Entropy Numbers of Besov Classes of Generalized Smoothness on the Sphere

We investigate the asymptotic behavior of the entropy numbers of Besov classes BBΩp,θ（Sd 1）of generalized smoothness on the sphere inL q（Sd 1）for 1≤p,q,θ≤∞,and get their asymptotic orders.We also obtain the exact orders of entropy numbers of Sobolev classesBWr p（Sd 1）inL q（Sd 1）whenpand/orqis equal to 1 or∞.This provides the last piece as far as exact orders of entropy numbers ofBWr p（Sd 1）inL q（Sd 1）are concerned.

Effect of Richardson number on entropy generation over backward facing step

The flow over a backward facing step （BFS） has been taken as a useful proto- type to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Richardson number on entropy generation over the BFS is absent yet, although the flow pattern and heat transfer characteristic both will receive significant influence caused by the variation of Richardson number in many prac- tical applications, such as in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in the BFS flow is reported in this paper for the first time. The entropy generation analysis is conducted through numerically solving the entropy generation equation. The velocity and temperature, which are the inputs of the entropy generation equation, are evaluated by the lattice Boltzmann method. It is found that the distributions of local entropy generation number and Bejan number are significantly influenced by the variation of Richardson number. The total entropy gen- eration number is a monotonic decreasing function of Richardson number, whereas the average Bejan number is a monotonic increasing function of Richardson number.

True Random Number Generator Realized by Extracting Entropy from a Negative-Inductance Superconducting Quantum Interference Device

A new type of superconductive true random number generator (TRNG) based on a negative-inductance superconducting quantum interference device (nSQUID) is proposed. The entropy harnessed to generate random numbers comes from the phenomenon of symmetry breaking in the nSQUID. The experimental circuit is fabricated by the Nb-based lift-off process. Low-temperature tests of the circuit verify the basic function of the proposed TRNG. The frequency characteristics of the TRNG have been analyzed by simulation. The generation rate of random numbers is expected to achieve hundreds of megahertz to tens of gigahertz.

Entropy analysis in electrical magnetohydrodynamic(MHD) flow of nanofluid with effects of thermal radiation,viscous dissipation,and chemical reaction

The unsteady mixed convection flow of electrical conducting nanofluid and heat transfer due to a permeable linear stretching sheet with the combined effects of an electric field, magnetic field, thermal radiation, viscous dissipation, and chemical reaction have been investigated. A similarity transformation is used to transform the constitutive equations into a system of nonlinear ordinary differential equations.The resultant system of equations is then solved numerically using implicit finite difference method.The velocity, temperature, concentration, entropy generation, and Bejan number are obtained with the dependence of different emerging parameters examined. It is noticed that the velocity is more sensible with high values of electric field and diminished with a magnetic field. The radiative heat transfer and viscous dissipation enhance the heat conduction in the system. Moreover, the impact of mixed convection parameter and Buoyancy ratio parameter on Bejan number profile has reverse effects. A chemical reaction reduced the nanoparticle concentration for higher values.

APPLICATIONS OF THE BERNSTEIN-DURRMEYER OPERATORS IN ESTIMATING THE NORM OF MERCER KERNEL MATRICES

The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2 -norm for general Mercer kernel matrices on [0, 1] x [0, 1] are provided.

Experimental Study on Performance of Supercritical CO_2 Heat Exchanger with Four Different Inner Tubes

The experiment was conducted to investigate the heat transfer performance of supercritical CO_2 in a casing heat exchanger by comparing their heat transfer,entropy production unit number,non-dimensional entropy production rate and field synergy factor.The results show that both heat transfer and entropy production unit number in four tubes decrease with water temperature increasing.Heat transfer and entropy production unit number in multiple tubes( i. e.,triple straight tube and double helix tube) is higher than their single counterparts; the non-dimensional entropy production rate increases with water temperature. Non-dimensional entropy production rate of triple straight tube and double helix tube is far below the single tube. Field synergy factor of double helix tube is much higher than that of the triple straight tube under the same condition. Further experiment was carried out in double helix tube,under various CO_2 pressure and inlet water temperature,the results are analyzed and reported in this paper.

On Effectiveness and Entropy Generation in Heat Exchanger

Some conceptual problems were discussed in the present paper. Firstly, according to the physical meaning of effectiveness, a new expression of effectiveness was developed by using an ideal heat exchanger model and temperature histogram method, in which the non-uniform inlet temperature profile was considered. Secondly, the relation of entropy generation number to effectiveness was studied, it was pointed out that both of them could express the perfect degree of a heat exchanger to the second thermodynamic law. Finally, to describe both quantity and quality of heat transferred in a heat exchanger,a criterion named as comprehensive thermal performance coefficient (CTPE) was presented.

Embedding theorems of Besov and Triebel-Lizorkin spaces on spaces of homogeneous type

In this paper, the author establishes the embedding theorems for different metrics of inhomoge-neous Besov and Triebel-Lizorkin spaces on spaces of homogeneous type. As an application, the author obtainssome estimates for the entropy numbers of the embeddings in the limiting cases between some Besov spacesand some logarithmic Lebesgue spaces.