The six-vertex model, first proposed by Pauling [36] in 1935 to study the residual entropy of ice, became the archetypical example of a planar integrable model with Lieb’s solution of the model in 1967 in its anti-ferroelectric and ferroelectric phases [29,30,31,32] using the Bethe Ansa...
Focusing on the reduced quantity a * instead of the dimensional free energy A itself which is an extensive quantity and therefore scales with N spins allows for a comparison between finite-size systems of all dimensions including the limiting case of N spins → ∞ . This is shown in Figure ...
The challenges this application presents include: (1) precise characterisation of the thermal and optical properties of fenestration systems, in which two- or three-dimensional heat transfer and/or light transmittance might exist due to the presence of complex structural geometries; (2) the potential...
Freudental magic square and its dimensional implication for Formula Not Shown and high energy physicsEl Naschie, M. S.CHAOS SOLITONS AND FRACTALSEl Naschie, M.S. (2008) Freudental Magic Square and Its Dimensional Implication for and High Energy Physics. Chaos, Solitons & Fractals, 36, 546-...
Two-dimensional coherent interface with nearest-neighbor broken bonds. In a general crystal structure, let zS be the number of bonds across the interface counted per atom and let nS be the number of surface atoms per unit area within the surface plane. Accordingly, we have (6.23)EAAbroken=...
Especially, we assume that the highly disordered DWO presented below and near T* is a particular nematic order that breaks the two-dimensional rotational symmetry on a large scale but maintains the unidirectional DWO locally. Therefore, in this work, we focus on the locally fluctuating ...
(Color online) The space-time correlation function of the fluctuation of heat, energy, momentum, and mass density in one-dimensional systems at a finite temperature. (a)–(d) Diatomic gas model; (e)–(h) FPUT-ββ model; (i)–(l) the ϕ4ϕ4 model. 4 能量均分假设的证明 在更...
Combining these formulae, we find an estimate for the energy cost of extracting a given amount of entanglement. For example, for one dimensional lattice systems, the entanglement entropy in the ground state of models close to the critical point is20,33 $$S(\rho _{\mathrm{I}}) = \frac{...
steeper efficiency scaling of the extreme ultraviolet harmonics as a function of the driving-field intensity25 and a higher cut-off energy26 for crystalline materials, pointing to the importance of long-range order in condensed-phase HHG, which has also been explored for one-dimensional models27,...
Stephen Hall, in Branan's Rules of Thumb for Chemical Engineers (Fifth Edition), 2012 Mass and Energy Transfer Computational Fluid Dynamics (CFD) software is used to create and visualize highly detailed mass and energy transfer models. Characterized by the colorful three-dimensional output plots, ...