scholarly journals General Formulation of a Perturbation Theory for Unsteady Cavity Flows

1965 ◽  
Vol 87 (4) ◽  
pp. 1006-1010 ◽  
Author(s):  
D. P. Wang ◽  
T. Yao-Tsu Wu
Keyword(s):  
Free Field ◽  
Cavity Flow ◽  
Present Theory ◽  
Unsteady Motion ◽  
Centrifugal Acceleration ◽  
Cavity Boundary ◽  
Classical Gravity ◽  
Potential Vortex ◽  
Fundamental Formulation

The problem of a two-dimensional cavity flow of an ideal fluid with small unsteady disturbances in a gravity free field is considered. By regarding the unsteady motion as a small-perturbation of an established steady cavity flow, a fundamental formulation of the problem is presented. It is shown that the unsteady disturbance generates a surface wave propagating downstream along the free cavity boundary, much in the same way as the classical gravity waves in water, only with the centrifugal acceleration owing to the curvature of the streamlines in the basic flow playing the role of an equivalent gravity effect. As a particularly simple example, the surface waves in a hollow potential vortex flow is calculated using the present theory.

scholarly journals Stabilizing electrodeposition in elastic solid electrolytes containing immobilized anions

2016 ◽  
Vol 2 (7) ◽  
pp. e1600320 ◽  
Author(s):  
Mukul D. Tikekar ◽  
Lynden A. Archer ◽  
Donald L. Koch
Keyword(s):  
Elastic Solid ◽  
Present Theory ◽  
Metal Electrode ◽  
Mitigation Strategies ◽  
Factors Affecting ◽  
Wide Range ◽  
Current Densities ◽  
Morphological Instabilities ◽  
The Stability

Ion transport–driven instabilities in electrodeposition of metals that lead to morphological instabilities and dendrites are receiving renewed attention because mitigation strategies are needed for improving rechargeability and safety of lithium batteries. The growth rate of these morphological instabilities can be slowed by immobilizing a fraction of anions within the electrolyte to reduce the electric field at the metal electrode. We analyze the role of elastic deformation of the solid electrolyte with immobilized anions and present theory combining the roles of separator elasticity and modified transport to evaluate the factors affecting the stability of planar deposition over a wide range of current densities. We find that stable electrodeposition can be easily achieved even at relatively high current densities in electrolytes/separators with moderate polymer-like mechanical moduli, provided a small fraction of anions are immobilized in the separator.

scholarly journals Cavity Detachment from a Wedge with Rounded Edges and the Surface Tension Effect

2021 ◽  
Vol 9 (11) ◽  
pp. 1253
Author(s):  
Yuriy N. Savchenko ◽  
Georgiy Y. Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Surface Tension ◽  
Weber Number ◽  
Solution Process ◽  
Cavity Flow ◽  
Surface Tension Effect ◽  
Force Coefficient ◽  
Hodograph Method ◽  
Wide Range ◽  
Critical Weber Number ◽  
Cavity Boundary

Cavity flow around a wedge with rounded edges was studied, taking into account the surface tension effect and the Brillouin–Villat criterion of cavity detachment. The liquid compressibility and viscosity were ignored. An analytical solution was obtained in parametric form by applying the integral hodograph method. This method gives the possibility of deriving analytical expressions for complex velocity and for potential, both defined in a parameter plane. An expression for the curvature of the cavity boundary was obtained analytically. By using the dynamic boundary condition on the cavity boundary, an integral equation in the velocity modulus was derived. The particular case of zero surface tension is a special case of the solution. The surface tension effect was computed over a wide range of the Weber number for various degrees of cavitation development. Numerical results are presented for the flow configuration, the drag force coefficient, and the position of cavity detachment. It was found that for each radius of the edges, there exists a critical Weber number, below which the iterative solution process fails to converge, so a steady flow solution cannot be computed. This critical Weber number increases as the radius of the edge decreases. As the edge radius tends to zero, the critical Weber number tends to infinity, or a steady cavity flow cannot be computed at any finite Weber number in the case of sharp wedge edges. This shows some limitations of the model based on the Brillouin–Villat criterion of cavity detachment.

