共查询到20条相似文献，搜索用时 15 毫秒
1.
Maria Jarzyńska 《Central European Journal of Physics》2007,5(4):586-598
The research problem presented in this work concerns modification of the Kedem-Katchalsky (K-K) equation for volume flow (J
v
) through system (h|M|l), consisting of a membrane M and boundary layers h and l. Such boundary layers appear in the vicinity of the membrane on both sides due to the lack of mixing of solutions. This paper
also includes the derivation of the equation for volume flow (J
vr
) dissipated on concentration boundary layers h and l. The derivation of these equations concerns the case in which the substance transport through the membrane is generated by
the osmotic pressure gradient
. On the basis of the equations for the volume flows (J
v
) and (J
vr
), some calculations for a nephrophane membrane, used in medicine, and for aqueous glucose solutions have been carried out.
In order to test the equations for (J
v
) and (J
vr
), we have also carried out calculations for the volume flow (J′
v
) that is transferred through the membrane in the case of mixed solutions on both sides of the membrane. This volume flux
has been calculated on the basis of the original (K-K) equation. The results are presented in Fig. 2.
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2.
3.
Peter Enders 《Entropy (Basel, Switzerland)》2021,23(7)
During the physical foundation of his radiation formula in his December 1900 talk and subsequent 1901 article, Planck refers to Boltzmann’s 1877 combinatorial-probabilistic treatment and obtains his quantum distribution function, while Boltzmann did not. For this, Boltzmann’s memoirs are usually ascribed to classical statistical mechanics. Agreeing with Bach, it is shown that Boltzmann’s 1868 and 1877 calculations can lead to a Planckian distribution function, where those of 1868 are even closer to Planck than that of 1877. Boltzmann’s and Planck’s calculations are compared based on Bach’s three-level scheme ‘configuration–occupation–occupancy’. Special attention is paid to the concepts of interchangeability and the indistinguishability of particles and states. In contrast to Bach, the level of exposition is most elementary. I hope to make Boltzmann’s work better known in English and to remove misunderstandings in the literature. 相似文献
4.
We calculate the possible interaction between a superconductor and the static Earth’s gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg–Landau theory. We try to estimate which are the most favorable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behavior of high– and classical low– superconductors with respect to the gravity/superfluid interplay. 相似文献
5.
When PINNs solve the Navier–Stokes equations, the loss function has a gradient imbalance problem during training. It is one of the reasons why the efficiency of PINNs is limited. This paper proposes a novel method of adaptively adjusting the weights of loss terms, which can balance the gradients of each loss term during training. The weight is updated by the idea of the minmax algorithm. The neural network identifies which types of training data are harder to train and forces it to focus on those data before training the next step. Specifically, it adjusts the weight of the data that are difficult to train to maximize the objective function. On this basis, one can adjust the network parameters to minimize the objective function and do this alternately until the objective function converges. We demonstrate that the dynamic weights are monotonically non-decreasing and convergent during training. This method can not only accelerate the convergence of the loss, but also reduce the generalization error, and the computational efficiency outperformed other state-of-the-art PINNs algorithms. The validity of the method is verified by solving the forward and inverse problems of the Navier–Stokes equation. 相似文献
6.
Yinnian He 《Entropy (Basel, Switzerland)》2021,23(12)
In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair . The method consists of transmitting the finite element solution of the 3D steady Navier–Stokes equations into the finite element solution pairs based on the finite element space pair of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair satisfies the discrete inf-sup condition in a 3D domain . Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to of the FE solution to the exact solution of the 3D steady Navier–Stokes equations in the norm. Finally, we also give the convergence order with respect to of the FE velocity to the exact velocity u of the 3D steady Navier–Stokes equations in the norm. 相似文献
7.
Ravi P. Agarwal Fatemah Mofarreh Rasool Shah Waewta Luangboon Kamsing Nonlaopon 《Entropy (Basel, Switzerland)》2021,23(8)
This research article is dedicated to solving fractional-order parabolic equations using an innovative analytical technique. The Adomian decomposition method is well supported by natural transform to establish closed form solutions for targeted problems. The procedure is simple, attractive and is preferred over other methods because it provides a closed form solution for the given problems. The solution graphs are plotted for both integer and fractional-order, which shows that the obtained results are in good contact with the exact solution of the problems. It is also observed that the solution of fractional-order problems are convergent to the solution of integer-order problem. In conclusion, the current technique is an accurate and straightforward approximate method that can be applied to solve other fractional-order partial differential equations. 相似文献
8.
