Showing papers on "Debye published in 2008"
TL;DR: An ultracold dense gas of potassium-rubidium (40K87Rb) polar molecules is created using a single step of STIRAP with two-frequency laser irradiation to coherently transfer extremely weakly bound KRb molecules to the rovibrational ground state of either the triplet or the singlet electronic ground molecular potential.
Abstract: A quantum gas of ultracold polar molecules, with long-range and anisotropic interactions, not only would enable explorations of a large class of many-body physics phenomena but also could be used for quantum information processing We report on the creation of an ultracold dense gas of potassium-rubidium (40K87Rb) polar molecules Using a single step of STIRAP (stimulated Raman adiabatic passage) with two-frequency laser irradiation, we coherently transfer extremely weakly bound KRb molecules to the rovibrational ground state of either the triplet or the singlet electronic ground molecular potential The polar molecular gas has a peak density of 1012 per cubic centimeter and an expansion-determined translational temperature of 350 nanokelvin The polar molecules have a permanent electric dipole moment, which we measure with Stark spectroscopy to be 0052(2) Debye (1 Debye = 3336 × 10–30 coulomb-meters) for the triplet rovibrational ground state and 0566(17) Debye for the singlet rovibrational ground state
1,466 citations
TL;DR: In this article, the authors studied the real-time evolution of a static quark-antiquark pair in a medium of gluons and light quarks at finite temperature, and derived the potential between the two static sources, and calculated their energy and thermal decay width.
Abstract: In a framework that makes close contact with modern effective field theories for nonrelativistic bound states at zero temperature, we study the real-time evolution of a static quark-antiquark pair in a medium of gluons and light quarks at finite temperature. For temperatures ranging from values larger to smaller than the inverse distance of the quark and antiquark, $1/r$, and at short distances, we derive the potential between the two static sources, and calculate their energy and thermal decay width. Two mechanisms contribute to the thermal decay width: the imaginary part of the gluon self-energy induced by the Landau damping phenomenon, and the quark-antiquark color-singlet to color-octet thermal breakup. Parametrically, the first mechanism dominates for temperatures such that the Debye mass is larger than the binding energy, while the latter, which we quantify here for the first time, dominates for temperatures such that the Debye mass is smaller than the binding energy. If the Debye mass is of the same order as $1/r$, our results are in agreement with a recent calculation of the static Wilson loop at finite temperature. For temperatures smaller than $1/r$, we find new contributions to the potential, both real and imaginary, which may be relevant to understand the onset of heavy quarkonium dissociation in a thermal medium.
406 citations
TL;DR: By using evanescent waves, the spectacular amplification of the zeta potential resulting from hydrodynamic slippage allows us to clarify for the first time the dynamic origin of theZeta potential.
Abstract: By using evanescent waves, we study equilibrium and dynamical properties of liquid-solid interfaces in the Debye layer for hydrophilic and hydrophobic surfaces. We measure velocity profiles and nanotracer concentration and diffusion profiles between 20 and 300 nm from the walls in pressure-driven and electro-osmotic flows. We extract electrostatic and zeta potentials and determine hydrodynamic slip lengths with 10 nm accuracy. The spectacular amplification of the zeta potential resulting from hydrodynamic slippage allows us to clarify for the first time the dynamic origin of the zeta potential.
218 citations
TL;DR: The spectra are dominated by a low-frequency process at approximately 1 GHz with a broad relaxation time distribution of the Cole-Davidson or Cole-Cole type, which is thought to correspond to the rotational diffusion of the dipolar cations.
Abstract: Precise dielectric spectra have been determined at 25 °C over the exceptionally broad frequency range of 0.1 ≤ ν/GHz ≤ 3000 for the imidazolium-based room-temperature ionic liquids (RTILs) [bmim][BF4], [bmim][PF6], [bmim][DCA], and [hmim][BF4]. The spectra are dominated by a low-frequency process at ∼1 GHz with a broad relaxation time distribution of the Cole−Davidson or Cole−Cole type, which is thought to correspond to the rotational diffusion of the dipolar cations. In addition, these RTILs possess two Debye relaxations at ∼5 GHz and ∼0.6 THz and a damped harmonic oscillation at ∼2.5 THz. The two higher-frequency modes are almost certainly due to cation librations, but the origin of the ∼5 GHz mode remains obscure.
