The surface pressure distribution over a circular cylinder with a small, full-span, triangular bump is examined. The geometry of the bump is an isosceles triangle, the height of which is varied from 1.33 % to 5.33 % of the diameter of the cylinder and positioned between
$60^{\circ }$
and
$120^{\circ }$
. The Reynolds number (
$Re = V_{\infty}D/\nu$
, where
$V_\infty$
is the velocity of the freestream,
$D$
is the diameter of the cylinder and
$\nu$
is the kinematic viscosity) is varied between
$1.1 \times 10^5$
and
$1.8 \times 10^5$
. The lift and drag are estimated through the surface integral of pressure over the cylinder. The results show that the smallest bump acts as a trip for the lower Re and orientations before
$70^{\circ }$
, leading to a separation farther upstream than in the case of no bump. For larger bumps, Re and orientation angles, the bump acts as a spoiler and fully separates the boundary layer at the bump. In addition, the surface pressure upstream of the bump is strongly dependent on the bump position. The lift is highest for bump position less than
$90^{\circ }$
and decreases significantly with increasing bump location angle. The drag is less sensitive to the position of the bump. These findings have implications for predicting the forces on bluff bodies due to small asymmetric surface geometry features and extension to applications such as atmospheric flow over topography.
The growing demand for convenience in the food industry has increased the fast-food restaurant (FFR) market. Key factors like order speed and accuracy, reinforced by technological advancements like self-service kiosks (SSK), shape overall service quality and customer expectations. Despite SSK implementation, FFR still faces long queues, extended waiting times, and customer dissatisfaction. This study uses discrete-event simulation through FlexSim simulation software to enhance operational efficiency and customer experience. The simulation explored system configurations for hybrid ordering systems and preventive maintenance policies. An economic analysis was conducted to improve wait times and queue lengths. Sensitivity analysis identified ideal SSK-to-counter ratios, and cost-benefit analysis evaluated their feasibility and impact on profitability and service quality. A 3:3 SSK-to-counter ratio proved to be most effective, reducing the total average wait time by 28% and reducing average queue length by 77% with segmented payment counters. Managers should balance technology with human-assisted service to ensure cost-efficiency, improve customer satisfaction, and support employee adaptability. This study contributes to service system design by integrating preventive maintenance into hybrid ordering simulations, offering practical insights on optimal kiosk-to-counter ratios to enhance customer experience, reduce wait times, and support strategic decision-making in fast-food operations.
An initial-boundary value problem for a loaded parabolic equation in a rectangular domain was considered. By discretization with respect to a spatial variable, the problem under study is reduced to the initial problem for a system of loaded ordinary differential equations. Based on the previously obtained results of Dzhumabaev and Assanova, an estimate for the solution of the original initial-boundary value problem for a loaded parabolic equation was established. An auxiliary initial problem for a system of loaded ordinary differential equations is solved by the Dzhumabaev parameterization method. Conditions of the unique solvability of the considering problem are obtained and algorithms for finding a solution are constructed. The results are illustrated with a numerical example.
In 1978, the journal Differential Equations published an article by A.M. Nakhushev, that presented a method for correctly formulating a boundary value problem for a class of second-order parabolic-hyperbolic equations in an arbitrarily bounded domain with a smooth or piecewise smooth boundary. In that work, a boundary value problem was formulated and investigated using the method of a priori estimates, which is currently called the first boundary value problem for a second-order mixed parabolic-hyperbolic equation. In this work, a boundary value problem for a third-order model parabolic-hyperbolic equation is formulated and investigated in a mixed domain, following the approach of A.M. Nakhushev for second-order mixed parabolic-hyperbolic equations. In one part of the mixed domain, the equation under consideration is a degenerate hyperbolic equation of the first kind of the second order, and in the other part, it is a nonhomogeneous equation of the third order with multiple characteristics and reverse-time parabolic type. For various values of the parameter, existence and uniqueness theorems for a regular solution are proved. The uniqueness theorem is proved using the method of energy integrals combined with A.M. Nakhushev’s method. The existence theorem is proved by the method of integral equations. In terms of the MittagLeffler function, the solution of the problem is found and written out explicitly. Sufficient smoothness conditions for the given functions are found, which ensure the regularity of the obtained solution.
This study presents exponentially fitted finite difference methods for solving a singularly perturbed nonlinear differential-difference equation that consists of a small negative shift. The quasilinearization technique is applied to the nonlinear problem and a sequence of linear problems is obtained. The resulting linear problems are treated with exponentially fitted finite difference methods of higher order. The methods developed in this paper are studied for stability and convergence. Numerical results using the proposed methods are presented for two test problems and hence the efficiency of the methods is demonstrated.
Pier Giuseppe Ledda, Maria Grazia Badas, Tommaso Rossi
et al.