Xiaoming Wang 《Physica D: Nonlinear Phenomena》2008,237(6):854-858
We prove a new upper bound on the vertical heat transport in Rayleigh-Bénard convection of the form under the assumption that the ratio of Prandtl number over Rayleigh number satisfies where the non-dimensional constant c0 depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) bound (modulo logarithmic correction) on vertical heat transport for the infinite Prandtl number model for convection due to Constantin and Doering [P. Constantin, C.R. Doering, Infinite Prandtl number convection, J. Stat. Phys. 94 (1) (1999) 159-172] and Doering, Otto and Reznikoff [C.R. Doering, F. Otto, M.G. Reznikoff, Bounds on vertical heat transport for infinite Prandtl number Rayleigh-Bénard convection, J. Fluid Mech. 560 (2006) 229-241]. It also improves a uniform (in Prandtl number) bound for the Nusselt number [P. Constantin, C.R. Doering, Heat transfer in convective turbulence, Nonlinearity 9 (1996) 1049-1060] in the case of large Prandtl number. 相似文献
9.
This paper presents a difference-type lower bound for the Bayes risk as a difference-type extension of the Borovkov–Sakhanenko bound. The resulting bound asymptotically improves the Bobrovsky–Mayor–Wolf–Zakai bound which is difference-type extension of the Van Trees bound. Some examples are also given. 相似文献
10.
Pawe&#x; A. Kluza 《Entropy (Basel, Switzerland)》2021,23(12)
In this paper, we introduce new divergences called Jensen–Sharma–Mittal and Jeffreys–Sharma–Mittal in relation to convex functions. Some theorems, which give the lower and upper bounds for two new introduced divergences, are provided. The obtained results imply some new inequalities corresponding to known divergences. Some examples, which show that these are the generalizations of Rényi, Tsallis, and Kullback–Leibler types of divergences, are provided in order to show a few applications of new divergences. 相似文献
11.
The definition of temperature in non-equilibrium situations is among the most controversial questions in thermodynamics and statistical physics. In this paper, by considering two numerical experiments simulating charge and phonon transport in graphene, two different definitions of local lattice temperature are investigated: one based on the properties of the phonon–phonon collision operator, and the other based on energy Lagrange multipliers. The results indicate that the first one can be interpreted as a measure of how fast the system is trying to approach the local equilibrium, while the second one as the local equilibrium lattice temperature. We also provide the explicit expression of the macroscopic entropy density for the system of phonons, by which we theoretically explain the approach of the system toward equilibrium and characterize the nature of the equilibria, in the spatially homogeneous case. 相似文献
12.
In this work, we first consider the discrete version of Fisher information measure and then propose Jensen–Fisher information, to develop some associated results. Next, we consider Fisher information and Bayes–Fisher information measures for mixing parameter vector of a finite mixture probability mass function and establish some results. We provide some connections between these measures with some known informational measures such as chi-square divergence, Shannon entropy, Kullback–Leibler, Jeffreys and Jensen–Shannon divergences. 相似文献
13.
Uniform error estimates with power-type asymptotic constants of the finite element method for the unsteady Navier–Stokes equations are deduced in this paper. By introducing an iterative scheme and studying its convergence, we firstly derive that the solution of the Navier–Stokes equations is bounded by power-type constants, where we avoid applying the Gronwall lemma, which generates exponential-type factors. Then, the technique is extended to the error estimate of the long-time finite element approximation. The analyses show that, under some assumptions on the given data, the asymptotic constants in the finite element error estimates for the unsteady Navier–Stokes equations are uniformly power functions with respect to the initial data, the viscosity, and the body force for all time . Finally, some numerical examples are shown to verify the theoretical predictions. 相似文献
14.
In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations. 相似文献
15.
Masoomeh Bararzadeh Ledari Yadollah Saboohi Antonio Valero Sara Azamian 《Entropy (Basel, Switzerland)》2021,23(1)
This paper explains a thorough exergy analysis of the most important reactions in soil–plant interactions. Soil, which is a prime mover of gases, metals, structural crystals, and electrolytes, constantly resembles an electric field of charge and discharge. The second law of thermodynamics reflects the deterioration of resources through the destruction of exergy. In this study, we developed a new method to assess the exergy of soil and plant formation processes. Depending on the types of soil, one may assess the efficiency and degradation of resources by incorporating or using biomass storage. According to the results of this study, during different processes from the mineralization process to nutrient uptake by the plant, about 62.5% of the input exergy will be destroyed because of the soil solution reactions. Most of the exergy destruction occurs in the biota–atmosphere subsystem, especially in the photosynthesis reaction, due to its low efficiency (about 15%). Humus and protonation reactions, with 14% and 13% exergy destruction, respectively, are the most exergy destroying reactions. Respiratory, weathering, and reverse weathering reactions account for the lowest percentage of exergy destruction and less than one percent of total exergy destruction in the soil system. The total exergy yield of the soil system is estimated at about 37.45%. 相似文献
16.