157 citations
TL;DR: In this paper, the hard-loop resummed propagator in an anisotropic QCD plasma in general covariant gauges was determined and a potential between heavy quarks from the Fourier transform of its static limit was defined.
131 citations
TL;DR: The experimental discovery of "electrorheological (ER) complex plasmas," where the control of the interparticle interaction by an externally applied electric field is due to distortion of the Debye spheres that surround microparticles in a plasma.
Abstract: We report the experimental discovery of "electrorheological (ER) complex plasmas," where the control of the interparticle interaction by an externally applied electric field is due to distortion of the Debye spheres that surround microparticles (dust) in a plasma. We show that interactions in ER plasmas under weak ac fields are mathematically equivalent to those in conventional ER fluids. Microgravity experiments, as well as molecular dynamics simulations, show a phase transition from an isotropic to an anisotropic (string) plasma state as the electric field is increased.
100 citations
TL;DR: The study emphasizes that the dielectric signature of the glass transition in monohydroxy alcohols is a dispersive loss peak that is faster and significantly smaller than the prominent Debye feature.
Abstract: An extensive comparison of calorimetric and dielectric measurements is carried out for generic molecular liquids and monohydroxy alcohols with focus on the identification of the dielectric modes which are associated with the glass transition. For generic liquids, the calorimetric glass transition temperatures (Tg-cal) are always greater than their kinetic counterparts (Tg-kin), but the difference remains below 3K. Also, the nonexponentiality parameters of the Tool-Narayanaswamy-Moynihan-Hodge model applied to the calorimetric data and the stretching exponents of the dielectric measurements show remarkable agreement. The same behavior is found for glass-forming monohydroxy alcohols, provided that the faster and smaller non-Debye relaxation rather than the large dielectric Debye process is assigned to the structural relaxation. The study emphasizes that the dielectric signature of the glass transition in monohydroxy alcohols is a dispersive loss peak that is faster and significantly smaller than the promine...
81 citations
TL;DR: In this article, the spectral properties of hydrogen-like ions in the plasma, including the transition frequencies, absorption oscillator strengths, radiative transition probabilities, as well as the line intensities of the Lyman and Balmer series, were investigated for a wide range of plasma screening parameters.
Abstract: Plasma screening effects on the properties of bound-bound transitions of hydrogenlike ions imbedded in Debye plasmas are investigated The electron eigenenergies and wave functions are determined by numerically solving the scaled Schr\"odinger equation with a Debye potential by the fourth-order symplectic integration scheme The scaled spectral properties of hydrogenlike ions in the plasma, including the transition frequencies, absorption oscillator strengths, radiative transition probabilities, as well as the line intensities of the Lyman and Balmer series, are presented for a wide range of plasma screening parameters While for the $\ensuremath{\Delta}n\ensuremath{
e}0$ transitions the oscillator strengths and spectral line intensities decrease with increasing the plasma screening, those for the $\ensuremath{\Delta}n=0$ transitions rapidly increase The lines associated with the $\ensuremath{\Delta}n\ensuremath{
e}0$ transitions are redshifted, whereas those for $\ensuremath{\Delta}n=0$ transitions are blueshifted Comparison of present results with those of other authors, when available, is made The results reported here should be useful in the interpretation of spectral properties of hydrogenlike ions in laboratory and astrophysical Debye plasmas
65 citations
TL;DR: Electrostatic analysis of phosphatidylcholine lipid membranes with the atomic force microscope reveals a repulsive force between the negatively charged probe tips and the zwitterionic lipids that has been analyzed quantitatively to reveal that the repulsion is due to a weak external field created by the internal membrane dipole potential.
