Constant Energy Flux Research Articles

C131 固液界面における熱伝導の分子熱工学的研究(OS-11 ナノスケール伝熱III)

Molecular dynamics simulation has been performed to clarify the mechanism and characteristics of the energy transfer at the solid-liquid interfaces. The system consists of a pair of parallel solid walls and a liquid film in between. The solid walls have different temperatures in order to generate a constant thermal energy flux, and three kinds of crystal planes that contact the liquid are employed. Investigating the intermolecular energy transfer at the solid-liquid interfaces, the characteristics of the energy transfer are found to be greatly influenced by the molecular surface configuration of the solid walls and the mechanism of the energy transfer is clarified.

Gamma Rays from Intergalactic Shocks

Structure formation in the intergalactic medium (IGM) produces large-scale, collisionless shock waves, where electrons can accelerate to highly relativistic energies. Such electrons can Compton scatter cosmic microwave background photons up to gamma-ray energies. We study the radiation emitted in this process using a hydrodynamic cosmological simulation of a LCDM universe. This radiation, extending beyond TeV energies, has roughly constant energy flux per decade in photon energy, in agreement with the predictions of Loeb & Waxman (2000). Assuming that a fraction xi_e=0.05 of the shock thermal energy is transferred to relativistic electrons, as inferred from collisionless non-relativistic shocks in the interstellar medium, we find that the radiation energy flux, e^2(dJ/de)~ 50-160 eV cm^-2 s^-1 sr^-1, constitutes ~10% of the extragalactic gamma-ray background. The associated point-sources are too faint to account for the ~60 unidentified EGRET gamma-ray sources, but GLAST should resolve several sources associated with large-scale IGM structures for xi_e~0.03, and many more sources for larger xi_e. The intergalactic origin of the radiation can be verified through a cross-correlation with, e.g., the galaxy distribution that traces the same structure. Its shock-origin may be tested by a cross-correlation with radio synchrotron radiation, emitted as the same electrons gyrate in post-shock magnetic fields. We predict that GLAST and Cherenkov telescopes such as MAGIC, VERITAS and HESS should resolve gamma-rays from nearby (redshifts z < 0.01) rich galaxy clusters, perhaps in the form of a \~5-10 Mpc diameter ring-like emission tracing the cluster accretion shock, with luminous peaks at its intersections with galaxy filaments detectable even at z~0.025.

On the Dynamics of the Jovian Ionosphere and Thermosphere: III. The Modelling of Auroral Conductivity

Recent work has been concerned with calculating the three-dimensional ion concentrations and Pedersen and Hall conductivities within the auroral region of Jupiter for varying conditions of incident electron precipitation. Using the jovian ionospheric model, we present results that show the auroral ionospheric response to changing the incoming flux of precipitating electrons (for constant initial energy) and also the response to changing the initial energy (for both constant flux and constant energy flux). The results show that, for expected energy fluxes of precipitating particles, the average auroral integrated Pedersen conductivity attains values in excess of 1 mho. In addition, it is shown that electrons with an initial energy of around 60 keV are particularly effective at generating auroral conductivity: Particles of this energy penetrate most effectively to the layer of the jovian ionosphere at which the auroral conductivity is at a maximum.

Catabolic enzyme levels in bacteria grown on binary and ternary substrate mixtures in continuous culture.

Bacteria grow on multicomponent substrates in most natural and engineered environments. To advance our ability to model bacterial growth on such substrates, axenic cultures were grown in chemostats at a low specific growth rate and a constant total energy flux on binary and ternary substrate mixtures and were assayed for key catabolic enzymes for each substrate. The substrates were benzoate, salicylate, and glucose, and the enzymes were catechol 1,2-dioxygenase, gentisate 1,2-dioxygenase, and glucose-6-phosphate dehydrogenase, respectively. The binary mixtures were salicylate with benzoate and salicylate with glucose. Measurements were also made of oxygen uptake rate by whole cells in response to each substrate. The effects of the substrate mixture on the oxygen uptake rate paralleled the effects on the measured enzymes. Catechol 1,2-dioxygenase exhibited a threshold response before synthesis occurred. Below the threshold flux of benzoate through the chemostat, either basal enzyme levels or nonspecific enzymes kept reactor concentrations too low for enzyme synthesis. Above the threshold, enzyme levels were linearly related to the fraction of the total energy flux through the chemostat due to benzoate. Gentisate 1,2-dioxygenase exhibited a linear response to the salicylate flux when mixed with benzoate, but a threshold response when mixed with glucose. Glucose-6-phosphate dehydrogenase activity increased in direct proportion to the glucose flux through the chemostat over the entire range studied. The results from two ternary mixtures were consistent with those from the binary mixtures.

