Term In Momentum Research Articles

A relaxation model for the non-isothermal Navier-Stokes-Korteweg equations in confined domains

The Navier-Stokes-Korteweg (NSK) system is a classical diffuse interface model which is based on van der Waals' theory of capillarity. Diffuse interface methods have gained much interest to model two-phase flow in porous media. However, for the numerical solution of the NSK equations two major challenges have to be faced. First, an extended numerical stencil is required due to a third-order term in the linear momentum and the total energy equations. In addition, the dispersive contribution in the linear momentum equations prevents the straightforward use of contact angle boundary conditions. Secondly, any real gas equation of state is based on a non-convex Helmholtz free energy potential which may cause the eigenvalues of the Jacobian of the first-order fluxes to become imaginary numbers inside the spinodal region.In this work, a thermodynamically consistent relaxation model is presented which is used to approximate the NSK equations. The model is complimented by thermodynamically consistent non-equilibrium boundary conditions which take contact angle effects into account. Due to the relaxation approach, the contribution of the Korteweg tensor in the linear momentum and total energy equations can be reduced to first-order terms which enables a straightforward implementation of contact angle boundary conditions in a numerical scheme. Moreover, the definition of a modified pressure function enables to formulate first-order fluxes which remain strictly hyperbolic in the entire spinodal region. The present work is a generalization of a previously presented parabolic relaxation model for the isothermal NSK equations.A high-order discontinuous Galerkin spectral element method which supports curved elements and hanging nodes is employed to discretize the system. The relaxation model and its corresponding boundary conditions are validated using solutions of the original NSK model and analytical results for one-, two- and three-dimensional test cases. The simulation of a spinodal decomposition in a three-dimensional porous structure underlines the capability of the presented approach.

Numerical Predication of Solidification Phenomena of Phase Change Material in Concentric Annulus Pipe

Two-dimensional numerical simulation is performed aiming to understand the role of buoyancy force convection during restricted solidification of phase change materials (PCMs) inside a shell and tube heat exchanger according to annulus cross section. Where the transient history of PCM solidification evolution was studied. The governing equations of mass, momentum and energy are solved to study the solidification behavior inside the annulus geometry. The fluid flow in the mushy zone was accounted for using the Darcy drag source term in momentum, and the liquid percentage in each cell was updated using the enthalpy-porosity method. Thermal conditions of the outer cylinder insulated (adiabatic) and the inner cylinder at constant temperature (isothermal). The results are presents as a temperature contour and liquid fraction distribution in the domain. The predicted result shows the capturing phenomenon: primary heat conduction in all regions, then heat convection and conduction become dominant in the top and bottom regions, respectively. The max. and min. temperature changes near the outer pipe surface during 16 hrs. are 56.25% and 42.5%, respectively.

Minimal length effect on the broadening of free wave packets and its physical implications

We study the Generalized Uncertainty Principle (GUP) modified time evolution for the width of wave-packets for a scalar potential. Free particle case is solved exactly where the wave-packet broadening is modified by a coupling between the GUP parameter and higher order moments in the probability distribution in momentum space. We consider two popular forms of deformations widely used in the literature - one of which modifies the commutator with a quadratic term in momentum, while the other modifies it with terms both linear and quadratic in momentum. Unlike the standard case, satisfying Heisenberg uncertainty, here the GUP modified broadening rates, for both deformations, not only depend on the initial size (both in position and momentum space) of the wave-packet, but also on the initial probability distribution and momentum of the particle. The new rates of wave-packet broadening, for both situations, are modified by a handful of new terms - such as the skewness and kurtosis coefficients, as well as the (constant) momentum of the particle. Comparisons with the standard Heisenberg Uncertainty Principle (HUP)-based results show potentially measurable differences in the rates of free wave-packet broadening for physical systems such as the $C_{60}$ and $C_{176}$ molecules, and more so for large organic molecular wave-packets. In doing so, we open a path to scan the GUP parameter space by several orders of magnitude inside the best existing upper bounds for both forms of GUP.

GUP parameter and black-hole temperature

Motivated by a recent work of Scardigli, Lambiase and Vagenas (SLV), we derive the GUP parameter, i.e., , when the GUP has a linear and quadratic term in momentum. The value of the GUP parameter is obtained by conjecturing that the GUP-deformed black-hole temperature of a Schwarzschild black hole and the modified Hawking temperature of a quantum-corrected Schwarzschild black hole are the same. The leading term in both cases is the standard Hawking temperature and since the corrections are considered as thermal, the modified and deformed expressions of temperature display a slight shift in the Hawking temperature. Finally, by equating the first correction terms, we obtain a value for the GUP parameter. In our analysis, the GUP parameter is not a pure number but depends on the ratio with the Planck mass and M the black-hole mass.