64 citations
TL;DR: In this paper, the authors studied the effect of the Debye sheath on the turbulence character of the scrape-off layer of a tokamak sheared magnetic field and found that the turbulence changes from an ion temperature gradient to a generic interchange type, crossing the last closed flux surface (LCFS) radially outward.
Abstract: The field line connection of a tokamak sheared magnetic field ensures a finite parallel dynamical response for every degree of freedom available in the system. In the scrape-off layer (SOL) the flux surfaces are open, and the field line connection property is broken by the presence of a Debye sheath arising where the field lines strike boundary plates, hence allowing the existence of convective cell modes for which there is no dynamical parallel response. This leads to a major distinction in terms of turbulence character between closed and open flux surface regions. We study this using three-dimensional electromagnetic gyrofluid computations. The turbulence is found to change character from an ion temperature gradient to a generic interchange type, crossing the last closed flux surface (LCFS) radially outward. The width of the transition zone is about ten ion gyroradii. Various poloidal configurations of the Debye sheaths retain this interface property but affect the interaction between the turbulence and the slowly varying, self-consistent background. The strongest effect is found in a case with sheath plates at both the top and bottom of the SOL, allowing the high-field and low-field sides of the SOL to decouple. In these sides the curvature is favourable and unfavourable, respectively. The clear asymmetry observed between these sides of the plasma is consistent with previous experimental results and makes room for future experimental qualitative comparisons, for instance, on double null configurations of the tokamak ASDEX Upgrade.
61 citations
TL;DR: In this article, the two-center atomic orbital close-coupling (AOCC) method was used to calculate the state-selective electron capture and excitation cross sections.
Abstract: Collision dynamics of the ${\mathrm{He}}^{2+}+\mathrm{H}(1s)$ system imbedded in a Debye plasma is studied by the two-center atomic orbital close-coupling (AOCC) method in the energy range $5--300\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{u}$. The atomic orbitals and electron binding energies of atomic states are calculated within Debye-H\"uckel approximation of the screened Coulomb potential and used in AOCC dynamics formalism to calculate the state-selective electron capture and excitation cross sections. The basis contained 174 orbitals centered on the target (all $n\ensuremath{\le}6$ discrete states and 117 quasicontinuum states) and 20 orbitals centered on the projectile (all $n\ensuremath{\le}4$ discrete states). It is demonstrated that the screening of Coulomb interactions in the system progressively reduces the number of available excitation and electron capture channels when the screening parameter increases. The screening of Coulomb interactions introduces changes also in the values of direct and exchange couplings, thus affecting the magnitude and energy behavior of the cross sections. The control of dynamics of collision processes in a Debye plasma by varying the plasma screening of Coulomb interactions in the collision system is discussed.
TL;DR: In this article, Reed and Morrison showed that the electrophoretic velocity of a collection of particles with identical zeta potential is the same as that of an isolated particle, unchanged by interactions.
Abstract: In the classical analysis of electrophoresis, particle motion is a consequence of the interfacial fluid slip that arises inside the ionic charge cloud (or Debye screening layer) surrounding the particle surface when an external field is applied. Under the assumptions of thin Debye layers, weak applied fields, and zero polarizability, it can be shown that the electrophoretic velocity of a collection of particles with identical zeta potential is the same as that of an isolated particle, unchanged by interactions [L. D. Reed and F. A. Morrison, “Hydrodynamic interaction in electrophoresis,” J. Colloid Interface Sci. 54, 117 (1976)]. When some of these assumptions are relaxed, nonlinear effects may also arise and result in relative motions. First, the perturbation of the external field around the particles creates field gradients, which may result in nonzero dielectrophoretic forces due to Maxwell stresses in the fluid. In addition, if the particles are able to polarize, they can acquire a nonuniform surface ...
TL;DR: In this article, the effect of weakly coupled plasmas on photodetachment cross sections of the hydrogen negative ion was investigated by using the asymptotic from of the bound state wave function and a plane wave form for the final-state wave function.
