Longitudinal vortices produced by a swirl-mixing grid are experimentally explored in an upscaled model of nuclear fuel assembly. The flow is mapped using particle image velocimetry in several planes downstream of the grid. The flow, an isothermal flow geometrically similar to that in one of the standard nuclear reactors, is compared between basic grids, swirl grids and the case without fuel rods, allowing for a link to previous studies of longitudinal vortex lattices. Individual vortices are recognised using a custom-made algorithm. Analysis of vortices shows that the meandering is enhanced by the presence of fuel rods and by the presence of an upstream swirl grid. The vortex core radii do not grow in the constrained case. There is a weak anticorrelation between the vortex velocity and the actual meandering amplitude. The neighbouring vortices show a weak correlation in their circumferential velocities or energies, but they do not display any significant correlations of positions or meandering amplitudes, cutting down any hypothetical “vortex dancing”.
Reflective thinking often predicts less belief in God or less religiosity — so-called analytic atheism. However, those correlations involve limitations: widely used tests of reflection confound reflection with ancillary abilities such as numeracy; some studies do not detect analytic atheism in every country; experimentally encouraging reflection makes some non-believers more open to believing in God; and one of the most common online research participant pools seems to produce lower data quality. So analytic atheism may be less than universal or partially explained by confounding factors. To test this, we developed better measures, controlled for more confounds, and employed more recruitment methods. All four studies detected signs of analytic atheism above and beyond confounds (N > 70,000 people from five of six continental regions). We also discovered analytic apostasy: the better a person performed on reflection tests, the greater their odds of losing their religion since childhood — even when controlling for confounds. Analytic apostasy even seemed to explain analytic atheism: apostates were more reflective than others and analytic atheism was undetected after excluding apostates. Religious conversion was rare and unrelated to reflection, suggesting reflection’s relationships to conversion and deconversion are asymmetric. Detected relationships were usually small, indicating reflective thinking is a reliable albeit marginal predictor of apostasy.
This paper explores the Monge–Ampere equation in the context of isotropic geometry. The study begins with an overview of the fundamental properties of isotropic space, including its scalar product, distance formula, and the nature of surfaces and curvatures within this geometric framework. A special focus is placed on dual transformations with respect to the isotropic sphere, and the self-inverse property of the dual surface is established. The article formulates the Monge–Ampere equation for isotropic space and studies its invariant solutions under isotropic motions. Several lemmas are proved to demonstrate how solutions transform under linear modifications and isotropic motions. A specific class of Monge–Ampere-type nonlinear partial differential equations is solved analytically using dual transformations and separation of variables. Additionally, translation surfaces and their curvature properties are studied in detail, particularly through the lens of dual curvature. The results demonstrate the deep relationship between curvature invariants and Monge–Ampere-type equations and show how duality simplifies the solution of nonlinear PDEs. These methods can be used for surface reconstruction and modeling in isotropic spaces.
Ayush Saraswat, Chintan Panigrahi, Kirtivardhan Singh
et al.
Cavitation inception and the associated flow structure in the tip region of a ducted propeller are investigated experimentally at varying advance ratios (J) using high-speed imaging and stereoscopic particle image velocimetry (SPIV) measurements in a refractive index-matched facility. At design and higher J values, inception occurs in axially aligned secondary vortices, located between the blade suction side and the tip leakage vortex (TLV), circumferentially after the trailing edge. With decreasing J, the inception shifts first to the TLV, and then along its core towards the leading edge. High-resolution SPIV data follow the evolution of TLV, tip leakage flow, near wake and several secondary vortices. Time-resolved SPIV at 30 kHz enables calculation of all three mean vorticity components, hence capturing axial vortices, and identifies the origin of flow structures. At high J values, inception occurs when quasi-axial vortices are stretched by the circumferential TLV and co-rotating secondary vortices located in the shear layer connecting the TLV to the suction side blade tip. With decreasing J, inception shifts to the TLV and towards the leading edge owing to earlier rollup and higher vortex strength, along with earlier breakup, evidenced by high core turbulence and a decrease in peak vorticity despite an increase in circulation.
Kosuke Osawa, V. Krishne Gowda, Tomas Rosén
et al.