scholarly journals Thrust Force Generated by Heaving Motion of a Plate: The Role of Vortex-Induced Force

2021 ◽  
Author(s):  
Kazuo Matsuuchi
Keyword(s):  
Vortex Shedding ◽  
Thrust Force ◽  
Unsteady Motion ◽  
Force Generation ◽  
Thrust Coefficient ◽  
Momentum Change ◽  
Vortex Element ◽  
Motion Characteristics ◽  
Vortex Systems

To understand the force acting on birds, insects, and fish, we take heaving motion as a simple example. This motion might deviate from the real one. However, since the mechanism of force generation is the vortex shedding due to the motion of an object, the heaving motion is important for understanding the force generated by unsteady motion. The vortices released from the object are closely related to the motion characteristics. To understand the force acting on an object, information about momentum change is necessary. However, in vortex systems, it is impossible to estimate the usual momentum. Instead of the momentum, the “virtual momentum,” or the impulse, is needed to generate the force. For calculating the virtual momentum, we traced all vortices over a whole period, which was carried out by using the vortex-element method. The force was then calculated based on the information on the vortices. We derived the thrust coefficient as a function of the ratio of the heaving to travelling velocity.

The Beneficial Role of Piles on the Seismic Loading of Structures

2019 ◽  
Vol 35 (3) ◽  
pp. 1141-1162 ◽  
Author(s):  
Maria Iovino ◽  
Raffaele Di Laora ◽  
Emmanouil Rovithis ◽  
Luca de Sanctis
Keyword(s):  
Seismic Waves ◽  
Rapid Assessment ◽  
Free Field ◽  
Dimensionless Frequency ◽  
Fe Model ◽  
Soil Stiffness ◽  
Interaction Factor ◽  
Power Law Function ◽  
Pile Length

We examine the kinematic response of fixed-head vertical floating piles embedded in continuously nonhomogeneous soils and subjected to upward propagating seismic waves. The problem is explored numerically by means of a rigorous finite element (FE) model of the soil-pile system to quantify the kinematically induced reduction of the horizontal free-field spectral acceleration. Soil stiffness varies continuously with depth according to a generalized power law function. We show that kinematic pile response in the harmonic regime is controlled by a unique dimensionless frequency parameter involving the active pile length in a generalized nonhomogeneous soil. A new, simplified expression for the horizontal kinematic interaction factor Iu is proposed for practical time-domain applications while a novel physical interpretation of the filtering action of piles is reported by introducing the role of pile stiffness in averaging soil motion over an effective pile length. Following a parametric study under transient motion, we propose a set of novel, ready-to-use formulae for a rapid assessment of the pile-induced filtering action. An application of the proposed formulae to clayey soils is finally presented, leading to useful indications for the selection of the pile diameter associated with the maximum filtering potential.

scholarly journals Antisymmetric tensor gauge fields on S4

2004 ◽  
Vol 82 (7) ◽  
pp. 541-548
Author(s):  
D.G.C. McKeon
Keyword(s):  
Field Model ◽  
Free Field ◽  
Flat Space ◽  
Antisymmetric Tensor ◽  
Gauge Fields ◽  
Scalar Model ◽  
Abelian Gauge ◽  
Five Dimensions ◽  
Higher Dimensional

Antisymmetric tensor gauge fields ϕab(η) are formulated on the surface of a sphere S4(η2 = a2) embedded in five dimensions. Such compact manifolds occur in the dimensional reduction of higher dimensional spaces that naturally occur in string theories. The free field model is equivalent to a scalar model on this sphere. Interactions with gauge fields are discussed. It is feasable to formulate models for interactions with U(1) gauge fields Aa(η) that are akin to those of Freedman and Townsend in flat space. In addition, it proves possible to have a novel interaction of ϕab with Aa and a spinor field Ψ(η) on S4 with both Abelian and non-Abelian gauge invariance. In these models, Aa plays the role of a Stueckelberg field.PACS No.: 11.30.Ly

scholarly journals Exact expressions for n-point maximal U(1)Y-violating integrated correlators in SU(N) $$ \mathcal{N} $$ = 4 SYM