Abstract: The effect of weakly coupled plasmas on photodetachment cross sections of the hydrogen negative ion is investigated by using the asymptotic from of the bound state wave function and a plane wave form for the final-state wave function. The Debye model is used to represent the plasma effects. The required normalization constant is determined from highly accurate, completely nonadiabatic wave functions for the three-particle systems. Photodetachment cross sections for the plasma-embedded H− ion are calculated for different Debye lengths (D) ranging from infinite (pure Coulomb) to D=1.0.
TL;DR: In this paper, the Casimir-Lifshitz force between two gold surfaces (a sphere and a plate) immersed in ethanol and study the effect of residual electrostatic forces, which are dominated by static fields within the apparatus and can be reduced with proper shielding.
Abstract: We present detailed measurements of the Casimir-Lifshitz force between two gold surfaces (a sphere and a plate) immersed in ethanol and study the effect of residual electrostatic forces, which are dominated by static fields within the apparatus and can be reduced with proper shielding. Electrostatic forces are further reduced by Debye screening through the addition of salt ions to the liquid. Additionally, the salt leads to a reduction of the Casimir-Lifshitz force by screening the zero-frequency contribution to the force; however, the effect is small between gold surfaces at the measured separations and within experimental error. An improved calibration procedure is described and compared with previous methods. Finally, the experimental results are compared with Lifshitz's theory and found to be consistent for the materials used in the experiment.
TL;DR: In this article, the authors explore the ability of molecular-dynamics simulation to elucidate thermal transport in Si-Ge alloys and find that point-defect scattering from mass disorder is dominant.
Abstract: We explore the ability of molecular-dynamics simulation to elucidate thermal transport in Si–Ge alloys. Simulations using Stillinger–Weber potentials yield values for the thermal resistivity significantly higher than experimental measurements. In agreement with experiment and theoretical predictions, we find that scattering from mass disorder is dominant, with bond disorder and strain effects playing a very minor role. To explore the origins of the large discrepancies with experiment, we use theoretical methods suitable for the limit where point-defect scattering dominates the resistivity. We find that point-defect scattering models based on a Debye spectrum cannot be used to fit our simulations, indicating that high-frequency modes may play an important role in the simulation. The results have important implications for using classical molecular-dynamics simulation to predict properties of alloy materials near and below the Debye temperature.
TL;DR: In this paper, a d-dimensional model for sound waves in a disordered environment, in which the local fluctuations of the elastic modulus are spatially correlated with a certain correlation length, is investigated analytically by means of a field-theoretical effective medium theory (selfconsistent Born approximation) and numerically on a square lattice.
Abstract: We investigate a d -dimensional model (d = 2,3) for sound waves in a disordered environment, in which the local fluctuations of the elastic modulus are spatially correlated with a certain correlation length. The model is solved analytically by means of a field-theoretical effective-medium theory (self-consistent Born approximation) and numerically on a square lattice. As in the uncorrelated case the theory predicts an enhancement of the density of states over Debye's ωd –1 law (“boson peak”) as a result of disorder. This anomay becomes reinforced for increasing correlation length ξ.
The theory predicts that ξ times the width of the Brillouin line should be a universal function of ξ times the wavenumber. Such a scaling is found in the 2d simulation data, so that they can be represented in a universal plot. In the low-wavenumber regime, where the lattice structure is irrelevant there is excellent agreement between the simulation at small disorder. At larger disorder the continuum theory deviates from the lattice simulation data. It is argued that this is due to an instability of the model with stronger disorder. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
TL;DR: It is suggested that in many cases an accurate approximation to the effective field can be obtained directly from the equilibrium charge density given by the Debye theory of screening, thus eliminating the need for a self-consistently determined effective external field.