We numerically investigate the fluid dynamics of the infusion of balanced salt solution into the vitreous chamber during ophthalmic surgery. A 25-gauge vitrectomy set consisting of an infusion cannula and a vitreous cutter is inserted in a realistic model of a human vitreous chamber. As the vitreous cutter aspirates at a constant flow rate (7.5–20 ml min−1 in the present study), the corresponding infusion flow generates a high-velocity laminar jet (1.00–2.65 m s−1) causing high stress on the retina (pressure up to 1200 Pa) and mixing. We analyse the Lagrangian coherent structures and quantify mixing. Results show a vortex ring around the jet impingement region, in the posterior part of the chamber. At higher infusion rates (Re > 600), interacting hairpin vortices emerge as a result of an instability in the vortex ring. This disordered flow enhances mixing, potentially dispersing substances such as vital dyes, with consequences on visibility and surgery time. We quantify the overall mixing and its evolution with height, observing a smooth transition from an ordered flow to an unsteady disordered one with the flow rate. These findings may pave the way towards strategies to minimise complications while optimising efficiency, especially given the trend towards minimally invasive surgery with progressively smaller infusion cannulas.
Abstract Depending on their mechanism of self-propulsion, active particles can exhibit time-dependent, often periodic, propulsion velocity. The precise propulsion velocity profile determines their mean square displacement and their effective diffusion coefficient at long times. Here, we demonstrate that any periodic propulsion profile results in a larger diffusion coefficient than the corresponding case with constant propulsion velocity. We investigate, in detail, periodic exponentially decaying velocity pulses, expected in propulsion mechanisms based on sudden absorption of finite amounts of energy. We show, both analytically and with numerical simulations, that in these cases the effective diffusion coefficient can be arbitrarily enhanced with respect to the case with constant velocity equal to the average speed. Our results may help interpret, in a new light observations on the diffusion enhancement of active particles.
Social physics is the application of ideas, concepts and tools from physics to study social phenomena. In this article, we present a mechanical theory underlying a mathematical treatment of social physics. We explore the possibility of using fundamental concepts like position, motion, inertia, and interaction, to effectively regard social phenomena analogously to particles interacting with each other in physics. From these concepts, along with heuristics of social change, we investigate the notions of free motion, motion under the influence of a net deterministic, as well as stochastic force. To test these ideas we model partisan preferences in the United States according to the outcomes of presidential elections.
Lorenzo Tiberi, Francesca Mignacco, Kazuki Irie
et al.
Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable. We develop a statistical mechanics theory of Bayesian learning in this model, deriving exact equations for the network's predictor statistics under the finite-width thermodynamic limit, i.e., $N,P\rightarrow\infty$, $P/N=\mathcal{O}(1)$, where $N$ is the network width and $P$ is the number of training examples. Our theory shows that the predictor statistics are expressed as a sum of independent kernels, each one pairing different 'attention paths', defined as information pathways through different attention heads across layers. The kernels are weighted according to a 'task-relevant kernel combination' mechanism that aligns the total kernel with the task labels. As a consequence, this interplay between attention paths enhances generalization performance. Experiments confirm our findings on both synthetic and real-world sequence classification tasks. Finally, our theory explicitly relates the kernel combination mechanism to properties of the learned weights, allowing for a qualitative transfer of its insights to models trained via gradient descent. As an illustration, we demonstrate an efficient size reduction of the network, by pruning those attention heads that are deemed less relevant by our theory.
A.R. Yeshkeyev, A.R. Yarullina, S.M. Amanbekov
et al.
Given article is devoted to the study of semantic Jonsson quasivariety of universal unars of signature containing only unary functional symbol. The first section of the article consists of basic necessary concepts. There were defined new notions of semantic Jonsson quasivariety of Robinson unars JCU , its elementary theory and semantic model. In order to prove the main result of the article, there were considered Robinson spectrum RSp(JCU ) and its partition onto equivalence classes [∆] by cosemanticness relation. The characteristic features of such equivalence classes [∆] ∈ RSp(JCU ) were analysed. The main result is the following theorem of the existence of: characteristic for every class [∆] the meaning of which is Robinson theories of unars; class [∆] for any arbitrary characteristic; criteria of equivalence of two classes [∆]1, [∆]2. The obtained results can be useful for continuation of the various Jonsson algebras’ research, particularly semantic Jonsson quasivariety of S-acts over cyclic monoid.
