Lifting Theory Research Articles

The Kudla–Millson form via the Mathai–Quillen formalism

AbstractA crucial ingredient in the theory of theta liftings of Kudla and Millson is the construction of a $q$ -form $\varphi_{KM}$ on an orthogonal symmetric space, using Howe's differential operators. This form can be seen as a Thom form of a real oriented vector bundle. We show that the Kudla-Millson form can be recovered from a canonical construction of Mathai and Quillen. A similar result was obtaind by Garcia for signature $(2,q)$ in case the symmetric space is hermitian and we extend it to arbitrary signature.

A strategy for modifying the effect of turbulence integral scale on fluctuating pressures of rectangular prisms

The turbulence integral scale has a significant effect on the fluctuating pressures encountered by prisms. At present, the turbulence integral scale cannot be adequately simulated, leading to errors in the fluctuating pressure. Based on the two-wavenumber aerodynamic admittance function of fluctuating pressure, this paper describes a strategy for modifying the fluctuating pressure of rectangular prisms in turbulent flows. Using the three-dimensional theory of lift, a three-dimensional model of fluctuating pressure is established, in which the two-wavenumber power spectrum of fluctuating pressure is the product of the two-wavenumber coherence and the one-wavenumber power spectrum of fluctuating pressure, and is also the product of the two-wavenumber aerodynamic admittance function and the two-wavenumber power spectrum of oncoming velocity. An empirical form of the-wavenumber coherence of fluctuating pressure is derived, allowing the two-wavenumber power spectrum of fluctuating pressure to be calculated, and the two-wavenumber aerodynamic admittance function of fluctuating pressure to be obtained. The two-wavenumber aerodynamic admittance function of fluctuating pressure on a given body is almost independent of the turbulence, indicating that only one test is needed to modify the simulated error of fluctuating pressure. Finally, the results for a prism with a 1:3 side-ratio show that the simulated error of fluctuating pressure can be ignored when the simulated turbulence integral scale is 0.5 or 1.1 times the target value, and the simulated error is reduced from 24% to around 10% when the simulated turbulence integral scale is 0.25 times the target value.

A grounded theory of weight lifting as a healing strategy for trauma

Research has found significant benefits in using exercise as an adjunct treatment for PTSD, depression, and anxiety. Weight lifting as an adjunct treatment for trauma is an emerging research area with very few empirically based studies. This study used a qualitative grounded theory approach to explore how weight lifting contributes to healing for persons with a trauma history. Forty-six persons (26 = women, 8 = men, 6 = nonbinary, 5 = transgender man, 1 = agender), recruited from a national sample of individuals, who identified as having experienced trauma and who engage in weight lifting, were individually interviewed. Data were analyzed using Charmaz's (2006) constructivist grounded theory strategies. Central themes revealed that past and current trauma experiences created relational and bodily disconnection fueled by hyper- or hypo-vigilance, impulsivity, and dysregulation. Weight lifting healed trauma through the felt sense of the mind-body connection, which created a healthier, more empowered, and connected trauma survivor. Study findings offer important insights to inform the development of trauma-informed gym spaces as well as the integration of weight lifting into trauma recovery programs.

Refining Kutta’s Flow over a Flat Plate: Necessary Conditions for Lift

In this paper, we present a variational theory of lift that, unlike Kutta’s theory, is derived from first principles in mechanics: Hertz’s principle of least curvature. In this theory, the unique value of circulation is determined by minimizing the Appellian of the flowfield. Interestingly, it recovers the Kutta condition in the special case of an airfoil with a sharp trailing edge. In this paper, we apply such a theory to the classical problem of the flow over a flat plate. The resulting ideal flow does not match Kutta’s solution in this case; it results in a nonlifting solution for any uncambered, fore-aft symmetric shape, confirming experimental findings in superfluids. This result provides necessary conditions for lift generation in an ideal fluid. For a real fluid over a flat plate with a sharp leading edge, viscosity plays an important role, leading to a flow separation at the leading edge, even at small angles of attack. This separation bubble creates asymmetry in the outer inviscid flowfield (outside the bubble), which enables lift. This problem is discussed in the light of the developed variational theory of lift and some historical details about the development of Kutta’s theory.