Abstract: We propose a simplified version of local molecular field (LMF) theory to treat Coulomb interactions in simulations of ionic fluids. LMF theory relies on splitting the Coulomb potential into a short-ranged part that combines with other short-ranged core interactions and is simulated explicitly. The averaged effects of the remaining long-ranged part are taken into account through a self-consistently determined effective external field. The theory contains an adjustable length parameter sigma that specifies the cutoff distance for the short-ranged interaction. This can be chosen to minimize the errors resulting from the mean-field treatment of the complementary long-ranged part. Here we suggest that in many cases an accurate approximation to the effective field can be obtained directly from the equilibrium charge density given by the Debye theory of screening, thus eliminating the need for a self-consistent treatment. In the limit sigma-->0, this assumption reduces to the classical Debye approximation. We examine the numerical performance of this approximation for a simple model of a symmetric ionic mixture. Our results for thermodynamic and structural properties of uniform ionic mixtures agree well with similar results of Ewald simulations of the full ionic system. In addition, we have used the simplified theory in a grand-canonical simulation of a nonuniform ionic mixture where an ion has been fixed at the origin. Simulations using short-ranged truncations of the Coulomb interactions alone do not satisfy the exact condition of complete screening of the fixed ion, but this condition is recovered when the effective field is taken into account. We argue that this simplified approach can also be used in the simulations of more complex nonuniform systems.
TL;DR: In this article, general mobility relations for the translation and rotation of submicrometer-size freely suspended conducting (ideally polarizable) particles of arbitrary shape under dc or ac spatially nonuniform electric forcing are derived.
Abstract: General mobility relations are derived for the translation and rotation of submicrometer-size freely suspended conducting (ideally polarizable) particles of arbitrary shape under dc or ac spatially nonuniform electric forcing. Both linear electrophoretic effects for an initially charged colloid and nonlinear induced-charge electrophoresis of an uncharged particle are considered within the same framework. A concise derivation of the total loads (electrostatic and hydrodynamic) exerted on a single colloid are obtained by integrating the Maxwell, shear and normal (relating to the unsteady Stokes equation) stresses over the particle. These newly derived expressions for the force and torque exerted on a nanoparticle, which is subject to any electric field, are given for an arbitrary Debye thickness and thus open the road to studying nonlinear phoretic motions on the nanoscale.
TL;DR: In this article, the authors derived exact strong contrast expansions for the effective dielectric tensor of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the n-point correlation functions of the medium.
Abstract: We derive exact strong-contrast expansions for the effective dielectric tensor ee of electromagnetic waves propagating in a two-phase composite random medium with isotropic components explicitly in terms of certain integrals over the n-point correlation functions of the medium Our focus is the long-wavelength regime, ie, when the wavelength is much larger than the scale of inhomogeneities in the medium Lower-order truncations of these expansions lead to approximations for the effective dielectric constant that depend upon whether the medium is below or above the percolation threshold In particular, we apply two- and three-point approximations for ee to a variety of different three-dimensional model microstructures, including dispersions of hard spheres, hard oriented spheroids, and fully penetrable spheres as well as Debye random media, the random checkerboard, and power-law-correlated materials We demonstrate the importance of employing n-point correlation functions of order higher than two for hig
TL;DR: In this paper, a theory for Casimir-Lifshitz and Casimir Polder interactions with semiconductor or insulator surfaces that takes into account charge drift in the bulk material through use of the classical Boltzmann equation was developed.
Abstract: We develop a theory for Casimir-Lifshitz and Casimir-Polder interactions with semiconductor or insulator surfaces that takes into account charge drift in the bulk material through use of the classical Boltzmann equation. We derive frequency-dependent dispersion relations that give the usual Lifshitz results for dielectrics as a limiting case and, in the quasistatic limit, coincide with those recently computed to account for Debye screening in the thermal Lifshitz force with conducting surfaces with small density of carriers.
TL;DR: Using resonant-ultrasound spectroscopy, this article measured diamond elastic-stiffness coefficients C11, C12, and C44, between 322 and 10 K.
