In the derivation leading to Eq. (1.102), only one quantum state ne = 1 was considered. Once E > Ee,z(2), as an example, an electron of a given total energy Ee can be found in either ne = 1 or ne = 2 state so that the density of states doubles. The total density of states...
A recent derivation of the density of states at the Fermi level of liquid 3d-transition metals has prompted us to present some results for the effect of the d-band on the specific heat and the latent heat of vaporization for these materials.\ndoi:10.1080/14786437708232963...
Long-standing unsolved “Gauss' circle problem” (or sphere in 3D case) that asks an analytical answer for “how many integer lattice points inside of a circle with a given radius” is profoundly related to the exact calculation of number of states in state space. Even though Gauss' circle...
The vibrational properties of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadraticω2low-frequency scaling of the vibrational density of states. However, the analogous framework for nanoconfined materials with fewer degrees of freedom has been far less ...
cumulant functional was used for calculating the correlation energy45,46,47. Chai obtained the same cross-entropy term in the derivation of the thermally-assisted-occupation DFT48. Following this rationale, we introduce here a one-parameter approximation to the CASSCF correlation energy in the form ...
However, the present derivation imposes a new expression for the flow, where the usual form only accounts for half the usual flow, the remaining term 12Tψ∂z∂tψ being entirely new. The strongest argument to dismiss ϱpot from a mathematical point of view, has been that it does not...
In this paper, by using the energy estimates, the structure of the equations, and the properties of one dimension, we establish the global existence and uniqueness of strong and classical solutions to the initial boundary value problem of compressible Navier–Stokes/Allen–Cahn system in one-dimens...
·yi , (1.4) Some of the recent developments in the semi-classical limit are the following: One can find results for the inverse power law potential in [43], for the rate of convergence in the Schatten norm in [30], for the Coulomb potential and mixed states in [42], and for the ...
Assume a layer of depth d confined between stress-free boundaries maintained at constant temperature and constant salinity. If we repeat the derivation of the perturbation equations for the normal modes of the system, the equations that replace (11.39) are found to be: (11.45)(d2dz∗2−K2...
Kårstad and Aadnøy (1998) did an analytical derivation of density of the entire mud consisting of water, oil and solids based on assumptions that the coefficients of isothermal compressibility and thermal expansion can be expressed as linear function of P and T. The result is an exponential...