Weak magnetohydrodynamic turbulence of a magnetized plasma

A weak turbulence of the magnetohydrodynamic waves in a strongly magnetized plasma was studied in the case when the plasma pressure is small as compared to the magnetic field pressure. In this case, the principal nonlinear mechanism is the resonance scattering of fast magnetoacoustic and Alfvén waves on slow magnetoacoustic waves. Since the former waves are high-frequency (HF) with respect to the latter, the total number of HF waves in the system is conserved (adiabatic invariant). In the weak turbulence regime, this integral of motion generates a Kolmogorov spectrum with a constant flux of the number of HF waves toward the longwave region. The shortwave region features a Kolmogorov spectrum with a constant energy flux. An exact angular dependence of the turbulence spectra is determined for the wave propagation angles close to the average magnetic field direction.

Measurement of interfacial temperatures during testing of a subscale aircraft brake

Interfacial temperatures have been measured using fibre opticinserts in the stationary brake ring during ring-on-ring, subscaledynamometer aircraft brake testing. The brake materials are carbonfibre-reinforced, carbon-matrix (carbon-carbon) composites. Thetemperature distribution varies with dynamometer test conditions anddemonstrates the non-uniformity of contact pressure within the interface.A two-dimensional, axis-symmetric finite element model (FEM) is presentedthat is used to estimate temperature profiles during braking using eithera constant pressure or constant energy flux assumption. The modelincorporates the measured temperature-dependence of the thermaldiffusivity and specific heat capacity for the composite materials. Thesurface temperatures obtained from the FEM are compared with the measuredsurface temperatures. Substantial differences between the two results areobserved and discussed.

Numerical modeling of the constant flux spectra for surface gravity waves in a case of angular anisotropy

The process of constant flux spectra formation is studied numerically, for the case of angular anisotropy. The method of investigation is based on a numerical solution of the nonlinear four-wave kinetic equation for gravity waves, added with the terms of a source and a sink for wave energy. Stationary solutions of such an equation are just the constant flux spectra under investigation. Two principally different situations were considered: the case of a constant energy flux to the high frequencies (the case of “flux up”) and the case of a constant wave action flux to the low frequencies (the case of “flux down”). It was found that, for the case of flux down, the stationary two-dimensional spectra are angularly isotropic, independently of the initial anisotropy of the system. But for the case of flux up, the stationary spectra have specific angular anisotropy. For both cases, corresponding one-dimensional spectra have shapes close to ones analytically derived in [Dokl. Akad. Nauk SSSR, 170 (1996) 1292–1295 (in Russian); Izv. Akad. S. USSR, Atmos. Ocean Phys. 18 (1982) 970–979], for the case of angular isotropy. Numerous features of the process considered are specified, and the mentioned peculiarities of the results are discussed.

Contrasts between equilibrium and non-equilibrium steady states: computer aided discoveries in simple lattice gases

A century ago, the foundations of equilibrium statistical mechanics were laid. For a system in equilibrium with a thermal bath, much is understood through the Boltzmann factor, e − H[ C]/kT , for the probability of finding the system in any microscopic configuration C . In contrast, apart from some special cases, little is known about the corresponding probabilities, if the same system is in contact with more than one reservoir of energy, so that, even in stationary states, there is a constant energy flux through our system. These non-equilibrium steady states display many surprising properties. In particular, even the simplest generalization of the Ising model offers a wealth of unexpected phenomena. Mostly discovered through Monte Carlo simulations, some of the novel properties are understood while many remain unexplained. A brief review and some recent results will be presented, highlighting the sharp contrasts between the equilibrium Ising system and this non-equilibrium counterpart.

Turbulent Solar Convection and Its Coupling with Rotation: The Effect of Prandtl Number and Thermal Boundary Conditions on the Resulting Differential Rotation