Abstract: Using resonant-ultrasound spectroscopy, we measured diamond’s monocrystal elastic-stiffness coefficients C11, C12, and C44, between 322 and 10 K. Changes are small and smooth: The bulk modulus B=(C11+2C12)/3 increases about 1 part in 1000, describable by a quasiharmonic Einstein-oscillator model. Zero-temperature Cij correspond to a 2244-K Debye characteristic temperature. Using a low-temperature form of the Gruneisen–Debye model, we calculated an overall thermodynamic Gruneisen parameter of γ=1.26; using a high-temperature form we calculated 0.71; the lattice specific heat yields γ=1.10.
TL;DR: In this article, the excitation and propagation of solitary waves were studied experimentally in a two-dimensional strongly coupled dusty (complex) plasma, where a single layer with ≈5000 microspheres (8μmdiam) was suspended in an argon plasma with a neutral gas pressure of 3.0mTorr.
Abstract: The excitation and propagation of solitary waves is studied experimentally in a two-dimensional strongly coupled dusty (complex) plasma. A single layer with ≈5000 microspheres (8μmdiam) was suspended in an argon plasma with a neutral gas pressure of 3.0mTorr. The measured Debye shielding parameter was κ≈1.6, where κ=a∕λ is the ratio of the lattice constant a to the Debye length λ. Nonlinear, planar longitudinal waves were launched by pushing all the particles in a rectangular region at the center of the crystal in the same direction using an 18W green laser. Compressive solitary waves with density perturbations δn∕n0≲0.8 and widths ≲5a were found to propagate in the forward direction at speeds exceeding the dust acoustic speed. For small amplitude solitary waves, the relations between amplitude, width, and velocity are consistent with those predicted for Korteweg–deVries solitons. Rarefactive perturbations were not observed to evolve into solitary waves. However, oscillatory shocks were seen to move in th...
TL;DR: This letter presents a scattered-field formulation for modeling dispersive media using the finite-difference time-domain (FDTD) method, and the auxiliary differential equation method is applied to Drude and Lorentz media for a scattered field FDTD model.
Abstract: This letter presents a scattered-field formulation for modeling dispersive media using the finite-difference time-domain (FDTD) method. Specifically, the auxiliary differential equation method is applied to Drude and Lorentz media for a scattered field FDTD model. The present technique can also be applied in a straightforward manner to Debye media. Excellent agreement is achieved between the FDTD-calculated and exact theoretical results for the reflection coefficient in half-space problems.
TL;DR: In this paper, the authors provided the first systematic test of validity of the embedded-atom potentials of Mei et al. via a complete study of the vibrational and thermodynamic properties of isoelectronic transition (Ni, Pd, Pt) and noble (Cu, Ag, Au) metals.
TL;DR: In this article, an effective method for extracting parameters of a Debye or a Lorentzian dispersive medium over a wideband frequency range using a GA and a transmission-line model is presented.
Abstract: An effective method for extracting parameters of a Debye or a Lorentzian dispersive medium over a wideband frequency range using a genetic algorithm (GA) and a transmission-line model is presented. Scattering parameters (S-parameters) of the transmission-line sections, including a parallel plate, microstrip, and stripline, are measured. Wave equations for TEM/quasi-TEM mode with a complex propagation constant and a frequency-dependent wave impedance are used to evaluate the corresponding S-parameters in an analytical model. The discrepancy between the modeled and measured S-parameters is defined as the objective function in the GA. The GA is used for search of the dispersive-medium parameters by means of minimizing the objective function over the entire frequency range of interest. The reconstructed Debye or Lorentzian dispersive material parameters are corroborated by comparing the original measurements with the FDTD modeling results. The self-consistency of the proposed method is demonstrated by constructing different test structures with an identical material, i.e., material parameters of a substrate extracted from different transmission-line configurations. The port effects on the material parameter extraction are examined by using through-reflection-line calibration.
TL;DR: In this article, the effect of weakly coupled hot plasma environment on the oscillator strengths of the ultraviolet and visible series and the polarizabilities of helium has been investigated using variational highly correlated wave functions within the non-relativistic framework.