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Daniele Dorigoni ◽  
Michael B. Green ◽  
Congkao Wen
Keyword(s):  
Modular Forms ◽  
Free Field ◽  
Perturbation Expansion ◽  
Flat Space ◽  
Low Energy ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Infinite Sums

Abstract The exact expressions for integrated maximal U(1)Y violating (MUV) n-point correlators in SU(N) $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory are determined. The analysis generalises previous results on the integrated correlator of four superconformal primaries and is based on supersymmetric localisation. The integrated correlators are functions of N and τ = θ/(2π) + 4πi/$$ {g}_{YM}^2 $$ g YM 2 , and are expressed as two-dimensional lattice sums that are modular forms with holomorphic and anti-holomorphic weights (w, −w) where w = n − 4. The correlators satisfy Laplace-difference equations that relate the SU(N+1), SU(N) and SU(N−1) expressions and generalise the equations previously found in the w = 0 case. The correlators can be expressed as infinite sums of Eisenstein modular forms of weight (w, −w). For any fixed value of N the perturbation expansion of this correlator is found to start at order ($$ {g}_{YM}^2 $$ g YM 2 N)w. The contributions of Yang-Mills instantons of charge k > 0 are of the form qkf(gYM), where q = e2πiτ and f(gYM) = O($$ {g}_{YM}^{-2w} $$ g YM − 2 w ) when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Anti-instanton contributions have charge k < 0 and are of the form $$ {\overline{q}}^{\left|k\right|}\hat{f}\left({g}_{YM}\right) $$ q ¯ k f ̂ g YM , where $$ \hat{f}\left({g}_{YM}\right)=O\left({g}_{YM}^{2w}\right) $$ f ̂ g YM = O g YM 2 w when $$ {g}_{YM}^2 $$ g YM 2 ≪ 1. Properties of the large-N expansion are in agreement with expectations based on the low energy expansion of flat-space type IIB superstring amplitudes. We also comment on the identification of n-point free-field MUV correlators with the integrands of (n − 4)-loop perturbative contributions to the four-point correlator. In particular, we emphasise the important rôle of SL(2, ℤ)-covariance in the construction.

Proton semiconductors and energy transduction in biological systems

1978 ◽  
Vol 235 (3) ◽  
pp. R99-R114 ◽  
Author(s):  
H. J. Morowitz
Keyword(s):  
Proton Transport ◽  
Hydrogen Transfer ◽  
Atp Synthesis ◽  
Present Theory ◽  
Energy Transduction ◽  
Ion Concentration ◽  
Hydrogen Ions ◽  
Detailed Model ◽  
Hydrogen Ion Concentration

Energy transduction processes in biology are analyzed in terms of ordered chains of hydrogen bonds. The theory is an extension of studies on proton conductance in ice and is stimulated by current ideas on the role of hydrogen ions in oxidative phosphorylation and photophosphorylation. The possibility of a protochemistry paralleling electrochemistry is presented along with experimental evidence. The theory relating transmembrane electrochemical potential difference of hydrogen ion concentration to the synthesis of ATP is reviewed. The thermodynamics of hydrogen transfer across a membrane is treated including electrochemical and electromechanical factors. As a prelude to considering ATP synthesis, the acid-base dissociation reactions of ATP, ADP, and phosphate are analyzed. The thermodynamics of ATP synthesis is discussed and a detailed model is presented coupling the synthesis to proton transport. The model assumes a gated proton semiconductor that carries protons and allows them to interact specifically with well-defined substrate molecules. The physics of proton transport is outlined and various methods examined in the context of biological membranes. Emphasis is placed on solid-state proton semiconductors and the present theory of such structures is given. A section is included on possible biological applications of these semiconductors.