The Role of Abolishing Gravity in Ancient Egyptian Pyramids Architecture

The pyramids are one of the most important signs and witnesses of pharaonic architecture which they reflect the accuracy and craftsmanship of the Egyptians’ ancient ancestors. Historians relied on prognostication in explaining the construction methods and finding indicators that document this prognostication. In this research, it is believed that the use of primitive methods of lifting and pushing blocks is not commensurate with the genius and skill of workmanship of the way the pyramids were constructed as these methods are scientifically poor and measured in the current simple concept. Hence, it is necessary to search for unconventional building and stone lifting techniques that were compatible with the status of the ancient Egyptians and their scientific progress. This has always been the stimulus to look for the brilliance and simplicity of the pyramids’ structures at the same time. The starting point is that pushing stone blocks required extraordinary effort which is practically illogical. Firstly, according to the traditional theories that have so far discussed the construction of the pyramids, masses were supposed to be pushed on a slope with distances exceeding hundreds of meters. Secondly, this article examines a suggested method of the ancient Egyptians’ use the means of abolishing the Earth’s gravity to move and lift blocks with ease from the perspective of the theory of Acoustic Lifting. Thirdly, this article suggests another method that could have stood behind the ability to move the pyramids’ huge stones to place them in their right positions which is Water Lifting and using the Nawamis with reference to a well-studied model according to Pascal’s law.

О группе автоморфизмов алгебры плюральных чисел

The algebra of dual numbers was first introduced by V. K. Clifford in 1873. The algebras of plural and dual numbers are analogous to the algebra of complex numbers. Dual numbers form an algebra, but not a field, because only dual numbers with a real part not equal to zero have an inverse element. In this work, automorphisms of algebras of plural numbers, which are a generalization of the algebra of dual numbers, are studied. Algebras of plural numbers were in the center of attention of the professor of Kazan University A. P. Shirokov. Studying the geometry of higher-order tangent bundles, he established that higher-order tangent bundles over smooth manifolds have the structure of a smooth manifold over algebras of plural numbers. This allowed him in the 70s of the twentieth century to construct a theory of lifts of tensor fields and linear connections from a smooth manifold to its tangent bundles of arbitrary order. In this paper, we study automorphisms of the algebra of plural numbers. It is proved that the set of all automorphisms of the algebra of plural numbers forms a group. The structure of this group is described. The groups of automorphisms of the algebra of plural numbers with small dimension are indicated as examples.

$p$-adic equidistribution of CM points

Let X be a modular curve and consider a sequence of Galois orbits of CM points in X , whose p -conductors tend to infinity. Its equidistribution properties in X(\mathbf{C}) and in the reductions of X modulo primes different from p are well understood. We study the equidistribution problem in the Berkovich analytification X_{p}^{\operatorname{an}} of X_{\operatorname{Q}_{p}} . We partition the set of CM points of sufficiently high conductor in X_{\operatorname{Q}_{p}} into finitely many explicit basins B_{V} , indexed by the irreducible components V of the \bmod\text{-}p reduction of the canonical model of X . We prove that a sequence z_{n} of local Galois orbits of CM points with p -conductor going to infinity has a limit in X_{p}^{\operatorname{an}} if and only if it is eventually supported in a single basin B_{V} . If so, the limit is the unique point of X_{p}^{\operatorname{an}} whose mod- p reduction is the generic point of V . The result is proved in the more general setting of Shimura curves over totally real fields. The proof combines Gross's theory of quasi-canonical liftings with a new formula for the intersection numbers of CM curves and vertical components in a Lubin–Tate space.

