And the dimensionless interfacial radius corresponding to the maximum value of the Nusselt number is different from that corresponding to the minimum value of the total entropy generation rate.A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a collocation method is applied to convert the time-delay fractional optimal control problem to a nonlinear programming one. By solving the resulting challenge, the unknown coefficients of the original one will be finally obtained. In this way, the proposed strategy introduces a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The algorithm's performance has been analyzed for several non-trivial examples, and the obtained results have shown that this scheme is more accurate, robust, and efficient than most previous methods.The purpose of this study is to analyze the dynamic properties of gas hydrate development from a large hydrate simulator through numerical simulation. A mathematical model of heat transfer and entropy production of methane hydrate dissociation by depressurization has been established, and the change behaviors of various heat flows and entropy generations have been evaluated. Simulation results show that most of the heat supplied from outside is assimilated by methane hydrate. The energy loss caused by the fluid production is insignificant in comparison to the heat assimilation of the hydrate reservoir. The entropy generation of gas hydrate can be considered as the entropy flow from the ambient environment to the hydrate particles, and it is favorable from the perspective of efficient hydrate exploitation. On the contrary, the undesirable entropy generations of water, gas and quartz sand are induced by the irreversible heat conduction and thermal convection under notable temperature gradient in the deposit.  https://www.selleckchem.com/products/pomhex.html  Although lower production pressure will lead to larger entropy production of the whole system, the irreversible energy loss is always extremely limited when compared with the amount of thermal energy utilized by methane hydrate. The production pressure should be set as low as possible for the purpose of enhancing exploitation efficiency, as the entropy production rate is not sensitive to the energy recovery rate under depressurization.Selective assembly is the method of obtaining high precision assemblies from relatively low precision components. For precision instruments, the geometric error on mating surface is an important factor affecting assembly accuracy. Different from the traditional selective assembly method, this paper proposes an optimization method of selective assembly for shafts and holes based on relative entropy and dynamic programming. In this method, relative entropy is applied to evaluate the clearance uniformity between shafts and holes, and dynamic programming is used to optimize selective assembly of batches of shafts and holes. In this paper, the case studied has 8 shafts and 20 holes, which need to be assembled into 8 products. The results show that optimal combinations are selected, which provide new insights into selective assembly optimization and lay the foundation for selective assembly of multi-batch precision parts.We discuss a possibility that the entire universe on its most fundamental level is a neural network. We identify two different types of dynamical degrees of freedom "trainable" variables (e.g., bias vector or weight matrix) and "hidden" variables (e.g., state vector of neurons). We first consider stochastic evolution of the trainable variables to argue that near equilibrium their dynamics is well approximated by Madelung equations (with free energy representing the phase) and further away from the equilibrium by Hamilton-Jacobi equations (with free energy representing the Hamilton's principal function). This shows that the trainable variables can indeed exhibit classical and quantum behaviors with the state vector of neurons representing the hidden variables. We then study stochastic evolution of the hidden variables by considering D non-interacting subsystems with average state vectors, x¯1, …, x¯D and an overall average state vector x¯0. In the limit when the weight matrix is a permutation matrix, the dynamics of x¯μ can be described in terms of relativistic strings in an emergent D+1 dimensional Minkowski space-time. If the subsystems are minimally interacting, with interactions that are described by a metric tensor, and then the emergent space-time becomes curved. We argue that the entropy production in such a system is a local function of the metric tensor which should be determined by the symmetries of the Onsager tensor. It turns out that a very simple and highly symmetric Onsager tensor leads to the entropy production described by the Einstein-Hilbert term. This shows that the learning dynamics of a neural network can indeed exhibit approximate behaviors that were described by both quantum mechanics and general relativity. We also discuss a possibility that the two descriptions are holographic duals of each other.The subject of this paper deals with the mathematical formulation of the Heisenberg Indeterminacy Principle in the framework of Quantum Gravity. The starting point is the establishment of the so-called time-conjugate momentum inequalities holding for non-relativistic and relativistic Quantum Mechanics. The validity of analogous Heisenberg inequalities in quantum gravity, which must be based on strictly physically observable quantities (i.e., necessarily either 4-scalar or 4-vector in nature), is shown to require the adoption of a manifestly covariant and unitary quantum theory of the gravitational field. Based on the prescription of a suitable notion of Hilbert space scalar product, the relevant Heisenberg inequalities are established. Besides the coordinate-conjugate momentum inequalities, these include a novel proper-time-conjugate extended momentum inequality. Physical implications and the connection with the deterministic limit recovering General Relativity are investigated.