In many applications of interacting systems, we are only interested in the dynamic behavior of a subset of all possible active species. For example, this is true in combustion models (many transient chemical species are not of interest in a given reaction) and in epidemiological models (only certain subpopulations are consequential). Thus, it is common to use greatly reduced or partial models in which only the interactions among the species of interest are known. In this work, we explore the use of an embedded, sparse, and data-driven discrepancy operator to augment these partial interaction models. Preliminary results show that the model error caused by severe reductions—e.g., elimination of hundreds of terms—can be captured with sparse operators, built with only a small fraction of that number. The operator is embedded within the differential equations of the model, which allows the action of the operator to be interpretable. Moreover, it is constrained by available physical information and calibrated over many scenarios. These qualities of the discrepancy model—interpretability, physical consistency, and robustness to different scenarios—are intended to support reliable predictions under extrapolative conditions. 相似文献
17.
We use stochastic simulations to investigate the performance of two recently developed methods for calculating the free energy profiles of ion channels and their electrophysiological properties, such as current–voltage dependence and reversal potential, from molecular dynamics simulations at a single applied voltage. These methods require neither knowledge of the diffusivity nor simulations at multiple voltages, which greatly reduces the computational effort required to probe the electrophysiological properties of ion channels. They can be used to determine the free energy profiles from either forward or backward one-sided properties of ions in the channel, such as ion fluxes, density profiles, committor probabilities, or from their two-sided combination. By generating large sets of stochastic trajectories, which are individually designed to mimic the molecular dynamics crossing statistics of models of channels of trichotoxin, p7 from hepatitis C and a bacterial homolog of the pentameric ligand-gated ion channel, GLIC, we find that the free energy profiles obtained from stochastic simulations corresponding to molecular dynamics simulations of even a modest length are burdened with statistical errors of only 0.3 kcal/mol. Even with many crossing events, applying two-sided formulas substantially reduces statistical errors compared to one-sided formulas. With a properly chosen reference voltage, the current–voltage curves can be reproduced with good accuracy from simulations at a single voltage in a range extending for over 200 mV. If possible, the reference voltages should be chosen not simply to drive a large current in one direction, but to observe crossing events in both directions. 相似文献
18.
In this paper, we discuss the decision optimization of tourism projects in Hebei Province, China. To improve the process of analyzing tourism projects, we introduce a model that includes multiple decision makers as subjects based on a standard four-dimensional evaluation system. In order to improve the effectiveness of decision-making results, we will increase the number of decision makers to 40. A novel large-scale group decision-making (LSGDM) algorithm that incorporates the trust–distrust asymmetric relationships between decision makers is proposed. This model contains three main innovations: firstly, in the evaluation of decision makers’ social network relations, the trust–distrust value is introduced as a new carrier, and a weighted directed network and data integration operator are constructed based on the evaluation between decision makers; secondly, an extended Girvan-Newman (GN) algorithm is constructed to cluster the decision makers from this weighted network; thirdly, the interval-valued intuitionistic fuzzy number (IVIFN) is used to evaluate the alternatives, studying the IVIFN’s geometric significance by placing in a rectangular coordinate system. Finally, a new LSGDM model is proposed. Using the development of a cultural tourism project in a township as an example, the effectiveness of the proposed model is illustrated. By comparing the results of our method to those of a LSGDM algorithm that does not incorporate trust relationships, we assess the performance of the new model. 相似文献
19.
Mohamed A. Abd Elgawad Haroon M. Barakat Shengwu Xiong Salem A. Alyami 《Entropy (Basel, Switzerland)》2021,23(3)
In this paper, we study the concomitants of dual generalized order statistics (and consequently generalized order statistics) when the parameters are assumed to be pairwise different from Huang–Kotz Farlie–Gumble–Morgenstern bivariate distribution. Some useful recurrence relations between single and product moments of concomitants are obtained. Moreover, Shannon’s entropy and the Fisher information number measures are derived. Finally, these measures are extensively studied for some well-known distributions such as exponential, Pareto and power distributions. The main motivation of the study of the concomitants of generalized order statistics (as an important practical kind to order the bivariate data) under this general framework is to enable researchers in different fields of statistics to use some of the important models contained in these generalized order statistics only under this general framework. These extended models are frequently used in the reliability theory, such as the progressive type-II censored order statistics. 相似文献
20.
We review thermal–statistical considerations on the odd–even staggering effect (OES) in fermions. There is a well known OES in nuclear binding energies at zero temperature. We discuss here a thermal OES (finite temperatures) that establishes links with the order–disorder disjunction. The present thermal considerations cannot be found in the nuclear literature. 相似文献