Lifting for Simplicity: Concise Descriptions of Convex Sets

This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many convex sets have lifts that are dramatically simpler to describe than the original set. Finding such simple lifts has significant algorithmic implications, particularly for optimization problems. We consider both the classical case of polyhedral lifts, described by linear inequalities, as well as spectrahedral lifts, defined by linear matrix inequalities, with a focus on recent developments related to spectrahedral lifts. Given a convex set, ideally we would either like to find a (low-complexity) polyhedral or spectrahedral lift, or find an obstruction proving that no such lift is possible. To this end, we explain the connection between the existence of lifts of a convex set and certain structured factorizations of its associated slack operator. Based on this characterization, we describe a uniform approach, via sums of squares, to the construction of spectrahedral lifts of convex sets and illustrate the method on several families of examples. Finally, we discuss two flavors of obstruction to the existence of lifts: one related to facial structure, and the other related to algebraic properties of the set in question. Rather than being exhaustive, our aim is to illustrate the richness of the area. We touch on a range of different topics related to the existence of lifts, and present many examples of lifts from different areas of mathematics and its applications.

A variational theory of lift

In this paper we revive a special, less-common, variational principle in analytical mechanics (Hertz’ principle of least curvature) to develop a novel variational analogue of Euler's equations for the dynamics of an ideal fluid. The new variational formulation is fundamentally different from those formulations based on Hamilton's principle of least action. Using this new variational formulation, we generalize the century-old problem of the flow over a two-dimensional body; we developed a variational closure condition that is, unlike the Kutta condition, derived from first principles. The developed variational principle reduces to the classical Kutta–Zhukovsky condition in the special case of a sharp-edged airfoil, which challenges the accepted wisdom about the Kutta condition being a manifestation of viscous effects. Rather, we found that it represents conservation of momentum. Moreover, the developed variational principle provides, for the first time, a theoretical model for lift over smooth shapes without sharp edges where the Kutta condition is not applicable. We discuss how this fundamental divergence from current theory can explain discrepancies in computational studies and experiments with superfluids.

Gender stereotypes: implicit threat to performance or boost for motivational aspects in primary school?

Based on stereotype threat and stereotype lift theory, this study explores implicit stereotype threat effects of gender stereotypes on the performance of primary school children in mathematics. Moreover, effects of implicit gender stereotypical cues (gender-specific task material) on motivational aspects were explored, which have revealed mixed results in stereotype threat research in the past. N = 151 German primary school children (47.7% female; mean age: M = 9.81, SD = 0.60) calculated either stereotypical or neutral mathematical text problems before motivational aspects were assessed. Contradicting our expectations, results neither revealed a stereotype threat effect on girls’ performance nor a lift effect on the boys. Instead, girls calculating stereotypical tasks outperformed girls in the control group, whereas boys’ performance did not significantly differ compared to the control group. Regarding motivational aspects, only traditional gender differences emerged as girls reported significantly more pressure and tension calculating the mathematical tasks. The discussion focuses on the way in which stereotypes can affect children’s cognitive performance and in turn, their mathematical performance.

Flow-induced periodic snap-through dynamics

Abstract

Анкетирование как средство реализации системного подхода в исследовании проблемных аспектов теории и практики атлетизма на примере гиревого спорта

An online questionnaire survey of leading kettlebell coaches allowed us to significantly expand the number of respondents and, most importantly, to track their point of view on the following aspects of the training process of kettlebell lifting: 1) the degree of significance and optimal ratio of volumes of general physical and special managerial training as structural elements of the system of the training process; 2) use of simulators as a means of increasing the effectiveness of special physical training in the system of the training process; 3) there is a paradoxical contradic-tion between a low degree of theoretical knowledge and a high degree of practical demand for scientific justification and systematic study of the role and significance of the pace of performance of competitive exercises in order to increase their effectiveness; 4) the need for personal correction rate in accordance with the characteristics of individual motor skills of the athlete. The survey allowed us to conceptually decide on the direction of further research in the field of theory and practice of kettlebell lifting.

