Energy Density Equation Research Articles

NUMERICAL STUDY OF MIXED BIOCONVECTION IN POROUS MEDIA SATURATED WITH NANOFLUID CONTAINING OXYTACTIC MICROORGANISMS

A mathematical model has been developed for steady-state boundary layer flow of a nanofluid past an impermeable vertical flat wall in a porous medium saturated with a water-based dilute nanofluid containing oxytactic microorganisms. The nanoparticles were distributed sufficiently to permit bioconvection. The product of chemotaxis constant and maximum cell swimming speed was assumed invariant. Using appropriate transformations, the partial differential conservation equations were non-dimensionalised to yield a quartet of coupled, non-linear ordinary differential equations for momentum, energy, nanoparticle concentration and dimensionless motile microorganism density, with appropriate boundary conditions. The dominant parameters emerging in the normalised model included the bioconvection Lewis number, bioconvection Peclet number, Lewis number, buoyancy ratio parameter, Brownian motion parameter, thermophoresis parameter, local Darcy-Rayleigh number and the local Peclet number. An implicit numerical solution to the well-posed two-point non-linear boundary value problem is developed using the well-tested and highly efficient Keller box method. Computations are validated with the Nakamura tridiagonal implicit finite difference method, demonstrating excellent agreement. Nanoparticle concentration and temperature were found to be generally enhanced through the boundary layer with increasing bioconvection Lewis number, whereas dimensionless motile microorganism density was only increased closer to the wall. Temperature, nanoparticle concentration and dimensionless motile microorganism density were all greatly increased with a rise in Peclet number. Temperature and dimensionless motile microorganism density were reduced with increasing buoyancy parameter, whereas nanoparticle concentration was increased. The present study found applications in the fluid mechanical design of microbial fuel cell and bioconvection nanotechnological devices.

High frequency S wave envelope synthesis using a multiple nonisotropic scattering model: application to aftershocks from the 2008 Wenchuan earthquake

Based on the formulation of a multiple non-isotropic scattering process, a characteristic source time is introduced to define the initial impulse width of energy density at the source. An analytical expression of the initial intensity spectral density of a seismic wave is incorporated into the integral equation of seismic wave energy density. And, a recursive formula of Green’s function is derived to obtain the higher order Green’s function, which is included to describe the stronger non-isotropic scattering process. Then, the effect of the scattering pattern on the energy density envelope is investigated by the modified scattering theory. Significant differences are found in the decay of the energy density envelopes with distances using different scattering patterns. The envelope synthesized by the forward dominated scattering pattern is larger than the results obtained by the isotropic and backward dominated scattering pattern. Different scattering patterns are also used to fit the observation data from the aftershocks of the 2008 Wenchuan earthquake. It is concluded that the envelopes synthesized by the forward scattering pattern can match the data better than the isotropic and backward dominated scattering cases, and a new interpretation of the coda wave is given. Finally, using the forward dominated scattering pattern, the envelope broadening of the observed data is reproduced.

Quantum Entanglement: Where Dark Energy and Negative Gravity plus Accelerated Expansion of the Universe Comes from

Dark energy is shown to be the absolute value of the negative kinetic energy of the halo-like quantum wave modeled mathematically by the empty set in a five dimensional Kaluza-Klein (K-K) spacetime. Ordinary or position energy of the particle on the other hand is the dual of dark energy and is contained in the dynamic of the quantum particle modeled by the zero set in the same five dimensional K-K spacetime. The sum of both dark energy of the wave and the ordinary energy of the particle is exactly equal to the energy given by the well known formula of Einstein E=mc2 which is set in a four dimensional spacetime. Various interpretations of the results are presented and discussed based on the three fundamental energy density equations developed. In particular where E is the energy, m is the mass and c is the speed of light, is Hardy’s quantum entanglement and gives results in complete agreement with the cosmological measurements of WMAP and Supernova. On the other hand gives an intuitive explanation of negative gravity and the observed increased rate of cosmic expansion. Adding E (ordinary) to E (dark) one finds which as we mentioned above is Einstein’s famous relativity formula. We conclude that similar to the fact that the quantum wave interpreted generally as probability wave which is devoid of ordinary energy decides upon the location of a quantum particle, it also exerts a negative gravity effect on the cosmic scale of our clopen, i.e. closed and open universe. Analysis and conclusions are framed in a reader friendly manner in Figures 1-14 with detailed commentary.