Interaction of Asymmetric Films Around Boiling Cylinder Array: Homogeneous Interface to Chaotic Phenomenon

We report numerical study of film boiling around hot and horizontal cylinders in a saturated water pool to establish interfacial interactions leading toward dryout. Volume of fluid-based finite-volume discretization is performed in the domain for incorporation of source term in mass momentum and energy conservation equations due to phase change. At first, film boiling around single cylinder is simulated at different surface temperatures to understand unconstrained film growth and subsequent film bubble release due to buoyancy. Using velocity vectors and temperature contours, effect of film flow dynamics on bubble departure is depicted. This study has been extended further with multiple cylinders in three different stacking arrangements in order to understand the interaction of films in vicinity. Vertical interaction between cylinders leads to suppression of bubble release at the lower cylinder in comparison to the upper one. In the case of horizontal interactions, bubbles attract each other and merge, provided favorable pitch between cylinders and temperatures of the surfaces is maintained. Offset four cylinders stack maintaining vertical and horizontal pitch allows both lateral vapor affinity and bubble suppression in the lower most cylinder simultaneously. With time interaction of accumulated vapor films around cylinders hinders replenishment of fresh liquid to the hot surfaces leading toward chaotic phenomena or dryout in boiling heat transfer.

Magneto-optical conductivity of Weyl semimetals with quadratic term in momentum

Weyl semimetal is a three-dimensional Dirac material whose low energy dispersion is linear in momentum. Adding a quadratic (Schrödinger) term to the Weyl node breaks the original particle-hole symmetry and also breaks the mirror symmetry between the positive and negative Landau levels in present of magnetic field. This asymmetry splits the absorption line of the longitudinal magneto-optical conductivity into a two peaks structure. It also results in an oscillation pattern in the absorption part of the Hall conductivity. The two split peaks in Reσxx (or the positive and negative oscillation in Imσxy) just correspond to the absorptions of left-handed (σ−) and right-handed (σ+) polarization light, respectively. The split in Reσxx and the displacement between the absorption of σ+ and σ− are decided by the magnitude of the quadratic term and the magnetic field.

Towards a cosmology with minimal length and maximal energy

The Friedmann–Robertson–Walker (FRW) universe and Bianchi I, II universes are investigated in the framework of the generalized uncertainty principle (GUP) with a linear and a quadratic term in Planck length and momentum, which predicts the minimum measurable length as well as maximum measurable momentum. We obtain a dynamic cosmological bounce for the FRW universe. With the Bianchi universe, we found that the universe may still be isotropic by implementing GUP. Moreover, the wall velocity appears to be stationary with respect to the universe velocity, which means that when the momentum of the universe evolves into a maximum measurable energy, the bounce is enhanced against the wall, which means that no maximum limit angle is manifested anymore.

Path integral action and Chern–Simons quantum mechanics in noncommutative plane

In this paper, the connection between the path integral representation of propagators in the coherent state basis with additional degrees of freedom (Rohwer et al 2010 J. Phys. A: Math. Theor. 43 345302) and the one without any such degrees of freedom (Gangopadhyay and Scholtz 2009 Phys. Rev. Lett. 102 241602) is established. We further demonstrate that the path integral formalism developed in the noncommutative plane using the coherent state basis leads to a quantum mechanics involving a Chern–Simons term in momentum which is of noncommutative origin. The origin of this term from the Bopp-shift point of view is also investigated. A relativistic generalization of the action derived from the path integral framework is then proposed. Finally, we construct a map from the commutative quantum Hall system to a particle in a noncommutative plane moving in a magnetic field. The value of the noncommutative parameter from this map is then computed and is found to agree with previous results.

The acceleration of a neutron in a static electric field

We show that when a non-relativistic neutron travels in a static electric field, the acceleration vector operator is perpendicular to the velocity operator. Kinetic energy is conserved. A spin-dependent field term in the canonical momentum gives rise to a non-dispersive contribution to the quantum mechanical (Aharonov–Casher) phase. This motion differs from that in a static magnetic field which has no field term in the canonical momentum and no conservation of kinetic energy. For the geometry of the Aharonov–Casher effect, there is no acceleration, while in Mott–Schwinger scattering, the acceleration causes a spin-dependent change in neutron direction.

Black hole entropy and the modified uncertainty principle: A heuristic analysis

Recently Ali et al. (2009) proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Plank length). Inspired by this idea here we calculate the quantum corrected value of a Schwarzschild black hole entropy and a Reissner–Nordström black hole with double horizon by utilizing the proposed generalized uncertainty principle. We find that the leading order correction goes with the square root of the horizon area contributing positively. We also find that the prefactor of the logarithmic contribution is negative and the value exactly matches with some earlier existing calculations. With the Reissner–Nordström black hole we see that this model-independent procedure is not only valid for single horizon spacetime but also valid for spacetimes with inner and outer horizons.