Aerodynamic analysis and structural integrity for optimal performance of sweeping and spanning morphing unmanned air vehicles

An optimized morphing unmanned aerial vehicle capable of sweeping and spanning its wings is proposed and analyzed aerodynamically and structurally in order to examine and improve its efficiency, flight transition analysis, and structural integrity. The lift to drag ratio of five different flight modes of the drone is examined using the Pollhamus lift theory to evaluate the aerodynamic performance during the transition phases. To verify Pollhamus lift theory in the determination of the aerodynamic loads for the four configurations of the morphing unmanned system, namely, fully compressed, fully expanded, fully swept, and fully expanded and swept, 3D panel and Vortex Lattice Methods are used. In order to improve the structural stability during the transition phase of the flight, a finite element analysis is conducted to approximate pressures on the wings of the unmanned system under a load and specific boundary conditions. The information from the finite element simulations is then utilized to determine the number of support rods needed for structural stability and the ideal positions of the rods. The vibratory qualities of the wings are also analyzed through modal and transient analyses. According to the results of the modal analysis, because of the low natural frequency of the wing, there is a strong possibility of flutter and a vibratory response due to the aerodynamic force and disturbances. The transient analysis demonstrates that the stress waves propagating through the wings, due to an excitation force, tend to localize around the circumference of the support rods.

The universal steady lift and drag theory and the physical origin of lift

Since the birth of modern aerodynamics, various theories on lift and drag have been developed and validated extensively in aeronautical applications. However, the far-field force theory had long remained at low-speed incompressible flow. Based on the analytical solutions of the linearized Navier-Stokes equations in the steady far field, the authors and their collaborators extended the classic Kutta-Joukowski lift theorem to both two- and three-dimensional viscous and compressible flows, and thus filled the long-standing gap in theoretical aerodynamics. Why can the simple formulas based on linearized approximation still be accurately valid for highly nonlinear complex flows? This issue of great interest involves the methodological characteristics and physical mechanism behind the unified force theory and is the first task of this article. Moreover, there has been an abnormal phenomenon regarding the physical origin of lift that, despite the already mature and fully verified rigorous lift theory, various different hypotheses still keep surfacing frequently in various nonscientific publications and media. This indicates that the issue is really complicated and has not been thoroughly clarified in textbooks, monographs, and classrooms around the world. Now, the universality and high conciseness of the unified theory enable one to reach a clear answer to this issue by rigorous logical arguments in the most direct way. This is the second task of this article.

Canonical lifts and $$\delta $$-structures

We extend the Serre–Tate theory of canonical lifts of ordinary abelian varieties to arbitrary unpolarised families of ordinary abelian varieties parameterised by a p-adic formal scheme S. We show that the canonical lift is the unique lift to W(S) which admits a $$\delta $$ -structure in the sense of Joyal, Buium, and Bousfield. We prove analogous statements for families of ordinary p-groups and p-divisible groups.

Influence of Piezoelectric Performance on Nonlinear Dynamic Characteristics of MFC Shells

Based on the structures of unmanned aerial vehicle (UAV) wings, nonlinear dynamic analysis of macrofiber composite (MFC) laminated shells is presented in this paper. The effects of piezoelectric properties and aerodynamic forces on the dynamic stability of the MFC laminated shell are studied. Firstly, under the flow condition of ideal incompressible fluid, the thin airfoil theory is employed to calculate the effects of the mean camber line to obtain the circulation distribution of the wings in subsonic air flow. The steady aerodynamic lift on UAV wings is derived by using the Kutta–Joukowski lift theory. Then, considering the geometric nonlinearity and piezoelectric properties of the MFC material, the nonlinear dynamic model of the MFC laminated shell is established with Hamilton’s principles and the Galerkin method. Next, the effects of electric field, external excitation force, and nonlinear parameters on the stability of the system are studied under 1 : 1 internal resonance and the effects of material parameters on the natural frequency of the structure are also analyzed. Furthermore, the influence of the aerodynamic forces and electric field on the nonlinear dynamic responses of MFC laminated shells is discussed by numerical simulation. The results indicate that the electric field and external excitation have great influence on the structural dynamic responses.