The dynamics of the vigorous convection in the outer envelope of the Sun must determine the transport of energy, angular momentum, and magnetic fields and must therefore be responsible for the observed surface activity and the angular velocity profile inferred helioseismically from SOI-MDI p-mode frequency splittings. Many different theoretical treatments have been applied to the problem, ranging from simple physical models such as mixing-length theory to sophisticated numerical simulations. Although mixing-length models provide a good first approximation to the structure of the convection zone, recent progress has mainly come from numerical simulations. Computational constraints have until now limited simulations in full spheres to essentially laminar convection. The angular velocity profiles have shown constancy on cylinders, in striking contrast to the approximately constant angular velocity on radial lines inferred for the Sun. In an effort to further our understanding of the dynamics of the solar convection zone, we have developed a new computer code that, by exploiting massively parallel architectures, enables us to study fully turbulent spherical shell convection. Here we present five fully evolved solutions. Motivated by the fact that a constant entropy upper boundary condition produces a latitudinal modulation of the emergent energy flux (of about 10%, i.e., far larger than is observed for the Sun), three of these solutions have a constant energy flux upper boundary condition. This leads to a latitudinal modulation of the specific entropy that breaks the constancy of the angular velocity on cylinders, making it more nearly constant on radial lines at midlatitudes. The effect of lowering the Prandtl number is also considered—highly time-dependent, vortical convective motions are revealed, and the Reynolds stresses are altered, leading to a reduced differential rotation. The differential rotation in all of our simulations shows a balance between driving by Reynolds stresses and damping by viscosity. This contrasts with the situation in the Sun, where the effect of viscosity on the mean differential rotation is almost negligible.

Ignition analysis of a porous energetic material: II. Ignition at a closed heated end

A continuation of an ignition analysis for porous energetic materials subjected to a constant energy flux is presented. In the first part (I), the analysis was developed for the case of an open-end, semi-infinite material such that gas flow, generated by thermal expansion, was directed out of the porous solid, thereby removing energy from the system. In the present study, the case of a closed end is considered, and thus the thermally induced gas flow is now directed into the solid. In these studies, an asymptotic perturbation analysis, based on the smallness of the gas-to-solid density ratio and the largeness of the activation energy, is utilized to describe the inert and transition stages leading to thermal runaway. In both cases it is found that the effects of porosity provide a leading-order reduction in the time to ignition relative to that for the non-porous problem, arising from the reduced amount of solid material that must be heated and the difference in thermal conductivities of the solid and gaseous phases. A correction to the leading-order ignition-delay time, however, is provided by the convective flow of gas through the solid, and the sign of this correction is shown to depend on the direction of the gas flow. Thus, gas flowing out of an open-end solid was shown previously to give a positive correction to the leading-order time to ignition. Here, however, it is demonstrated that when the flow of gas is directed into the porous solid, the relative transport effects associated with the gas flow serve to preheat the material, resulting in a negative correction and hence a decrease in the ignition-delay time.

Lagrangian tetrad dynamics and the phenomenology of turbulence

A new phenomenological model of turbulent fluctuations is constructed by considering the Lagrangian dynamics of four points (the tetrad). The closure of the equations of motion is achieved by postulating an anisotropic, i.e., tetrad shape dependent, relation of the local pressure and the velocity gradient defined on the tetrad. The nonlocal contribution to the pressure and the incoherent small scale fluctuations are modeled as Gaussian white “noise.” The resulting stochastic model for the coarse-grained velocity gradient is analyzed approximately, yielding predictions for the probability distribution functions of different second- and third-order invariants. The results are compared with the direct numerical simulation of the Navier–Stokes. The model provides a reasonable representation of the nonlinear dynamics involved in energy transfer and vortex stretching and allows the study of interesting aspects of the statistical geometry of turbulence, e.g., vorticity/strain alignment. In a state with a constant energy flux (and K41 power spectrum), it exhibits the anomalous scaling of high moments associated with formation of high gradient sheets—events associated with large energy transfer. An approach to the more complete analysis of the stochastic model, properly including the effect of fluctuations, is outlined and will enable further quantitative juxtaposition of the model with the results of the direct numerical simulations.

Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence?

The statistical features of turbulence can be studied either through spectral quantities, such as the kinetic energy spectrum, or through structure functions, which are statistical moments of the difference between velocities at two points separated by a variable distance. In this paper structure function relations for two-dimensional turbulence are derived and compared with calculations based on wind data from 5754 airplane flights, reported in the MOZAIC data set. For the third-order structure function two relations are derived, showing that this function is generally positive in the two-dimensional case, contrary to the three-dimensional case. In the energy inertial range the third-order structure function grows linearly with separation distance and in the enstrophy inertial range it grows cubically with separation distance. A Fourier analysis shows that the linear growth is a reflection of a constant negative spectral energy flux, and the cubic growth is a reflection of a constant positive spectral enstrophy flux. Various relations between second-order structure functions and spectral quantities are also derived. The measured second-order structure functions can be divided into two different types of terms, one of the form r2/3, giving a k−5/3-range and another, including a logarithmic dependence, giving a k−3-range in the energy spectrum. The structure functions agree better with the two-dimensional isotropic relation for larger separations than for smaller separations. The flatness factor is found to grow very fast for separations of the order of some kilometres. The third-order structure function is accurately measured in the interval [30, 300] km and is found to be positive. The average enstrophy flux is measured as Πω≈1.8×10−13 s−3 and the constant in the k−3-law is measured as [Kscr ]≈0.19. It is argued that the k−3-range can be explained by two-dimensional turbulence and can be interpreted as an enstrophy inertial range, while the k−5/3-range can probably not be explained by two-dimensional turbulence and should not be interpreted as a two-dimensional energy inertial range.

