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196
Analogue gravity from Bose–Einstein condensates
- CLASS. QUANTUM GRAV. 18 (2001) 1137–1156
, 2001
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Mathematical Modelling of Microelectronics Semiconductor Devices
"... This paper first reviews some basic facts about electron transport in semiconductor materials. Then, it develops several macroscopic models from the diffusion approximation of the semiconductor Boltzmann equation. The first model to be derived is the 'Spherical Harmonics Expansion model', ..."
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This paper first reviews some basic facts about electron transport in semiconductor materials. Then, it develops several macroscopic models from the diffusion approximation of the semiconductor Boltzmann equation. The first model to be derived is the 'Spherical Harmonics Expansion model', which consists of a parabolic equation for the energy distribution function. A second model is then deduced, known as the 'Energy-Transport' model, of which the standard 'DriftDiffusion ' model is a submodel. It consists of a parabolic system for the electron density and energy. Various properties of these models are investigated.
On the Equilibrium Thickness of Intergranular Glass Phases in Ceramic Materials
"... The fundamental question as to whether thin intergranular films can adopt an equilibrium thickness in polycrystalline ceramics is addressed. Two continuum approaches are presented, one based on interfacial energies and the other on the force balance normal to the boundary. These indicate that there ..."
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Cited by 15 (0 self)
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The fundamental question as to whether thin intergranular films can adopt an equilibrium thickness in polycrystalline ceramics is addressed. Two continuum approaches are presented, one based on interfacial energies and the other on the force balance normal to the boundary. These indicate that there will exist a stable thickness for the intergranular film and that it will be of the order of 1 nm. The origin of an equilibrium thickness is shown to be the result of two competing interactions, an attractive van der Waals-disperson interaction between the grains on either side of the boundary acting to thin the film and a repulsive term, due to the structure of the intergranular liquid, opposing this attraction. As both of these interactions are of short range (<lo nm), it is a natural consequence that the equilibrium thickness is of the order of 1 nm, a value commensurate with that observed experimentally in a wide range of ceramics. Two further consequences of importance are indicated. The first is that thin intergranular liquid phases can support a normal stress. The second is that the dielectric constants of the adjacent grains play an important role in determining the thicknesses of the intergranular phase. This leads to the conclusion, consistent with observations, that the thickness of the intergranular phase in polyphase ceramics is expected to be different at boundaries between dissimilar phases than that between like phases. I.
Optical Absorption Spectra of Nanocrystal Gold Molecules
- J. Phys. Chem. B 1997
"... The optical absorption spectra of a series of nanocrystal gold moleculesslarger, crystalline Au clusters that are passivated by a compact monolayer of n-alkylthiol(ate)sshave been measured across the electronic range (1.1-4.0 eV) in dilute solution at ordinary temperature. Each of the 20 samples, ra ..."
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Cited by 14 (0 self)
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The optical absorption spectra of a series of nanocrystal gold moleculesslarger, crystalline Au clusters that are passivated by a compact monolayer of n-alkylthiol(ate)sshave been measured across the electronic range (1.1-4.0 eV) in dilute solution at ordinary temperature. Each of the 20 samples, ranging in effective core diameter from 1.4 to 3.2 nm (70 to 800 Au atoms), has been purified by fractional crystallization and has undergone a separate compositional and structural characterization by mass spectrometry and X-ray diffraction. With decreasing core mass (crystallite size) the spectra uniformly show a systematic evolution, specifically (i) a broadening of the so-called surface-plasmon band until it is essentially unidentifiable for crystallites of less than 2.0 nm effective diameter, (ii) the emergence of a distinct onset for strong absorption near the energy (1.7 eV) of the interbandgap (5d f 6sp), and (iii) the appearance in the smallest crystallites of a weak steplike structure above this onset, which is interpreted as arising from a series of transitions from the continuum d-band to the discrete level structure of the conduction band just above the Fermi level. The classical electrodynamic (Mie) theory, based on bulk optical properties, can reproduce this spectral evolutionsand thereby yield a consistent core-sizingsonly by making a strong assumption about the surface chemical interaction. Quantitative agreement with the spectral line shape requires a size-dependent offset of the frequency-dependent dielectric function, which may be explained by a transition in electronic structure just below 2.0 nm (200 atoms), as proposed earlier. I.