Abstract: The effect of weakly coupled hot plasma environment on the oscillator strengths of the ultraviolet and visible series and the polarizabilities of helium has been investigated using variational highly correlated wave functions within the non-relativistic framework. The Debye shielding approach that admits a variety of plasma conditions is used to simulate the plasma effects. For each shielding parameter, dipole oscillator strengths are calculated for the 1 1S–n 1P (n=2, 3), 2 1S–2 1P, 2 3S–n 3P (n=2, 3) and 2 1,3P–n 1,3D (n=3, 4) transitions. The dipole and quadrupole polarizabilities for the ground He (1s2 1S) state are also reported for each screening parameter. Results obtained are useful in plasma diagnostic purposes besides several other applications.
TL;DR: In this paper, the pseudostate method has been applied to calculate energy eigenvalues and corresponding eigenfunctions of the hydrogen atom in Debye plasma environments, and a two-photon transparency is found in correspondence to each resonance for 1s-3s.
Abstract: The pseudostate method has been applied to calculate energy eigenvalues and corresponding eigenfunctions of the hydrogen atom in Debye plasma environments. Resonant two-photon transition rates from the ground state of atomic hydrogen to 2s and 3s excited states have been computed as a function of photon frequency in the length and velocity gauges for different Debye lengths. A two-photon transparency is found in correspondence to each resonance for 1s–3s. The transparency frequency and resonance enhancement frequency vary significantly with the Debye length.
TL;DR: In this work an inversion formula based on an eigenfunction representation is derived and presented which allows a field distribution in a plane in the focal region to be specified and the appropriate pupil plane distribution to be calculated.
Abstract: The forward problem of focusing light using a high numerical aperture lens can be described using the Debye-Wolf integral, however a solution to the inverse problem does not currently exist. In this work an inversion formula based on an eigenfunction representation is derived and presented which allows a field distribution in a plane in the focal region to be specified and the appropriate pupil plane distribution to be calculated. Various additional considerations constrain the inversion to ensure physicality and practicality of the results and these are also discussed. A number of inversion examples are given.
TL;DR: In this paper, the total energy and elastic properties of the L12-based Al3RE (RE = Sc, Y, Lanthanide) at T = 0 K are performed by using the projector augmented-wave method within the generalized gradient approximation.
Abstract: First-principles calculations of the total energy and elastic properties of the L12-based Al3RE (RE = Sc, Y, Lanthanide) at T = 0 K are performed by using the projector augmented-wave method within the generalized gradient approximation. The lattice constants, formation enthalpies, elastic constants and bulk modulus of the L12-based Al3RE are obtained. Young's modulus, shear modulus and Poisson's ratios are also estimated in the present work. By using the Debye – Gruneisen model, the Debye temperatures, Gruneisen constants and the sound velocity are obtained for the L12-based Al3RE. All the calculated results are in good agreement with experimental values and other theoretical calculations available.
TL;DR: In this article, a general methodology is presented for evaluating the dielectrophoretic velocity of a freely suspended spherical colloid in an electrolyte solutes under the action of a nonuniform electric field and for a Debye layer of arbitrary thickness.
Abstract: A general methodology is presented for evaluating the dielectrophoretic velocity of a freely suspended spherical colloid in an electrolyte solutes under the action of a nonuniform electric field and for a Debye layer of arbitrary thickness. The nonlinear induced charge electrophoretic problem is first considered. General analytic expressions are derived for the mobility of an uncharged particle in the form of products between adjacent modes of the ambient electric field demonstrating a symmetry-breaking-type phenomena. It is shown that the mobility of a conducting (i.e., ideally polarizable) spherical particle vanishes for a quadratic electric field in the limiting case of a thin Debye layer. For an infinitely thick Debye layer it attains asymptotically a positive finite value. Yet, there is another value of a finite Debye length for which the mobility changes sign. This interesting nonintuitive effect may have implications to separation of particles by size. The linear case of a uniformly charged colloid...