Alejandro Stefan-Zavala, Isabel Scherl, Ioannis Mandralis
et al.
Fan-array wind tunnels are an emerging technology to prescribe wind fields through grids of individually controllable fans. This design is especially suited for the turbulent, dynamic, non-uniform flow conditions found close to the ground, and has enabled applications from entomology to flight on Mars. However, due to the high dimensionality of fan-array actuation and the complexity of unsteady flow, the physics of fan arrays are not fully characterised, making it difficult to prescribe arbitrary flow fields. Accessing the full capability of fan arrays requires resolving the map from time-varying grids of fan speeds to three-dimensional unsteady flow fields, which remains an open problem. In this paper, we study the case of constant fan speeds and time-averaged streamwise velocities with one homogeneous spanwise axis. We produce a proof-of-concept surrogate model by fitting a regularised linear map to a dataset of fan-array measurements. We use this model as basis for an open-loop control scheme to prescribe flow profiles subject to constraints on fan speeds. We experimentally validate our model and control scheme, provide a physical interpretation of our model as a superposition of self-similar jet profiles and conclude that the physics relating constant fan-array speeds to time-averaged streamwise velocities are dominantly linear.
Abstract The trajectories and interaction forces of four bodies with equal masses are analytically described. The bodies follow a choreographic motion in a trisectrix limax periodic orbit without collisions. The curve is similar to a numerical curve of a folded figure of eight. The center of mass is fixed at the origin. The moment of inertia, the non-zero angular momentum as well as the kinetic and potential energies of the system are constant. The interaction forces are not Newtonian but linear attractive and repulsive forces along the lines joining the bodies. To the best of our knowledge, this is the first analytical solution to a four-body choreography in a curve other than the circle.
Abstract Levitation of macroscopic objects in a vacuum is a key step towards the development of high-precision inertial sensors and pressure sensors, as well as towards the fundamental studies of quantum mechanics and its relation to gravity. Diamagnetic levitation offers a passive method at room temperature to isolate macroscopic objects in vacuum environments, yet eddy current damping remains a critical limitation for electrically conductive materials. We show that there are situations where the motion of conductors in magnetic fields does not, in principle, produce eddy damping, and demonstrate an electrically conducting rotor diamagnetically levitated in an axially symmetric magnetic field in high vacuum. Experimental measurements and finite-element simulations reveal gas collision damping as the dominant loss mechanism at high pressures, while residual eddy damping, which arises from symmetry-breaking factors such as platform tilt or material imperfections, dominates at low pressures. The conclusion is supported by an analytic proof and an analytic example of zero steady current density for a rotating conductor in an axially symmetric magnetic field. This demonstrates a macroscopic levitated rotor with extremely low rotational damping and paves the way to fully suppress rotor damping, enabling ultra-low-loss rotors for gyroscopes, pressure sensing, and fundamental physics tests.
Particle diffusometry (PD) is a technique of measuring the diffusion coefficient of a fluid sample by seeding it with tracer particles and observing their motion under a microscope. In microfluidic set-ups, the observed particles are often defocused and their motion is affected by factors such as fluid flow, which leads to high errors for conventional and deep learning-based PD (DPD) algorithms. This work improves the performance of DPD models by updating their architecture, avoiding temporal averaging in the input, and exploring the impact of various choices during training. These models provide state-of-the-art performance for generalised datasets regardless of particle shapes, concentration, flow or image noise and are called DPD-v2. These models provide a mean absolute error of 0.09
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m2s−1 for Gaussian particles and 0.07
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m2s−1 for defocused particles, which is 2x–4x lower errors as compared with the two following best methods. The performance of DPD-v2 models increases with crop size and the use of multiple stacks of images. The outputs of the DPD-v2 models were compared against the outputs from conventional algorithms on Gaussianised experimental no flow datasets, which provided < 0.5
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m2s−1 mean absolute difference. Hence, the DPD-v2 models can be used in real-world scenarios.