Diffusion in Random Media
- Papanicolaou (Eds.), Surveys in Applied Mathematics
, 1995
"... We present a survey of homogenization methods for diffusion equations with periodic and random diffusivity. Contents 1 Introduction 2 2 One-Dimensional Conductors 3 2.1 Effective conductivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2.2 Homogenization : : : : : : : : : : : : : ..."
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We present a survey of homogenization methods for diffusion equations with periodic and random diffusivity. Contents 1 Introduction 2 2 One-Dimensional Conductors 3 2.1 Effective conductivity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 2.2 Homogenization : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.3 General homogenization : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 2.4 Anomalous diffusion : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 8 3 Multidimensional Diffusion 9 3.1 Periodic homogenization : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 3.1.1 The multiple scale expansion : : : : : : : : : : : : : : : : : : : : : : 9 3.1.2 Initial layer : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13 3.1.3 Interpretation of homogenization and the cell problem : : : : : : : : 15 3.1.4 Boundary conditions, boundary layers and the projection method : : 15 3.2 Random cell problem : : : : : : : ...
Asymptotic Analysis Of Quasistatic Transport In High Contrast Conductive Media
"... . We show that transport in high contrast, conductive media has a discrete behavior. In the asymptotic limit of infinitely high contrast, the effective impedance and the magnetic field in such media are given by discrete min-max variational principles. Furthermore, we show that the transport problem ..."
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Cited by 11 (6 self)
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. We show that transport in high contrast, conductive media has a discrete behavior. In the asymptotic limit of infinitely high contrast, the effective impedance and the magnetic field in such media are given by discrete min-max variational principles. Furthermore, we show that the transport problem has an asymptotic, resistor-inductor-capacitor network approximation. We use new variational formulations of the effective impedance of the media and we assess the accuracy of the asymptotic approximation by numerical computations. Key words. high contrast, conductive media, network approximation, effective impedance AMS subject classifications. 35J25, 35Q60, 86A25, 78A25 1. Introduction. High contrast electromagnetic transport problems arise frequently in geophysical applications. The subsurface electrical conductivity typically has large variations in magnitude (high contrast) because the rock matrix can be insulating in comparison to liquid-filled pores. The conductivity of pore fluids...
Thermodynamics and Lattice Vibrations of Minerals: 1. Mineral Heat Capacities and Their Relationships to Simple Lattice Vibrational Models
- VOL. 17, NO. I REVIEWS OF GEOPHYSICS AND SPACE PHYSICS FEBRUARY 1979
, 1979
"... This is the first of a series of five papers in which the thermodynamic properties of minerals are interpreted in terms of lattice vibrational spectra. In this paper, measured heat capacities for minerals are examined in terms of the Debye theory of lattice vibrations, and it is demonstrated that he ..."
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This is the first of a series of five papers in which the thermodynamic properties of minerals are interpreted in terms of lattice vibrational spectra. In this paper, measured heat capacities for minerals are examined in terms of the Debye theory of lattice vibrations, and it is demonstrated that heat capacities of silicates show large deviations from the behavior expected from Debye theory. The underlying assumptions of Debye theory are critically reviewed, and it is shown that the observed thermodynamic deviations in minerals probably arise from four effects not included in the Debye model: anisotropy of elastic parameters, dispersion of acoustic waves toward Brillouin zone boundaries, optic vibrations in excess of the Debye spectrum at low frequencies, and optic vibrations at frequencies much greater than the Debye cutoff frequency predicted by acoustic measurements. Each of the four effects influences the heat capacity in a particular temperature range: anisotropy, dispersion and low-frequency optic vibrations are important at low temperatures (0øK to • 100øK); high-frequency vibrations are important at higher temperatures. It is necessary to include all four effects in a generalized lattice vibrational model for minerals; such a model is developed in papers 2-5 of this series. The minerals included in this study are halite, periclase, brucite,
A Text-book of Physics
- Properties of Matter
, 1913
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This copy is for your personal, non-commercial use only. clicking here.colleagues, clients, or customers by, you can order high-quality copies for yourIf you wish to distribute this article to others here.following the guidelines can be obtained byPermission to republish or repurpose articles or portions of articles): July 8, 2013 www.sciencemag.org (this information is current as of The following resources related to this article are available online at