Locomoting organisms often carry loads such as captured prey or young. Load-carrying effects on high-Reynolds-number flight have been studied, but the fluid dynamics of load carrying by low-Reynolds-number microorganisms has not. We studied low-Reynolds-number load carrying using unicellular choanoflagellates, which wave a flagellum to swim and create a water current transporting bacterial prey to a food-capturing collar of microvilli. A regularized Stokeslet framework was used to model the hydrodynamics of a swimming choanoflagellate with bacterial prey on its collar. Both the model and microvideography of choanoflagellates showed that swimming speed decreases as number of prey being carried increases. Flux of water into the capture zone is reduced by bacteria on the collar, which redirect the water flow and occlude parts of the collar. Feeding efficiency (prey captured per work to produce the feeding current) is decreased more by large prey, prey in the plane of flagellar beating and prey near microvillar tips than by prey in other locations. Some choanoflagellates can attach themselves to surfaces. We found that the reduction in flux due to bacterial prey on the collars of these attached thecate cells was similar to the reduction in flux for swimmers.
The theory of fractional calculus developed rapidly as the applications of this branch are extensive nowadays. There is no discipline of modern engineering and science that remains untouched by the techniques of fractional calculus. In fact, one could argue that real world processes are fractional order systems in general. In this article, we obtain the semi-integrals of certain algebraic functions in terms of difference of two complete elliptic integrals of different kinds by using series manipulation technique.
In this paper we calculate cohomology of a classical Lie algebra of type A 2 over an algebraically field k of characteristic p = 3 with coefficients in simple modules. To describe their structure we will consider them as modules over an algebraic group SL 3( k ) . In the case of characteristic p = 3 , there are only two peculiar simple modules: a simple that module isomorphic to the quotient module of the adjoint module by the center, and a one-dimensional trivial module. The results on the cohomology of simple nontrivial module are used for calculating the cohomology of the adjoint module. We also calculate cohomology of the simple quotient algebra Lie of A 2 by the center.
A ternary semigroup is a nonempty set with a ternary operation which is associative. The purpose of the present paper is to give a characterization of open sets of finite-dimensional Euclidean spaces by ternary semigroups of pairs of homeomorphic transformations and extend to ternary semigroups certain results of L.M. Gluskin concerned with semigroups of homeomorphic transformations of finite-dimensional Euclidean spaces.
In this paper, we consider the model-theoretical properties of the essential base of the central types of convex theory. Also shows the connection between the center and Jonsson theory in permissible enrichment signatures. Moreover, the theories under consideration are hereditary. This article is divided into 2 sections: 1) an essential types and an essential base of central types (in this case, the concepts of an essential type and an essential base are defined using the Rudin-Keisler order on the set of central types of some hereditary Jonsson theory in the permissible enrichment); 2) the atomicity and the primeness of ϕ(x)-sets. In this paper, new concepts are introduced: the ϕ(x)-Jonsson set, the AP A-set, the AP A-existentially closed model, the ϕ(x)-convex theory, the ϕ(x)-transcendental theory, the AP A-transcendental theory. One of the ideas of this article refers to the fact that in the work of Mustafin T.G. it was noticed that any universal model of a quasi-transcendental theory with a strong base is saturated, but we generalized this result taking into account that: the concept of quasi-transcendence will be replaced by the ϕ(x)-transcendence, where ϕ(x) defines some Jonsson set; and the notion of a strong base is replaced by the notion of an essential base, but in a permissible enrichment of the hereditary Jonsson theory. The main result of our work shows that the number of fragments obtained under a closure of an algebraic or definable type does not exceed the number of homogeneous models of a some Jonsson theory, which is obtained as a result of a permissible enrichment of the hereditary Jonsson theory.
Abstract The applicability of peridynamic models to problems with irregularly non-uniformly discretized solution domain is critical. In this study, a systematic comparison study on results predicted using eight different peridynamic models, including bond-based, ordinary state-based and non-ordinary state-based mechanics and heat conduction models, for three different types of mechanical problems, including thermal, mechanics and coupled thermo-mechanics, with irregular non-uniform spatial discretization is performed. It is found that for the case of irregular but semi-uniform spatial discretization, all these models yield good predictions compared to analytical local solutions. For the case of irregular and non-uniform spatial discretization, models formulated specifically for this configuration give much better results than the conventional formulations which do not consider the neighborhood difference among material points in the spatial discretization. For either cases of spatial discretization, the bond-associated correspondence material model predicts the most accurate results.
An analytic stress solution is presented for a circular tunnel problem in a half plane with a concentrated force acting on any position in the field under gravity. The solution uses the complex variable method and the power series method. The influence of the unbalanced force system on the tunnel boundary is considered. The relationship between two analytic functions is established by using surface stress boundary condition. The analytic functions can be determined from the tunnel stress boundary condition. Based on the principle of superposition, the stresses of the surrounding rock can be calculated by superimposing three partial solutions which are obtained separately. The examples give contour plots of the principal stresses in the surrounding rock, focus on the stress distribution on the ground surface and the tunnel boundary and analyze the effect on the stress distribution of some main parameters.