In this work, a model boundary value problem for a parabolic equation with a Bessel operator was investigated. The solution to the problem under consideration is sought as a sum of thermal potentials: the double-layer and volume potentials, which reduces the problem to a Volterra integral equation of the second kind. The questions of existence and uniqueness of the obtained integral equation were investigated. The existence condition for the solution to the given problem was found. It is shown that if this condition is fulfilled, the problem has a single solution. The problem considered in this paper is called a model problem because the region in which the solution of the problem is sought is cylindrical and its results will be used in solving boundary value problems for the parabolic equation in noncylindrical regions having different order of degeneracy of the solution region to a point at the initial moment of time.
Artificial intelligence (AI) has achieved human-level performance in specialised tasks such as Go, image recognition and protein folding, raising the prospect of an AI singularity – where machines not only match, but surpass human reasoning. Here, we demonstrate a step towards this vision in the context of turbulence modelling. By treating a large language model (LLM), DeepSeek-R1, as an equal partner, we establish a closed-loop, iterative workflow in which the LLM proposes, refines and reasons about near-wall turbulence models under adverse pressure gradients (APGs), system rotation and surface roughness. Through multiple rounds of interaction involving long-chain reasoning and a priori and a posteriori evaluations, the LLM generates models that not only rediscover established strategies, but also synthesise new ones that outperform baseline wall models. Specifically, it recommends incorporating a material derivative to capture history effects in APG flows, modifying the law of the wall to account for system rotation and developing rough-wall models informed by surface statistics. In contrast to conventional data-driven turbulence modelling – often characterised by human-designed, black-box architectures – the models developed here are physically interpretable and grounded in clear reasoning.
A new method for solving the problem of controllability and optimal transient behavior of nonlinear systems subject to boundary conditions and constraints on control values was proposed. Unlike existing methods, this new approach is based on constructing a general solution of the integral equation for a linear controlled system, followed by transforming the original problem into a special initial optimal control problem. We propose a new method for studying the global asymptotic stability of dynamical systems with a cylindrical phase space with a countable equilibrium position based on a non-singular transformation of the equation of motion and estimation of improper integrals along the solution of the system. Conditions for global asymptotic stability were obtained without involving any periodic Lyapunov function, as well as the frequency theorem. The effectiveness of the proposed method is shown with an example.
Abstract We compute instanton corrections to the partition function of sine-Liouville (SL) theory, which provides a worldsheet description of two-dimensional string theory in a non-trivial tachyon background. We derive these corrections using a matrix model formulation based on a chiral representation of matrix quantum mechanics and using string theory methods. In both cases we restrict to the leading and subleading orders in the string coupling expansion. Then the CFT technique is used to compute two orders of the expansion in the SL perturbation parameter λ, while the matrix model gives results which are non-perturbative in λ. The matrix model results perfectly match those of string theory in the small λ expansion. We also generalize our findings to the case of perturbation by several tachyon vertex operators carrying different momenta, and obtain interesting analytic predictions for the disk two-point and annulus one-point functions with ZZ boundary condition.
Nuclear and particle physics. Atomic energy. Radioactivity
The question of the existence of a solution of linear integro-differential systems of parabolic type limited on the semiaxis in a spatial variable and multiperiodic in time variables was considered. Sufficient conditions of multiperiodic oscillations in time variables in a linear homogeneous equation with a boundary condition and in a linear inhomogeneous equation were established. A linear homogeneous and inhomogeneous finitehereditarity integro-differential equation of convective-diffusion type were investigated.
This paper deals with some differential inequalities for generalized fractional integro-differential equations by using the technique of upper and lower solutions. The fractional differential operator is taken in Caputo’s sense and the nonlinear term divided into two parts depends on the fractional integrals of an unknown function with two different fractional orders. The results are studied by employing a variety of coupled upper and lower solutions. These theorems have some potential for extending the iterative techniques to fractional order integro-differential equations and to coupled systems of integro-differential fractional equations to obtain the existence of solutions as well as approximate solutions for the considered problem.
A.T. Assanova, S.S. Zhumatov, S.T. Mynbayeva
et al.