Quantum black hole and the modified uncertainty principle

Recently Ali et al. (2009) [13] proposed a Generalized Uncertainty Principle (or GUP) with a linear term in momentum (accompanied by Planck length). Inspired by this idea we examine the Wheeler–DeWitt equation for a Schwarzschild black hole with a modified Heisenberg algebra which has a linear term in momentum. We found that the leading contribution to mass comes from the square root of the quantum number n which coincides with Bekensteinʼs proposal. We also found that the mass of the black hole is directly proportional to the quantum number n when quantum gravity effects are taken into consideration via the modified uncertainty relation but it reduces the value of mass for a particular value of the quantum number.

TOPOLOGICAL INSULATOR AND THE DIRAC EQUATION

We present a general description of topological insulators from the point of view of Dirac equations. The Z2 index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, i.e., m → m − Bp2, the Z2 index is modified as 1 for mB > 0 and 0 for mB < 0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a nontrivial system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation is obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z2 index we establish a relation between the Dirac equation and topological insulators.

Bulk viscosities for cold Fermi superfluids close to the unitary limit

We compute the coefficients of bulk viscosity for a non-relativistic superfluid corresponding to a fermionic system close to the unitarity limit. We consider the low temperature regime assuming that the transport properties of the system are dominated by phonons. To compute the coefficients of bulk viscosity we use kinetic theory in the relaxation time approximation and the low energy effective field theory of the corresponding system. We show that the three independent bulk viscosity coefficients, $\zeta_1, \zeta_2, \zeta_3$, associated with irreversible flows vanish for phonons with a linear dispersion law. Considering a phonon dispersion law with a cubic term in momentum we find that in the conformal limit $\zeta_1 = \zeta_2=0$, while $\zeta_3$ is non-zero. Including a conformal breaking term which arises for a large but finite s-wave scattering length, $a$, at the leading order in $1/a$ we obtain that $\zeta_1 \propto 1/a$ and $\zeta_2 \propto 1/a^2$.

Fast Numerical Simulation of Two-Phase Transport Model in the Cathode of a Polymer Electrolyte Fuel Cell

In this paper, we apply streamline-diffusion and Galerkin-least-squares fi- nite element methods for 2D steady-state two-phase model in the cathode of polymer electrolyte fuel cell (PEFC) that contains a gas channel and a gas diffusion layer (GDL). This two-phase PEFC model is typically modeled by a modified Navier-Stokes equa- tion for the mass and momentum, with Darcy's drag as an additional source term in momentum for flows through GDL, and a discontinuous and degenerate convection- diffusion equation for water concentration. Based on the mixed finite element method for the modified Navier-Stokes equation and standard finite element method for wa- ter equation, we design streamline-diffusion and Galerkin-least-squares to overcome the dominant convection arising from the gas channel. Meanwhile, we employ Kirch- hoff transformation to deal with the discontinuous and degenerate diffusivity in water concentration. Numerical experiments demonstrate that our finite element methods, together with these numerical techniques, are able to get accurate physical solutions with fast convergence.

Reply to the ‘Comment on ‘Generalization of the Darboux transformation and generalized harmonic oscillators’’

In the comment on our paper, Schulze-Halberg introduces a gauge transformation to gauge away the linear term in momentum. He explicitly shows that the gauge transformation works for n-fold Darboux transformed system. The comment is, however, entirely on the formalism of the Darboux transformation, while most pages of our paper are devoted to the applications of the formalism. In this reply, we add some considerations so that his gauge transformation method can be used to reproduce the solvable Hermitian Hamiltonian systems given in our paper.

Monte Carlo modeling of spin injection through a Schottky barrier and spin transport in a semiconductor quantum well

We develop a Monte Carlo model to study injection of spin-polarized electrons through a Schottky barrier from a ferromagnetic metal contact into a nonmagnetic low-dimensional semiconductor structure. Both mechanisms of thermionic emission and tunneling injection are included in the model. Due to the barrier shape, the injected electrons are nonthermalized. Spin dynamics in the semiconductor heterostructure is controlled by the Rashba and Dresselhaus spin-orbit interactions and described by a single electron spin density matrix formalism. In addition to the linear term, the third-order term in momentum for the Dresselhaus interaction is included. Effect of the Schottky potential on the spin dynamics in a two-dimensional semiconductor device channel is studied. It is found that the injected current can maintain substantial spin polarization to a length scale in the order of 1μm at room temperature without external magnetic fields.

Rotational anomaly and fractional spin in the gauged CP1 nonlinear sigma model with the Chern-Simons term.

We consider the interacting ${\mathrm{CP}}^{1}$ nonlinear $\ensuremath{\sigma}$ model in 2 + 1 dimensions in the presence of an Abelian Chern-Simons term and quantize it canonically using the Dirac-Bergmann algorithm. There arises an anomalous term in the angular momentum in presence of the interaction, which in the long-range limit yields the fractional spin for the excitations.