Nash Embedding of Witten’s M-Theory and the Hawking-Hartle Quantum Wave of Dark Energy

Euclidean embedding of the 11-dimensional M-theory turned out to require a very large space leaving lavish amounts of 242 dimensional pseudo truly empty “regions” devoid of space and time and consequently of anything resembling ordinary physical energy density. It is shown here using Nash embedding that the ratio of “solid” M-theory spacetime to its required embedding “non-spacetime” is 1/22 for a classical theory and 1/22.18033989 for an analogous fractal theory. This then leads to a maximal ordinary energy density equation equal to that of Einstein’s famous formula E=mc2 but multiplied with in full agreement with previous results obtained using relatively more conventional methods including running the electromagnetic fine structure constant in the exact solution of the hydrogen atom. Consequently, the new equation corresponds to a quantum relativity theory which unlike Einstein’s original equation gives quantitative predictions which agree perfectly with the cosmological measurements of WMAP and the analysis of certain supernova events. Never the less in our view dark energy also exists being the energy of the quantum wave amounting to 95.5 present of the total Einstein theoretical energy which is blind to any distinction between ordinary energy of the quantum particle and the dark energy of the quantum wave. However, since measurement leads to the collapse of the Hawking-Hartle quantum wave, dark energy being a quantum wave non-ordinary energy could not possibly be measured in the usual way unless highly refined quantum wave non-demolition technology is developed if possible. It is a further reason that dark energy having a different sign to ordinary energy is the cause behind the anti gravity force which is pushing the universe apart and accelerating cosmic expansion. Consequently it can be seen as the result of anticlastic Cartan-like curvature caused by extra compactified dimensions of spacetime. A simple toy model demonstration of the effect of curvature in a “material” space is briefly discussed.

Local electron mean energy profile of positive primary streamer discharge with pin-plate electrodes in oxygen—nitrogen mixtures

Local electron mean energy (LEME) has a direct effect on the rates of collisional ionization of molecules and atoms by electrons. Electron-impact ionization plays an important role and is the main process for the production of charged particles in a primary streamer discharge. Detailed research on the LEME profile in a primary streamer discharge is extremely important for a comprehensive understanding of the local physical mechanism of a streamer. In this study, the LEME profile of the primary streamer discharge in oxygen-nitrogen mixtures with a pin-plate gap of 0.5 cm under an impulse voltage is investigated using a fluid model. The fluid model includes the electron mean energy density equation, as well as continuity equations for electrons and ions and Poisson's electric field equation. The study finds that, except in the initial stage of the primary streamer, the LEME in the primary streamer tip tends to increase as the oxygen-nitrogen mole ratio increases and the pressure decreases. When the primary streamer bridges the gap, the LEME in the primary streamer channel is smaller than the first ionization energies of oxygen and nitrogen. The LEME in the primary streamer channel then decreases as the oxygen-nitrogen mole ratio increases and the pressure increases. The LEME in the primary streamer tip is primarily dependent on the reduced electric field with mole ratios of oxygen-nitrogen given in the oxygen-nitrogen mixtures.

Electromagnetic energy, momentum, and angular momentum in an inhomogeneous linear dielectric

In a previous work, Optics Communications 284 (2011) 2460–2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy–momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy–momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy–momentum matrix has tensor transformation properties under a symmetry group of space–time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.