Properties and functions of materials assembled from nanofibrils critically depend on alignment. A material with aligned nanofibrils is typically stiffer compared with a material with a less anisotropic orientation distribution. In this work, we investigate nanofibril alignment during flow focusing, a flow case used for spinning of filaments from nanofibril dispersions. In particular, we combine experimental measurements and simulations of the flow and fibril alignment to demonstrate how a numerical model can be used to investigate how the flow geometry affects and can be used to tailor the nanofibril alignment and filament shape. The confluence angle between sheath flow and core flow, the aspect ratio of the channel and the contractions in the sheath and/or core flow channels are varied. Successful spinning of stiff filaments requires: (i) detachment of the core flow from the top and bottom channel walls and (ii) a high and homogeneous fibril alignment. Somewhat expected, the results show that the confluence angle has a relatively small effect on alignment compared with contractions. Contractions in the sheath flow channels are seen to be beneficial for detachment, and contractions in the core flow channel are found to be an efficient way to increase and homogenise the degree of alignment.
A novel integrability condition for the Riccati equation, the simplest form of nonlinear ordinary differential equations, is obtained by using elementary quadrature method. Under this condition, the analytic general solution is presented, which can be extended to second-order linear ordinary differential equation. This result may provide valuable mathematical criteria for in-depth research on quantum mechanics, relativity and dynamical systems.
Difference schemes of the finite difference method and the finite element method of high-order accuracy in time and space are proposed and investigated for a pseudo-parabolic Sobolev type equation. The order of accuracy in space is improved in two ways using the finite difference method and the finite element method. The order of accuracy of the scheme in time is improved by a special discretization of the time variable. The corresponding a priori estimates are determined and, on their basis, the accuracy estimates of the proposed difference schemes are obtained with sufficient smoothness of the solution to the original differential problem. Algorithms for the implementation of the constructed difference schemes are proposed.
The problem of constructing equivalent equations with a given structure of forces by the given system of stochastic equations is considered. The equivalence of equations in the sense of almost surely is investigated. The paper determines the conditions under which a given system of second-order Ito stochastic differential equations is represented in the form of stochastic Lagrange equations with non-potential forces of a certain structure. Necessary and sufficient conditions for the representability of stochastic equations in the form of stochastic equations with non-potential forces admitting the Rayleigh function are obtained. The obtained results are illustrated by an example of motion of a symmetric satellite in a circular orbit, assuming a change in pitch under the action of gravitational and aerodynamic forces.
The harmonic oscillator is one of the most studied systems in Physics with a myriad of applications. One of the first problems solved in a Quantum Mechanics course is calculating the energy spectrum of the simple harmonic oscillator with analytic and algebraic approaches. In the algebraic solution, creation and annihilation operators are introduced to factorize the Hamiltonian. This work presents an algebraic solution for the simple harmonic oscillator in the context of Classical Mechanics, exploring the Hamiltonian formalism. In this solution, similarities between the canonical coordinates in a convenient basis for the classical problem and the corresponding operators in Quantum Mechanics are highlighted. Moreover, the presented algebraic solution provides a straightforward procedure for the quantization of the classical harmonic oscillator, motivating and justifying some operator definitions commonly used to solve the correspondent problem in Quantum Mechanics.
In this paper, the boundary value problem of heat conduction in a domain was considered, boundary of which changes with time, as well as there is no the problem solution domain at the initial time, that is, it degenerates into a point. To solve the problem, the method of heat potentials was used, which makes it possible to reduce it to a singular Volterra type integral equations of the second kind. The peculiarity of the obtained integral equation is that it fundamentally differs from the classical Volterra integral equations, since the Picard method is not applicable to it and the corresponding homogeneous integral equation has a nonzero solution.
This paper studies an ordinary second-order differential equation with a fractional differentiation operator in the sense of Riemann-Liouville with a variable coefficient. We use the Green’s function’s method to find a representation of the solution of the Dirichlet problem for the equation under consideration when the solvability condition is satisfied. Green’s function to the problem is constructed in terms of the fundamental solution of the equation under study and its properties are proved. The necessary integral condition for the existence of a nontrivial solution to the homogeneous Dirichlet problem, called an analogue of the Lyapunov inequality, is found.
The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced in "Analytic Hypoellipticity for Sums of Squares and the Treves Conjecture" by P. Albano and A. Bove and M. Mughetti, and in "Analytic Hypoellipticity for Sums of Squares and the Treves Conjecture. II" by A. Bove and M. Mughetti, satisfying the Hörmander condition and which fail to be neither locally nor microlocally analytic hypoelliptic.