The paper proposes a constructive method to solve a nonlinear boundary value problem for a Fredholm integro-differential equation. Using D.S. Dzhumabaev parametrization method, the problem under consideration is transformed into an equivalent boundary value problem for a system of nonlinear integrodifferential equations with parameters on the subintervals. When applying the parametrization method to a nonlinear Fredholm integro-differential equation, the intermediate problem is a special Cauchy problem for a system of nonlinear integro-differential equations with parameters. By substitution the solution to the special Cauchy problem with parameters into the boundary condition and the continuity conditions of the solution to the original problem at the interior partition points, we construct a system of nonlinear algebraic equations in parameters. It is proved that the solvability of this system provides the existence of a solution to the original boundary value problem. The iterative methods are used to solve both the constructed system of algebraic equations in parameters and the special Cauchy problem. An algorithm for solving boundary value problem under consideration is provided.
The article deals with the vibration control problem described by one dimensional wave equation with integral type boundary condition. As usual, the initial and final moments of time for arbitrary displacements and velocities of the wave are specified by points on a string (Cauchy data). It is shown that the minimum time for the realizable control is uniquely determined by the condition of correct solvability to the Cauchy problem involving data lying on disconnected manifold. This suggests that the internal boundary conditions does not affect the minimum time value. Necessary and sufficient conditions for the existence of the desired internal-boundary controls that move the process from the state initially specified to a predetermined final one are obtained and written out. The controls are presented in explicit analytical form. Moreover, it is shown that for the inner-boundary controls expressions, one should use not the representation of the solution to the Cauchy problem in the sought-for domain, but the formula for the general solution of the string oscillation equation (d’Alembert’s formula).
The aim of this paper is to show how North Cyprus fought with Covid-19 by using R0 and Rt, as herd immunity. For that purpose, we used a SEIR model for basic reproduction number, R0, and calculated Rt values by using R0 values. North Cyprus is the first country in Europe to free from Covid-19 epidemic. One of the most important reasons for this is that the government decided to tackle Covid-19 pandemic by using R0 and Rt daily. For R0, we constructed a new SEIR model by using real data for North Cyprus. From March 11, 2020 to May 15, 2020, R0 varies from 0.65 to 2.38.
In this paper, we consider questions related to the study of the cohomology of simple and simply connected algebraic groups with coefficients in simple modules. There are various calculating methods for them. One of the effective methods is to study the properties of the Lyndon–Hochschild–Serre spectral sequence with respect to the infinitesimal subgroup, the Frobenius kernel of a given algebraic group, and the properties of various cohomological sequences. We have studied the properties of various short exact and corresponding long exact cohomological sequences of modules over an algebraic group associated with simple modules with highest restricted weights. Some properties of the cohomology of the Frobenius kernel with coefficients in simple modules with higher restricted weights are described. We also studied the properties of the Lyndon–Hochschild–Serre spectral sequence on the first quadrant for simple modules with highest restricted weights. The limiting values of the points of the first quadrant of the spectral sequence are described. It is proved that for the simple, simply connected algebraic group G over an algebraically closed field k of characteristic p > h with an irreducible root system R and for a simple G-module V with restricted highest weight, there is an isomorphism of G-modules Hj (G, V ) ∼= HomG(k, Hj (G1,V)(−1)) for all j ≥ 0, where G1 is the Frobenius map kernel for G, h is the Coxeter number of the root system R. This isomorphism allows us to reduce the calculation of the cohomology of group G with coefficients in simple modules with higher restricted weights to the calculation of the corresponding cohomology of the Frobenius kernel G1.
Доктору физико-математических наук, профессору, академику НАН РК С.Н. Харину исполнилось 80 лет. Станислав Николаевич Харин является высококвалифицированным специалистом в области математического моделирования теплофизических и электромагнитных явлений. С.Н. Харин имеет более 300 публикаций, включая 4 монографии и 12 авторских свидетельств на изобретения.
G.A. Yessenbayeva, F.M. Akhanov, T.Kh. Makazhanova
The article is devoted to the question of applying the method of single trigonometric series to solving the plate bending problems. In this article the structure of this method is described, its main components are highlighted, the classical approach of calculating rectangular plates hinged supported on two parallel sides and with arbitrary boundary conditions on each of the other two sides is characterized. The mathematical apparatus of the method of single trigonometric series is presented in the volume necessary for calculating the plates. The detailed example of calculating a rectangular plate by the stated method is given. The article is focused mainly on students and undergraduates engaged in research work in the field of mechanics and applied mathematics.