Analysis of ignition of a porous energetic material

A theory of ignition is presented to analyse the effect of porosity on the time to ignition of a semi-infinite porous energetic solid subjected to a constant energy flux. An asymptotic perturbation analysis, based on the smallness of the gas-to-solid density ratio and the largeness of the activation energy, is utilized to describe the inert and transition stages leading to thermal runaway. As in the classical study of a nonporous solid, the transition stage consists of three spatial regions in the limit of large activation energy: a thin reactive–diffusive layer adjacent to the exposed surface of the material where chemical effects are first felt, a somewhat thicker transient–diffusive zone and, finally, an inert region where the temperature field is still governed solely by conductive heat transfer. Solutions in each region are constructed at each order with respect to the density-ratio parameter and matched to one another using asymptotic matching principles. It is found that the effects of porosity provide a leading-order reduction in the time to ignition relative to that for the nonporous problem, arising from the reduced amount of solid material that must be heated and the difference in thermal conductivities of the solid and gaseous phases. A positive correction to the leading-order ignition-delay time, however, is provided by the convective flow of gas out of the solid, which stems from the effects of thermal expansion and removes energy from the system. The latter phenomenon is absent from the corresponding calculation for the nonporous problem and produces a number of modifications at the next order in the analysis arising from the relative transport effects associated with the gas flow.

Systematic modeling of soft‐electron precipitation effects on high‐latitude F region and topside ionospheric upflows

An ionospheric plasma fluid transport model is used to investigate the effects of soft (&lt;1 keV) electron precipitation on high‐latitude F region/topside ionospheric O+ upflows. In this paper we present a systematic modeling study of ionospheric effects of varying soft‐electron precipitation, focusing on the resulting upward O+ ion velocities and fluxes, as well as the elevated ion and electron temperatures, due to the precipitation. Recent satellite observations [Seo et al., 1997] suggest an inverse relationship between upward O+ fluxes and the characteristic energy of the precipitating electrons for the same energy flux level. The modeling results presented here show this inverse relationship explicitly. Our interpretation is that a declining characteristic energy at constant energy flux increases the number of precipitating electrons available to heat the thermal electrons, and thus enhances the thermal electron temperature and hence the ambipolar electric field for propelling the upward O+ flows. The modeled increase of the thermal electron temperature with enhanced auroral electron precipitation is also generally consistent with the Seo et al. [1997] topside ionospheric plasma measurements. In addition, the modeling results presented here illustrate characteristic temporal development responses, showing dramatic increases in velocity, Mach number, and flux values during the first 10–13 min after the precipitation is turned on. By ∼1 hour after the initiation of a soft‐electron precipitation event the ion upward velocities and fluxes approach nearly stable, asymptotic values.

Dynamic Thermal Stresses in a Functionally Graded Material Subjected to Electromagnetic Radiation.

A numerical study is made of the dynamic thermal stresses in a ceramic metal Functionally Graded Material (FGM) subjected to impulsive electromagnetic radiation. The radiation absorption is assumed to maintain a constant energy flux throughout the pulse duration, and to diminish exponentially with depth. Since the wave travel time is small compared with the time necessary to reach thermal equilibrium. the thermal diffusion term is ignored in the transient heat conduction equation. In treating problems, the material properties of FGM are assumed to be temperaturedependent. In this paper, a set of unified equations is presented, which is applicable to the propagation of plane, cylindrical and spherical waves in clastic media. The characteristic equations are then derived and the numerical procedures involving stepwise integration along the characteristics are established. Numerical calculations are carried out for various FGM plates, and the significance of the temperature-dependent material properties and the effects of composition distribution of the FGM on the magnitude of the dynamic thermal stresses are discussed.

