Some explicit solutions of the three-dimensional Euler equations with a free surface

We present a family of radial solutions (given in Eulerian coordinates) to the three-dimensional Euler equations in a fluid domain with a free surface and having finite depth. The solutions that we find exhibit vertical structure and a non-constant vorticity vector. Moreover, the flows described by these solutions display a density that depends on the depth. While the velocity field and the pressure function corresponding to these solutions are given explicitly through (relatively) simple formulas, the free surface defining function is specified (in general) implicitly by a functional equation which is analysed by functional analytic methods. The elaborate nature of the latter functional equation becomes simpler when the density function has a particular form leading to an explicit formula of the free surface. We subject these solutions to a stability analysis by means of a Wentzel–Kramers–Brillouin (WKB) ansatz.

Continuity of sub-additive topological pressure with matrix cocycles *

Let A = {A 1, A 2, …, A k } be a finite collection of contracting affine maps, the corresponding pressure function P(A, s) plays the fundamental role in the study of dimension of self-affine sets. The zero of the pressure function always give the upper bound of the dimension of a self-affine set, and is exactly the dimension of ‘typical’ self-affine sets. In this paper, we consider an expanding base dynamical system, and establish the continuity of the pressure with the singular value function of a Hölder continuous matrix cocycle. This extends Feng and Shmerkin’s result in (Feng and Shmerkin 2014 Geom. Funct. Anal. 24 1101–1128) to a general setting.

Decay properties for the incompressible Navier-Stokes flows in a half space

In this article, we give a comprehensive characterization of $L^1$ -summability for the Navier-Stokes flows in the half space, which is a long-standing problem. The main difficulties are that $L^q-L^r$ estimates for the Stokes flow don't work in this end-point case: $q=r=1$ ; the projection operator $P: L^1\longrightarrow L^1_\sigma$ is not bounded any more; useful information on the pressure function is missing, which arises in the net force exerted by the fluid on the noncompact boundary. In order to achieve our aims, by making full use of the special structure of the half space, we decompose the pressure function into two parts. Then the knotty problem of handling the pressure term can be transformed into establishing a crucial and new weighted $L^1$ -estimate, which plays a fundamental role. In addition, we overcome the unboundedness of the projection $P$ by solving an elliptic problem with homogeneous Neumann boundary condition.

Pressure Function and Limit Theorems for Almost Anosov Flows

We obtain limit theorems (Stable Laws and Central Limit Theorems, both standard and non-standard) and thermodynamic properties for a class of non-uniformly hyperbolic flows: almost Anosov flows, constructed here. The link between the pressure function and limit theorems is studied in an abstract functional analytic framework, which may be applicable to other classes of non-uniformly hyperbolic flows.

TEKANAN UDARA DALAM PERSPEKTIF SAINS DAN AL-QUR’AN

The objectives of this study are: 1. To see the function of air pressure from a scientific perspective. 2. To see the function of air pressure in the perspective of the Qur'an. 3. To see the relationship between the study of the function of air pressure from a scientific perspective and the Koran. This study used qualitative research methods. The type of research used in this research is library research. The instrument in qualitative research is a person or human instrument, namely the researcher himself. As a human instrument in this study, researchers must have broad insight and theory in order to be able to ask, analyze, take pictures and construct the social conditions under study to be clearer and show. The technique of reading data that researchers use in library research is by reading, interviewing and triangulation. Research results: 1. Study of Air Pressure Function in Science Perspective is according to science air pressure is a force that moves air particles carrying air particles in the direction of the earth's force. 2. The study of the function of air pressure in the perspective of the Koran is based on the perspective of the Koran, the air pressure is described into the atmospheric layer which is described in QS: Al-An'am (6) verse 125. 3. The relationship between the study of the pressure function The air in the perspective of science and the Koran is the relationship between science and the Qur'an expressed as an integrated relationship. This integration can be described in two forms, namely natural theology (natural theology) which views scientific findings as a means of reaching God, and natural theology (theology of nature).

-spectra of measures on planar non-conformal attractors

We study the $L^{q}$ -spectrum of measures in the plane generated by certain nonlinear maps. In particular, we consider attractors of iterated function systems consisting of maps whose components are $C^{1+\alpha }$ and for which the Jacobian is a lower triangular matrix at every point subject to a natural domination condition on the entries. We calculate the $L^{q}$ -spectrum of Bernoulli measures supported on such sets by using an appropriately defined analogue of the singular value function and an appropriate pressure function.

The Analysis of Electronic Circuit Fault Diagnosis Based on Neural Network Data Fusion Algorithm

Symmetries play very important roles in the dynamics of electrical systems. The relevant electronic circuits with fault diagnostics, including the optimized neural network algorithm model, are designed on the basis of symmetry principles. In order to improve the efficiency of the circuit pressure test, a circuit pressure function equivalent compression test method based on the parallel neural network algorithm is proposed. For the implementation stage of the circuit pressure test, the improved modified node algorithm (MNA) is used to build an optimization model, and the circuit network is converted into an ordinary differential equation for the circuit pressure function equivalent compression test. The test aims to minimize flux. Then, backpropagation (BP) neural network algorithm data fusion is introduced to optimize the minimum flux model of the cyclic pressure functional equivalent compression test. Finally, a simulation experiment is carried out to verify the effectiveness of the algorithm in the accuracy and efficiency of the pressure test. The results show that the improved BP neural network improves the data fusion accuracy and shortens the sample training time; compared with the uncompressed algorithm, the running time of the proposed algorithm is greatly reduced and the execution efficiency is high; compared with the vascular pressure test method, there is no significant difference in the convergence accuracy and it is at a level of 10−5. Since the parallel computing problem is not considered in either of the two-pulse tube pressure test methods, the convergence time of the algorithm increases exponentially with the increase in the number of parallel threads. However, the algorithm in this research considers the problem of parallel execution and uses a quad-core processor, with no significant change in computing time and high computing efficiency. Therefore, BP neural network data fusion can be used for the fault diagnosis of electronic circuits, with a high operating efficiency and good development prospects.

Establishing IPR in Gas-Condensate Reservoir: An Alternative Approach

Inflow performance relationship (IPR) accuracy in the condensate reservoir is a long-standing problem in the oil industry. This paper presents a new approach to project the gas phase IPR in condensate reservoirs. IPR is estimated by Rawlins and Schellhardt equation whereas the gas pseudo-pressure function is solved by two methods and the results are compared. Both two pseudo-pressure equations are used to estimate IPR. Additionally, an average of both IPR’s is estimated and compared. At the reservoir pressure, the difference between both flow rates is negligible i.e. at 6750 psi, the flow rate difference is 0.55 MMSCF/D. As pressure declines the difference is increasing at one stage, it is observed approximately 15 MMSCF/D.