Topic

# Debye

About: Debye is a(n) research topic. Over the lifetime, 5339 publication(s) have been published within this topic receiving 124744 citation(s). The topic is also known as: D.

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Abstract: The dispersion and absorption of a considerable number of liquid and dielectrics are represented by the empirical formula e*−e∞=(e0−e∞)/[1+(iωτ0)1−α]. In this equation, e* is the complex dielectric constant, e0 and e∞ are the ``static'' and ``infinite frequency'' dielectric constants, ω=2π times the frequency, and τ0 is a generalized relaxation time. The parameter α can assume values between 0 and 1, the former value giving the result of Debye for polar dielectrics. The expression (1) requires that the locus of the dielectric constant in the complex plane be a circular arc with end points on the axis of reals and center below this axis.If a distribution of relaxation times is assumed to account for Eq. (1), it is possible to calculate the necessary distribution function by the method of Fuoss and Kirkwood. It is, however, difficult to understand the physical significance of this formal result.If a dielectric satisfying Eq. (1) is represented by a three‐element electrical circuit, the mechanism responsible...

7,796 citations

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Abstract: The coefficients of electrical and thermal conductivity have been computed for completely ionized gases with a wide variety of mean ionic charges. The effect of mutual electron encounters is considered as a problem of diffusion in velocity space, taking into account a term which previously had been neglected. The appropriate integro-differential equations are then solved numerically. The resultant conductivities are very close to the less extensive results obtained with the higher approximations on the Chapman-Cowling method, provided the Debye shielding distance is used as the cutoff in summing the effects of two-body encounters.

1,720 citations

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TL;DR: It is shown that a single-parameter potential is sufficient to reproduce the slow dynamics of proteins obtained with vastly more complex empirical potentials, which inevitably leads to unstable modes which must be eliminated through elaborate methods, and which cast doubts on the validity of the analysis.

Abstract: Normal mode analysis (NMA) is a leading method for studying long-time dynamics and elasticity of biomolecules. The method proceeds from complex semiempirical potentials characterizing the covalent and noncovalent interactions between atoms. It is widely accepted that such detailed potentials are essential to the success of NMA’s. We show that a single-parameter potential is sufficient to reproduce the slow dynamics in good detail. Costly and inaccurate energy minimizations are eliminated, permitting direct analysis of crystal coordinates. The technique can be used for new applications, such as mapping of one crystal form to another by means of slow modes, and studying anomalous dynamics of large proteins and complexes. [S0031-9007(96)01063-0] PACS numbers: 87.15.By, 87.15.He Thermal equilibrium fluctuations of the x-ray crystal coordinates of proteins provide a basis for understanding the complex dynamics and elasticity of biological macromolecules [1]. Analysis of the normal modes of globular proteins shows an interesting anomaly. The density of the slow vibrational modes is proportional to their frequency, gsv d, v, rather than gsv d, v 2 as predicted by Debye’s theory [2]. Yet, the atoms in globular proteins are packed as tightly as in solids. We show that a single-parameter potential reproduces the slow elastic modes of proteins obtained with vastly more complex empirical potentials. The simplicity of the potential permits greater insight and understanding of the mechanisms that underlie the slow, anomalous motions in biological macromolecules such as proteins. To date, normal modes of globular proteins have been used to reproduce crystallographic temperature factors [3] and diffuse scatter [4]. Normal mode analyses (NMA’s) shed light on shear and hinge motions necessary for catalytic reactions, and have been used with some success to map one crystal form of a protein into another [5]. Finally, NMA’s yield macroscopic elastic moduli of large protein assemblies, based on their microscopic structure [6]. NMA studies of macromolecules are handicapped, however, by the complex phenomenological potentials used to model the covalent and nonbonded interactions between atom pairs. The necessary initial energy minimization requires a great deal of computer time and memory, and is virtually impossible for even moderately large proteins (with typically thousands of degrees of freedom) with a reasonable degree of accuracy. This inevitably leads to unstable modes which must be eliminated through elaborate methods, and which cast doubts on the validity of the analysis. Moreover, partly because the minimization is carried out in vacuo, the final configuration disagrees with the known crystallographic structure, complicating the interpretation of the results of NMA. A typical example of a semiempirical potential used in molecular dynamics studies and NMA’s has the form [7] Ep › 1 X bonds Kbsb 2 b0d 2 1 1 X angles Kus u2u 0 d 2

1,538 citations

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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

1,346 citations

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TL;DR: Paul Scherrer and Peter Debye developed powder X-ray diffraction together, but it was Scherrer who figured out how to determine the size of crystallites from the broadening of diffraction peaks.

Abstract: Paul Scherrer and Peter Debye developed powder X-ray diffraction together, but it was Scherrer who figured out how to determine the size of crystallites from the broadening of diffraction peaks.

1,297 citations