Stable, Planar Self Propulsion Using a Hinged Flap

This paper discusses planar self-propelled motion of a primary body in water generated by using a hinged flap at its trailing edge. The coupled dynamic model incorporates unsteady loads based on Theodorsen’s unsteady lifting theory for sinusoidal flapping at a given reduced frequency and tailored for their application within the framework of the body motion. Numerical simulations and stability analysis are provided for an example based on the geometry of the saithe or pollock.

To the theory of particle lifting by terrestrial and Martian dust devils

The combined Rankine vortex model is applied to describe the radial profile of azimuthal velocity in atmospheric dust devils, and a simplified model version is proposed of the turbulent surface boundary layer beneath the Rankine vortex periphery that corresponds to the potential vortex. Based on the results by Burggraf et al. (1971), it is accepted that the radial velocity near the ground in the potential vortex greatly exceeds the azimuthal velocity, which makes tractable the problem of the surface shear stress determination, including the case of the turbulent surface boundary layer. The constructed model explains exceeding the threshold shear velocity for aeolian transport in typical dust-devil vortices both on Earth and on Mars.

Nonlinear dynamical behaviors of deploying wings in subsonic air flow

In recent years, the morphing wing, which is able to improve the lift–drag characteristics of the aircraft by changing wingspans and aspect ratios, has become a popular research issue. However, aeroelasticity is still a bottleneck for the development of morphing wings. The development of the aerodynamic calculations of deploying wings in subsonic air flow will be further promoted by this research. In this paper, we consider the aerodynamics of a deploying wing and investigate the nonlinear dynamic behaviors of the deploying wing. Under the flow condition of ideal incompressible fluid, the flow field is a potential field and the potential function must satisfy the Laplace linear equation and the superposition principle. When the thickness, curvature and angle of attack of the airfoil are small, the thin airfoil theory can be used to calculate the effects of the mean camber line to obtain the circulation distribution of the deploying wings in subsonic air flow. The steady aerodynamic lift on the deploying wing is derived by using the Kutta–Joukowski lift theory. Then, the aerodynamic lift is applied on a deploying wing, which is modeled as a cantilevered thin shell deploying in the axial direction. The nonlinear partial differential governing equations of motion for the deploying cantilevered thin shell subjected to the aerodynamic force in subsonic air flow are established based on Hamilton’s principle. The time-varying dependent vibration mode-shape functions are chosen using the boundary conditions, and then the Galerkin method is employed to transform the partial differential equation into two time-varying nonlinear ordinary differential equations. Numerical simulations are performed for the nonlinear dynamic responses of the deploying wing subjected to the aerodynamic force, and then the influence of different parameters, including the extending velocity and disturbance velocity, on the stability of the wing are analyzed. The effects of deploying velocities on the nonlinear vibrations of the first-order and second-order modes for the deploying wing are studied.

Dimension formulas of paramodular forms of squarefree level and comparison with inner twist

In this paper, we give an explicit dimension formula for the spaces of Siegel paramodular cusp forms of degree two of squarefree level. As an application, we propose a conjecture on symplectic group version of Eichler–Jacquet–Langlands type correspondence. It is a generalization of the previous conjecture of the first named author for prime levels published in 1985, where inner twists corresponding to binary quaternion hermitian forms over definite quaternion algebras were treated. Our present study contains also the case of indefinite quaternion algebras. Additionally, we give numerical examples of $L$ functions which support the conjecture. These comparisons of dimensions and examples give also evidence for conjecture on a certain precise lifting theory. This is related to the lifting theory from pairs of elliptic cusp forms initiated by Y. Ihara in 1964 in the case of compact twist, but no such construction is known in the case of non-split symplectic groups corresponding to quaternion hermitian groups over indefinite quaternion algebras and this is new in that sense.