Non-minimal coupling of torsion–matter satisfying null energy condition for wormhole solutions

We explore wormhole solutions in a non-minimal torsion–matter coupled gravity by taking an explicit non-minimal coupling between the matter Lagrangian density and an arbitrary function of the torsion scalar. This coupling describes the transfer of energy and momentum between matter and torsion scalar terms. The violation of the null energy condition occurred through an effective energy-momentum tensor incorporating the torsion–matter non-minimal coupling, while normal matter is responsible for supporting the respective wormhole geometries. We consider the energy density in the form of non-monotonically decreasing function along with two types of models. The first model is analogous to the curvature–matter coupling scenario, that is, the torsion scalar with T-matter coupling, while the second one involves a quadratic torsion term. In both cases, we obtain wormhole solutions satisfying the null energy condition. Also, we find that the increasing value of the coupling constant minimizes or vanishes on the violation of the null energy condition through matter.     

Boosted cylindrical magnetized Kaluza–Klein wormhole

In this work, we consider a vacuum solution of Kaluza–Klein theory with cylindrical symmetry. We investigate the physical properties of the solution as viewed in four dimensional spacetime, which turns out to be a stationary, cylindrical wormhole supported by a scalar field and a magnetic field oriented along the wormhole. We then apply a boost to the five dimensional solution along the extra dimension, and perform the Kaluza–Klein reduction. As a result, we show that the new solution is still a wormhole with a radial electric field and a magnetic field stretched along the wormhole throat.     

Nonsymmetric dynamical thin-shell wormhole in Robinson–Trautman class

The thin-shell wormhole created using the Darmois–Israel formalism applied to Robinson–Trautman family of spacetimes is presented. The stress energy tensor created on the throat is interpreted in terms of two dust streams and it is shown that asymptotically this wormhole settles to the Schwarzschild wormhole with a throat located at the position of the horizon. This behavior shows a nonlinear stability (within the Robinson–Trautman class) of this spherically symmetric wormhole. The gravitational radiation emitted by the Robinson–Trautman wormhole during the transition to spherical symmetry is indistinguishable from that of the corresponding black hole Robinson–Trautman spacetime. Subsequently, we show that the higher-dimensional generalization of Robinson–Trautman geometry offers a possibility of constructing wormholes without the need to violate the energy conditions for matter induced on the throat.     

An optimal analysis for Darcy–Forchheimer 3D flow of nanofluid with convective condition and homogeneous–heterogeneous reactions

Here Darcy–Forchheimer 3D stretching flow of nanoliquid in the presence of convective condition and homogeneous–heterogeneous reactions is analyzed. Impacts of thermophoresis, Brownian diffusion and zero nanoparticles mass flux condition are considered. Adequate transformation procedure give rise to system in terms of ordinary differential equations. The governing mathematical system has been tackled by optimal homotopic technique. Graphical results have been presented for temperature and concentration dsitributions. Numerical benchmark is provided to study the values of skin friction coefficients and local Nusselt number. Skin friction coefficients are declared increasing functions of porosity and Forchheimer parameters. Furthermore the local Nusselt number is reduced for larger values of porosity and Forchheimer parameters.     

The zero active mass condition in Friedmann–Robertson–Walker cosmologies

Many cosmological measurements today suggest that the Universe is expanding at a constant rate. This is inferred from the observed age versus redshift relationship and various distance indicators, all of which point to a cosmic equation of state (EoS) p = -ρ/3, where ρ and p are, respectively, the total energy density and pressure of the cosmic fluid. It has recently been shown that this result is not a coincidence and simply confirms the fact that the symmetries in the Friedmann–Robertson–Walker (FRW) metric appear to be viable only for a medium with zero active mass, i.e., ρ + 3p = 0. In their latest paper, however, Kim, Lasenby and Hobson (2016) have provided what they believe to be a counter argument to this conclusion. Here, we show that these authors are merely repeating the conventional mistake of incorrectly placing the observer simultaneously in a comoving frame, where the lapse function gtt is coordinate dependent when ρ + 3p ≠ 0, and a supposedly different, freefalling frame, in which g_tt = 1, implying no time dilation. We demonstrate that the Hubble flow is not inertial when ρ + 3p ≠ 0, so the comoving frame is generally not in free fall, even though in FRW, the comoving and free-falling frames are supposed to be identical at every spacetime point. So this confusion of frames not only constitutes an inconsistency with the fundamental tenets of general relativity but, additionally, there is no possibility of using a gauge transformation to select a set of coordinates for which g_tt = 1 when ρ + 3p ≠ 0.     

On the stability of the shear–free condition

The evolution equation for the shear is reobtained for a spherically symmetric anisotropic, viscous dissipative fluid distribution, which allows us to investigate conditions for the stability of the shear–free condition. The specific case of geodesic fluids is considered in detail, showing that the shear–free condition, in this particular case, may be unstable, the departure from the shear–free condition being controlled by the expansion scalar and a single scalar function defined in terms of the anisotropy of the pressure, the shear viscosity and the Weyl tensor or, alternatively, in terms of the anisotropy of the pressure, the dissipative variables and the energy density inhomogeneity.     

Homological unimodularity and Calabi–Yau condition for Poisson algebras

In this paper, we show that the twisted Poincaré duality between Poisson homology and cohomology can be derived from the Serre invertible bimodule. This gives another definition of a unimodular Poisson algebra in terms of its Poisson Picard group. We also achieve twisted Poincaré duality for Hochschild (co)homology of Poisson bimodules using rigid dualizing complex. For a smooth Poisson affine variety with the trivial canonical bundle, we prove that its enveloping algebra is a Calabi–Yau algebra if the Poisson structure is unimodular.     