scholarly journals 3D study of centrifugal acceleration in isotropic photon fields

2019 ◽  
Vol 28 (11) ◽  
pp. 1950141
Author(s):  
G. G. Bakhtadze ◽  
V. I. Berezhiani ◽  
Z. Osmanov
Keyword(s):  
Magnetic Field ◽  
Single Particle ◽  
Stable Equilibrium ◽  
Charged Particles ◽  
Relativistic Dynamics ◽  
Centrifugal Acceleration ◽  
Study Behavior ◽  
Field Lines ◽  
Particle Approach

In this paper, we study relativistic dynamics of charged particles corotating with prescribed trajectories, having the shape of dipolar magnetic field lines. In particular, we consider the role of the drag force caused by the photon field the forming of equilibrium positions of the charged particles. Alongside a single particle approach, we also study behavior of ensemble of particles in the context of stable positions. As we have shown, the together they create surfaces where particles are at stable equilibrium positions. In this paper, we examine these shapes and study parameters they depend on. It has been found that under certain conditions, there are two distinct surfaces with stable equilibrium positions.

scholarly journals Role of the tip vortex in the force generation of low-aspect-ratio normal flat plates

2007 ◽  
Vol 581 ◽  
pp. 453-468 ◽  
Author(s):  
MATTHEW J. RINGUETTE ◽  
MICHELE MILANO ◽  
MORTEZA GHARIB
Keyword(s):  
Aspect Ratio ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Unsteady Motion ◽  
Tip Vortex ◽  
Flat Plates ◽  
Low Aspect Ratio ◽  
Start Up ◽  
Image Velocimetry

We investigate experimentally the force generated by the unsteady vortex formation of low-aspect-ratio normal flat plates with one end free. The objective of this study is to determine the role of the free end, or tip, vortex. Understanding this simple case provides insight into flapping-wing propulsion, which involves the unsteady motion of low-aspect-ratio appendages. As a simple model of a propulsive half-stroke, we consider a rectangular normal flat plate undergoing a translating start-up motion in a towing tank. Digital particle image velocimetry is used to measure multiple perpendicular sections of the flow velocity and vorticity, in order to correlate vortex circulation with the measured plate force. The three-dimensional wake structure is captured using flow visualization. We show that the tip vortex produces a significant maximum in the plate force. Suppressing its formation results in a force minimum. Comparing plates of aspect ratio six and two, the flow is similar in terms of absolute distance from the tip, but evolves faster for aspect ratio two. The plate drag coefficient increases with decreasing aspect ratio.

The Role of Eigensolutions in Nonlinear Inverse Cavity-Flow Theory

1988 ◽  
Vol 110 (3) ◽  
pp. 315-324
Author(s):  
B. R. Parkin
Keyword(s):  
Inverse Problem ◽  
Free Surface ◽  
Direct Problem ◽  
Cavity Flow ◽  
Cavitation Number ◽  
The Novel ◽  
Cavity Shape ◽  
Linearized Theory ◽  
Exact Point

The method of Levi Civita is applied to an isolated fully cavitating body at zero cavitation number and adapted to the solution of the inverse problem in which one prescribes the pressure distribution on the wetted surface and then calculates the shape. The novel feature of this work is the finding that the exact theory admits the existence of a “point drag” function or eigensolution. While this fact is of no particular importance in the classical direct problem, we already know from the linearized theory that the eigensolution plays an important role. In the present discussion, the basic properties of the exact “point-drag” solution are explored under the simplest of conditions. In this way, complications which arise from non-zero cavitation numbers, free surface effects, or cascade interactions are avoided. The effects of this simple eigensolution on hydrodynamic forces and cavity shape are discussed. Finally, we give a tentative example of how this eigensolution might be used in the design process.

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