Analysis of the Temporal Occurrence of Seismicity at Deception Island (Antarctica). A Nonlinear Approach

—Deception Island is characterized by small magnitude local events with constant energy flux and very low stress drop. To obtain information about its origin, an interevent time series of 546 events, corresponding to an observational period of two month, has been analyzed. From a statistical point of view, data satisfies a Weibull distribution and presents clustering. A rescaled range analysis reveals that data are not independent, i.e. have memory, and the correlation dimension saturates at 2.2; as a consequence, the system can be modeled as a nonlinear iterative equation with three degrees of freedom that presents chaotic behavior. Taking into account that the average interevent time is of the order of 130 minutes, too short to be only due to tectonic activity, the above results indicate that some other mechanism may coexist with the regional tectonic one. According to several geological and geophysical observations, we suggest that most of the local events may be originated by pressure waves generated by a sudden change of phase, of sea and fresh water infiltrated into the main fractures and faults and also from shallow and confined water-saturated layers.

Plasma wall interaction for TiN x film deposition in a hollow cathode arc discharge

The present work discusses the relation between plasma parameters and the film microstructure. Both, plasma diagnostic and film characterization were carried out. The plasma in front of the substrate was analysed by Langmuir probe measurements and energy resolved mass spectrometry. Film properties were determined by X-ray photoelectron spectroscopy (XPS), X-ray diffraction (XRD) and X-ray reflectometry. TiN was used as film material. Thin TiN x films were deposited on Si (100) wafers using a hollow cathode arc evaporation device (HCAED). Films were grown at different nitrogen gas flows, substrate voltages and discharge powers. We observe a correlation between thin TiN x film properties and the characterics of the plasma. Increasing the N 2 gas flow as well as increasing negative substrate voltage at medium N 2 gas flow results in an increasing energy flux to the surface due to ion bombardment. An increase of the nitrogen content x can be observed with the increase of ion bombardment. Higher ion bombardment leads to a small broadening of the X-ray profile. The higher ion bombardment also induces a diminishing of film texture. With increasing nitrogen gas flow the strongly preferred (002) α-Ti and (111) δ-TiN x orientations change to polycrystalline TiN. Different discharge powers result in a nearly constant ion energy flux to the substrate and lead to the same film properties. These results demonstrate the dominant influence of ions on the properties of the deposited TiN x film.

Bottleneck effects in turbulence: Scaling phenomena in r versus p space.

We (analytically) calculate the energy spectrum corresponding to various experimental and numerical turbulence data analyzed by Benzi et al. We find two bottleneck phenomena: While the local scaling exponent ${\ensuremath{\zeta}}_{r}(r)$ of the structure function decreases monotonically, the local scaling exponent ${\ensuremath{\zeta}}_{p}(p)$ of the corresponding spectrum has a minimum of ${\ensuremath{\zeta}}_{p}({p}_{\mathrm{min}})\ensuremath{\approx}0.45$ at ${p}_{\mathrm{min}}\ensuremath{\approx}(10\ensuremath{\eta}{)}^{\ensuremath{-}1}$ and a maximum of ${\ensuremath{\zeta}}_{p}({p}_{\mathrm{max}})\ensuremath{\approx}0.77$ at ${p}_{\mathrm{max}}\ensuremath{\approx}{8L}^{\ensuremath{-}1}$. A physical argument starting from the constant energy flux in $p$ space reveals the general mechanism underlying the energy pileups at both ends of the $p$-space scaling range. In the case studied here, they are induced by viscous dissipation and the reduced spectral strength on the scale of the system size, respectively.

BOUNDARY DYNAMICS IN DILATON GRAVITY

We study the dynamics of the boundary in two-dimensional dilaton gravity coupled to N massless scalars. We rederive the boundary conditions of Refs. 1 and 3 in a way which makes the requirement of reparametrization invariance and the role of conformal anomaly explicit. We then study the semiclassical behavior of the boundary in the N = 24 theory in the presence of an incoming matter wave with a constant energy flux spread over a finite interval. There is a critical value of the matter energy density below which the boundary is stable and all the matter is reflected back. For energy densities greater than this critical value there is a similar behavior for small values of the total energy thrown in. However, when the total energy exceeds another critical value the boundary exhibits a runaway behavior and the space-time develops singularities and horizons.

Superscattering matrix for two-dimensional black holes

A consistent Euclidean semi classical calculation is given for the superscattering operator $\$ $ in the RST model for states with a constant flux of energy. The $\$ $ operator is CPT invariant. There is no loss of quantum coherence when the energy flux is less than a critical rate and complete loss when the energy flux is critical.