Ultrasound assisted arylation of benzyl alcohol with 4-nitrochlorobenzene under a new multi-site phase-transfer catalyst in solid–liquid condition

The ultrasound assisted preparation of 1-(benzyloxy)-4-nitrobenzene from the reaction of 4-chloronitrobenzene (CNB) and benzyl alcohol was carried out successfully using potassium hydroxide and catalyzed by a new multi-site phase-transfer catalyst (MPTC) viz., 1,3,5-triethyl-1,3,5-trihexyl-1,3,5-triazinane-1,3,5-triium trichloride in a solid–liquid reaction condition (SL-MPTC). The advantage of using SL-MPTC is to avoid a serious hydration of potassium salt of benzyl alcohol in the reaction between 4-chloronitrobenzene (CNB) and benzyl alcohol. The reaction is greatly enhanced in the solid–liquid system, catalyzed by multi-site quaternary ammonium salt (MPTC) and ultrasound irradiation (40 kHz, 300 W) in a batch reactor, it shows that the overall reaction greatly enhanced with ultrasound irradiation than without ultrasound. The reaction mechanism is proposed and verified by examining the experimental evidence. A kinetic model is proposed in which a pseudo first-order rate law is sufficient to describe the results, such as the effects of agitation speed, ultrasound, different phase transfer catalysts and the effect of organic solvents, the amount of newly prepared MPTC, the effect of temperature, the amount of water, the concentration of 4-chloronitrobenzene (CNB) and potassium hydroxide concentrations. The apparent rate constant (k_app) were investigated in detail. Rational explanations to account for the phenomena on the results were made.     

The A+B→0 diffusion-limited reaction with correlated initial condition

We show some inaccuracies in recent arguments claiming that in the long-time limit the initially correlated A+B0 diffusion-limited reaction can be faster than the A+A0 one. With the errors corrected, these arguments seem to confirm the former theory of Toussant and Wilczek according to which the global rate of both reactions should ultimately be the same. This hypothesis is also supported by our numerical simulations of a two-dimensional lattice system.     

Confinement of atoms with Robin’s condition: Spontaneous symmetry breaking

The properties of the ground state of the hydrogen atom in a spherical vacuum cavity with general boundary “not going out” conditions (i.e., when the probability current through the boundary vanishes) are studied. It is shown that in contrast to the confinement of an atom by a potential barrier, in this case depending on the parameters of the cavity, the atom could be in stable equilibrium at the center of the cavity or shift towards its periphery: spontaneous breaking of spherical symmetry occurs. The phase diagram of the shift and the dependence of the shift value and the binding energy of the ground state of the atom on the cavity parameters are presented. At the same time, the deformation properties of the electron wave function (WF) for an asymmetric distortion are so nontrivial that a non-zero shift occurs even when an electron is repulsed from the cavity boundary.     

Coherent superpositions of states in coupled Hilbert-space using step by step Morris–Shore transformation

Creation of coherent superpositions in quantum systems with N_a$N_a$ states in the lower set and N_b$N_b$ states in the upper set is presented. The solution is drived by using the Morris–Shore transformation, which step by step reduces the fully coupled system to a three-state Λ$\Lambda$-like system and a set of decoupled states. It is shown that, for properly timed pulse, robust population transfer from an initial ground state (or superposition of M$M$ ground states) to an arbitrary coherent superposition of the ground states can be achieved by coincident pulses and/or STIRAP techniques.     

Instability of collapsing source under expansion-free condition in einstein Gauss–Bonnet gravity

In this work, we have investigated the dynamical instability of spherically symmetric gravitating object under expansion-free condition in Einstein Gauss–Bonnet gravity. In this context, the field equations and dynamical equations have been established in the Gauss–Bonnet gravity. The linear perturbation scheme has been used on the dynamical equations to construct the collapse equation. The Newtonian, post Newtonian and post Newtonian approximations have been applied to investigate the general dynamical (in)stability equations. It has been observed that the instability range of the collapsing source is independent of adiabatic index Γ (stiffness of the fluid does not play any role). The instability range can be determined by the pressure anisotropy, energy density profile, Gauss–Bonnet parameter α and some constraints at Newtonian, post Newtonian and post Newtonian order.     

Adaptive artificial boundary condition for the two-level Schrödinger equation with conical crossings

In this paper, we present an adaptive approach to design the artificial boundary conditions for the two-level Schrödinger equation with conical crossings on the unbounded domain. We use the windowed Fourier transform to obtain the local wave number information in the vicinity of artificial boundaries, and adopt the operator splitting method to obtain an adaptive local artificial boundary condition. Then reduce the original problem into an initial boundary value problem on the bounded computational domain, which can be solved by the finite difference method. By this numerical method, we observe the surface hopping phenomena of the two-level Schrödinger equation with conical crossings. Several numerical examples are provided to show the accuracy and convergence of the proposed method.     

Do the generalized Fock-state wave functions have some relations with classical initial condition?

We examine whether the general type Fock-state wave functions for the harmonic oscillator have some relations with the classical initial condition.     

Flame capturing with an advection–reaction–diffusion model

We conduct several verification tests of the advection–reaction–diffusion flame-capturing model, developed by Khokhlov in 1995 for subsonic nuclear burning fronts in supernova simulations. We find that energy conservation is satisfied, but there is systematic error in the computed flame speed due to thermal expansion, which was neglected in the original model. We decouple the model from the full system, determine the necessary corrections for thermal expansion, and then demonstrate that these corrections produce the correct flame speed. The flame-capturing model is an alternative to other popular interface tracking techniques, and might be useful for applications beyond astrophysics.