Cosmological evolution for dark energy models in f(T) gravity

In this paper, we investigate the behavior of equation of state parameter and energy density for dark energy in the framework of f(T) gravity. For this purpose, we use anisotropic LRS Bianchi type I universe model. The behavior of accelerating universe is discussed for some well-known f(T) models. It is found that the universe takes a transition between phantom and non-phantom phases for f(T) models except exponential and logarithmic models. We conclude that our results are relativity analogous to the results of FRW universe.

Study of the characteristics of a streamer discharge in air based on a plasma chemical model

A detailed research on the streamer discharge local mechanism is necessary to enhance and develop the streamer theory. In the present paper, the characteristics of a streamer discharge in air at an atmospheric pressure are investigated using a hydrodynamic model based on plasma chemistry. Aside from continuity equations for electrons and ions, as well as Poisson's equation for the electric field, the model includes the electron mean energy density equation and the neutral particle density continuity equation. The electric field strength and the velocities of streamer propagations obtained from proposed model are in good agreement with experimental and simulation results in literature. The mean electron energy is nearly constant in the streamer channel, except for a peak value at the streamer tip. Although the mole fraction of oxygen is only about 0.2 in air, oxygen ions are the dominant charged particles in the streamer discharge. At the electrode surface, the charged particle densities significantly decrease in the direction of the electrode because of surface reactions.

The effects and interactions of fabrication parameters on the properties of selective laser sintered hydroxyapatite polyamide composite biomaterials

PurposeHydroxyapatite‐polymer composite materials are being researched for the development of low‐load bearing implants because of their bioactive and osteoconductive properties, while avoiding modulus mismatch found in homogenous materials. For the direct production of hydroxyapatite‐polymer composite implants, selective laser sintering (SLS) has been used and various parameters and their effects on the physical properties (micro and macro morphologies) have been investigated. The purpose of this paper is to identify the most influential parameters on the micro and macro pore morphologies of sintered hydroxyapatite‐polymer composites.Design/methodology/approachA two‐level full factorial experiment was designed to evaluate the effects of the various processing parameters and their effects on the physical properties, including open porosity, average pore width and the percentage of pores which could enable potential bone regeneration and ingrowth of the sintered parts. The density of the sintered parts was measured by weight and volume; optical microscopy combined with the interception method was used to determine the average pore size and proportion of pores suitable to enable bone regeneration.FindingsIt was found that the effect of build layer thickness was the most influential parameter with respect to physical and pore morphology features. Consequently, it is found that the energy density equation with the layer thickness parameter provides a better estimation of part porosity of composite structures than the energy density equation without the layer thickness parameter. However, further work needs to be conducted to overcome the existing error of variance.Originality/valueThis work is the first step in identifying the most significant SLS parameters and their effects on the porosity, micro and macro pore morphologies of the fabricated parts. This is an important step in the further development of implants which may be required.

Analysis of ECRH Pre-Ionization for Plasma Start-Up in JT-60SA

Plasma start-up assisted by electron cyclotron resonance heating (ECRH) pre-ionization is theoretically studied for the superconducting tokamak JT-60SA by using a zero-dimensional (0-D) model. Because the toroidal electric field is limited to 0.5 Vm −1 , we clarify the conditions for a robust plasma initiation. Five temporal equations are solved for a spatially-uniform plasma: the electron and neutral density equations, the electron and ion energy density equations, and the electric circuit equation. The numerical calculation results show that an absorbed ECRH power of 150 kW is required to start up the plasma, assuming an initial neutral density of 3.0 × 10 18 m −3 , and that reducing the oxygen and carbon impurity densities facilitates successful start-up. We discuss the dependence of the absorbed ECRH power on the neutral density and impurities. The simulation qualitatively reproduces experimental results from JT-60U.

