), the compositeness energy scale Lambda, and the gauge coupling factor f. No signal above the standard model expectation is observed. We exclude 107相似文献   

Exact characterization of O(n) tricriticality in two dimensions

We propose exact expressions for the conformal anomaly and for three critical exponents of the tricritical O(n) loop model as a function of n in the range -2相似文献   

A high-order super-grid-scale absorbing layer and its application to linear hyperbolic systems

We continue the development of the super-grid-scale model initiated in [T. Colonius, H. Ran, A super-grid-scale model for simulating compressible flow on unbounded domains, J. Comput. Phys. 182 (1) (2002) 191–212] and consider its application to linear hyperbolic systems. The super-grid-scale model consists of two parts: reduction of an unbounded to a bounded domain by a smooth coordinate transformation and a damping of those scales. For linear problems the super-grid scales are analogous to spurious numerical waves. We damp these waves by high-order undivided differences. We compute reflection coefficients for different orders of the damping and find that significant improvements are obtained when high-order damping is used.     

Avalanche dynamics of crackle sound in the lung

We analyze a sequence of short transient sound waves, called "crackles," which are associated with explosive openings of airways during lung inflation. The distribution of time intervals between consecutive crackles Delta(t) shows two regimes of power law behavior. We develop an avalanche model which fits the data over five decades of Delta(t). We find that the regime for large Delta(t) is related to the dynamics of distinct avalanches in a Cayley tree, and the regime for small Delta(t) is determined by the dynamics of crackle propagation within a single avalanche. We also obtain a mean-field solution of the model which provides information about lung inflation.     

Use of the Richtmyer-Meshkov instability to infer yield stress at high-energy densities

We use the Richtmyer-Meshkov instability (RMI) at a metal-gas interface to infer the metal's yield stress (Y) under shock loading and release. We first model how Y stabilizes the RMI using hydrodynamics simulations with a perfectly plastic constitutive relation for copper (Cu). The model is then tested with molecular dynamics (MD) of crystalline Cu by comparing the inferred Y from RMI simulations with direct stress-strain calculations, both with MD at the same conditions. Finally, new RMI experiments with solid Cu validate our simulation-based model and infer Y~0.47 GPa for a 36 GPa shock.     

Creation and destruction of a spin gap in weakly coupled quarter-filled ladders

We investigate weakly coupled quarter-filled ladders with model parameters relevant for NaV(2)O(5) using density-matrix renormalization group calculations on an extended Hubbard model coupled to the lattice. NaV(2)O(5) exhibits super-antiferroelectric charge order with a zigzag pattern on each ladder. We show that this order causes a spin dimerization along the ladder and is accompanied by a spin gap of the same magnitude as that observed experimentally. The spin gap is destroyed again at large charge order due to a restructuring of the spins. An analysis of an effective spin model predicts a recreation of the gap by interladder singlets when the charge order increases further.     

Determination of structure parameters in molecular tunnelling ionisation model

We extracted the accurate structure parameters in a molecular tunnelling ionisation model (the so-called MO-ADK model) for 23 selected linear molecules including some inner orbitals. The molecular wave functions with the correct asymptotic behaviour are obtained by solving the time-independent Schrödinger equation with B-spline functions and molecular potentials numerically constructed using the modified Leeuwen–Baerends (LBα) model. We show that the orientation-dependent ionisation rate reflects the shape of the ionising orbitals in general. The influences of the Stark shifts of the energy levels on the orientation-dependent ionisation rates of the polar molecules are studied. We also examine the angle-dependent ionisation rates (or probabilities) based on the MO-ADK model by comparing with the molecular strong-field approximation calculations and with recent experimental measurements.