Biopolymer networks are common in biological systems from the cytoskeleton of individual cells to collagen in the extracellular matrix. The mechanics of these systems under applied strain can be explained in some cases by a phase transition from soft to rigid states. For collagen networks, it has been shown that this transition is critical in nature and it is predicted to exhibit diverging fluctuations near a critical strain that depends on the network's connectivity and structure. Whereas prior work focused mostly on shear deformation that is more accessible experimentally, here we study the mechanics of such networks under an applied bulk or isotropic extension. We confirm that the bulk modulus of subisostatic fiber networks exhibits similar critical behavior as a function of bulk strain. We find different non-mean-field exponents for bulk as opposed to shear. We also confirm a similar hyperscaling relation to what previously found for shear.
Motivated by applications of statistical mechanics in which the system of interest is spatially unconfined, we present an exact solution to the maximum entropy problem for assigning a stationary probability distribution on the phase space of an unconfined ideal gas in an anti-de Sitter background. Notwithstanding the gas's freedom to move in an infinite volume, we establish necessary conditions for the stationary probability distribution to be normalizable. As a part of our analysis, we develop a novel method for identifying dynamical constraints based on local measurements. With no appeal to \emph{a priori} information about globally-defined conserved quantities, it is thereby applicable to a much wider range of problems.
Alexandru Aleman, Carme Cascante, Joan Fàbrega
et al.
For a fixed analytic function $g$ on the unit disc $\mathbb{D}$, we consider the analytic paraproducts induced by $g$, which are defined by $T_gf(z)= \int_0^z f(ζ)g'(ζ)\,dζ$, $S_gf(z)= \int_0^z f'(ζ)g(ζ)\,dζ$, and $M_gf(z)= f(z)g(z)$. The boundedness of these operators on various spaces of analytic functions on $\mathbb{D}$ is well understood. The original motivation for this work is to understand the boundedness of compositions of two of these operators, for example $T_g^2, \,T_gS_g,\, M_gT_g$, etc. Our methods yield a characterization of the boundedness of a large class of operators contained in the algebra generated by these analytic paraproducts acting on the classical weighted Bergman and Hardy spaces in terms of the symbol $g$. In some cases it turns out that this property is not affected by cancellation, while in others it requires stronger and more subtle restrictions on the oscillation of the symbol $g$ than the case of a single paraproduct.
Nurgali Ashirbayev, Zhansaya Ashirbayeva, Manat Shomanbayeva
et al.
In the linear formulation, the problem of the propagation of unsteady stress waves in an elastic body with symmetrically located rectangular holes is considered. Formulated in terms of stresses and velocities, the mixed problem is modeled numerically using an explicit difference scheme of the end - to - end calculation based on the method of spatial characteristics. The wave process is caused by applying an external dynamic load on the front border of the rectangular region, and the side boundaries of the region are free of stresses. The lower boundary of the rectangular region is rigidly fixed. The contour of symmetrically arranged rectangular openings is free of stress. Based on the numerical technique developed in this work, the calculated finite - difference relations of dynamic problems are obtained at the corner points of a rectangular hole, where the "smoothness"of functions "familiar"to dynamic problems is violated. At these corner points, the first and second derivatives of the desired functions suffer a discontinuity of the first kind. The isoline presents the results of changes in wave fields in an elastic body with symmetrically located rectangular holes. The concentration of dynamic stresses in the vicinity of the corner points of a rectangular hole is investigated. By numerical implementation, the stability of computational algorithms for a sufficiently large time is established.
This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified linear units (ReLU). To achieve meshing from learned implicit functions, existing methods adopt the de-facto standard algorithm of marching cubes; while promising, they suffer from loss of precision learned in the MLPs, due to the discretization nature of marching cubes. Motivated by the knowledge that a ReLU based MLP partitions its input space into a number of linear regions, we identify from these regions analytic cells and analytic faces that are associated with zero-level isosurface of the implicit function, and characterize the theoretical conditions under which the identified analytic faces are guaranteed to connect and form a closed, piecewise planar surface. Based on our theorem, we propose a naturally parallelizable algorithm of analytic marching, which marches among analytic cells to exactly recover the mesh captured by a learned MLP. Experiments on deep learning mesh reconstruction verify the advantages of our algorithm over existing ones.
The article is devoted to the research of boundary value problems for the spectrum - loaded operator of heat conduction with the moving point of loading to the temporary axle in zero or on infinity. For strongly loaded parabolic 2k - order equations the adjoint boundary value problems, when order of loaded term is greater then one of differential part of equation, is studied. In this article we continue a investigation of the boundary value problems for spectrally loaded parabolic equations in unbounded domains.The boundary value problem for the spectral - loaded equation of thermal conductivity, which on the one hand is quite close to the problems with the load containing the second derivative of the spatial variable, and is of independent interest on the other hand in this work, is considered.