Simulative Analysis of Carry Out Fontusing near Field Photolithography

Adopting the concepts of integration and cumulative sum of exposure energy in the intersecting region between two fabricated line segments, an analytical method of exposure energy density equation for near field photolithography of font fabrication is established. At the same time, cutting photoresist into limited nodes, together with the use of the integral equation of exposure energy density and Mack’s developing model, the full-width at half maximum (FWHM) and fabrication profile of font can be calculated. As analyzed in the study, in the intersecting region between two fabricated line segments, the greater the exposure energy, the deeper the fabrication depth; while in the straight-line region of fabricated lines, as the exposure energy is equal, all the fabrication depths are the same. The research analysis of the paper can be a reference for near field photolithography of font.

Combining the Taguchi method with artificial neural network to construct a prediction model of a CO2 laser cutting experiment

When using the Taguchi method, an L18 or L27 orthogonal array is usually adopted. However, this requires many experiments (18 or 27 runs, respectively), consuming time, and resources. This study proposes a progressive Taguchi neural network model, which combines the Taguchi method with the artificial neural network to construct a prediction model for a CO2 laser cutting experiment. During CO2 laser cutting, energy from the moving laser is accumulative. The paper develops an integral equation of energy density during laser beam movement and lets it determine the sliding level of control factor. Meanwhile, the paper proposes that in Stage 1, only less number of experiments is required to be conducted by L9 orthogonal array. After the crucial supplementary experimental training samples proposed in Stage 2 are also included, high-accuracy prediction of artificial neural network can be completed. Based on analysis from the progressive Taguchi neural network, the Stage 1 preliminary network—with only a few available experimental examples—has achieved good predictive ability from regions near the Taguchi control points. For regions further out, the predictions have been increasingly unreliable. Nevertheless, the high precision of Stage 2 Taguchi network has good predictive results for all regions.

Development of a parallel implicit solver of fluid modeling equations for gas discharges

A parallel fully implicit PETSc-based fluid modeling equations solver for simulating gas discharges is developed. Fluid modeling equations include: the neutral species continuity equation, the charged species continuity equation with drift-diffusion approximation for mass fluxes, the electron energy density equation, and Poisson's equation for electrostatic potential. Except for Poisson's equation, all model equations are discretized by the fully implicit backward Euler method as a time integrator, and finite differences with the Scharfetter–Gummel scheme for mass fluxes on the spatial domain. At each time step, the resulting large sparse algebraic nonlinear system is solved by the Newton–Krylov–Schwarz algorithm. A 2D-GEC RF discharge is used as a benchmark to validate our solver by comparing the numerical results with both the published experimental data and the theoretical prediction. The parallel performance of the solver is investigated.

TIME VARIABLE COSMOLOGICAL CONSTANT FROM RENORMALIZATION GROUP EQUATIONS

In this paper, a time variable cosmological constant (CC) from renormalization group equations (RGEs) is explored, where the renormalization scales μ2 = Ḣ + 2H2 and μ2 = - Ḣ are taken respectively. The cosmological parameters, such as dimensionless energy density, deceleration parameter and effective equation of state of CC etc., are derived. Also, the cosmic observational constraints are implemented to test the model's consistency. The results show that it is compatible with cosmic data. So, it would be a viable dark energy model.

2D modeling of a Cepheid, moving grid approach

Die Serie Communications in Asteroseismology (CoAst) stellt eine international gefragte Plattform für wissenschaftliche Publikationen der neuesten Forschungsergebnisse auf dem Gebiet der Asteroseismologie dar. Forschungsgegenstand der Asteroseismologie sind veränderliche und pulsierende Sterne. Neben den halbjährlich erscheinenden regulären Ausgaben mit Beiträgen aus der laufenden Forschung werden auch Sonderausgaben für Konferenzberichte bzw. Programmhandbücher herausgegeben. JENAM (Joint European and National Astronomy Meeting) ist die größte jährliche Zusammenkunft der europäischen Berufsastronomen, die diesmal im September 2008 in Wien stattfand. Die Konferenz beherbergte neun Minisymposien, wobei eines der Asteroseismologie gewidmet war. Die neuesten Entwicklungen auf diesem Gebiet sind im vorliegenden Band im Rahmen von Übersichts- und Detailartikeln zusammengefasst.

Modified Chapman-Enskog moment approach to diffusive phonon heat transport

A detailed treatment of the Chapman-Enskog method for a phonon gas is given within the framework of an infinite system of moment equations obtained from Callaway's model of the Boltzmann-Peierls equation. Introducing no limitations on the magnitudes of the individual components of the drift velocity or the heat flux, this method is used to derive various systems of hydrodynamic equations for the energy density and the drift velocity. For one-dimensional flow problems, assuming that normal processes dominate over resistive ones, it is found that the first three levels of the expansion (i.e., the zeroth-, first-, and second-order approximations) yield the equations of hydrodynamics which are linearly stable at all wavelengths. This result can be achieved either by examining the dispersion relations for linear plane waves or by constructing the explicit quadratic Lyapunov entropy functionals for the linear perturbation equations. The next order in the Chapman-Enskog expansion leads to equations which are unstable to some perturbations. Precisely speaking, the linearized equations of motion that describe the propagation of small disturbances in the flow have unstable plane-wave solutions in the short-wavelength limit of the dispersion relations. This poses no problem if the equations are used in their proper range of validity.

INTERACTING CONSTITUENTS IN COSMOLOGY

Universe evolution, as described by Friedmann's equations, is determined by source terms fixed by the choice of pressure × energy density equations of state p(ρ). The usual approach in cosmology considers equations of state accounting only for kinematic terms, ignoring the contribution from the interactions between the particles constituting the source fluid. In this work the importance of these neglected terms is emphasized. A systematic method, based on the statistical mechanics of real fluids, is proposed to include them. A toy model is presented which shows how such interaction terms could be applied to engender significant cosmological effects.

Towards 640 Gbit/s wavelength conversion based on nonlinear polarization rotation in a semiconductor optical amplifier

Taking into account ultra-fast carrier dynamics, this paper models 640 Gbit/s wavelength conversion scheme based on nonlinear polarization rotation (NPR) in a single semiconductor optical amplifier (SOA) and investigates the performance of this kind of wavelength conversion scheme in detail. In this model, two carrier temperature equations are introduced to substitute two energy density equations, which reduce the complexity of calculation in comparison with the previous model. The temporary gain and phase shift dynamics induced by ultra-short optical pulses are numerically simulated and the simulated results are qualitatively in good agreement with reported experimental results. Simulated results show that non-inverted and inverted 640 Gbit/s wavelength conversions based on NPR are achieved with clear open eye diagrams. To further investigate the performance of the non-inverted wavelength conversion scheme, the dependence of output extinction ratio (ER) on some key parameters used in simulation is illustrated. Furthermore, simulated analyses show that high performance non-inverted wavelength conversion based on NPR can be achieved by using a red-shifted filtering scheme.

SPIN-DEPENDENCE OF THERMODYNAMIC QUANTITIES AROUND A HOROWITZ–STROMINGER BLACK HOLE

Making use of the brick wall method, we investigate the energy density, entropy density, pressure, and state equation for a perfect relativistic gas with spin s = 1/2, 1, 3/2, 2 around a Horowitz–Strominger black hole (HSBH). We show that there exists an additional spin-dependent term in the expression of these thermodynamic quantities except the leading term which is the same as that in flat spacetime.

Thermodynamic quantities for gases in static spherically symmetric backgrounds possessing a horizon

The brick-wall method is used to study the thermodynamic quantities for perfect relativistic gases in generic spherically symmetric and static background spacetimes possessing a horizon. The Wentzel-Kramers-Brillouin (WKB) approximation is employed for the Teukolsky-type master equation. It is shown that the entropy density, energy density, pressure, and state equation all contain a subleading term, which depends on the spins of the particles of the gases. When particularizing to the Schwarzschild and Reissner-Nordstrom geometries, the results previously found in the literature for those geometries are recovered.