scholarly journals Two-dimensional pulse dynamics and the formation of bound states on electrified falling films

2018 ◽  
Vol 855 ◽  
pp. 210-235 ◽  
Author(s):  
M. G. Blyth ◽  
D. Tseluiko ◽  
T.-S. Lin ◽  
S. Kalliadasis
Keyword(s):  
Electric Field ◽  
Bound States ◽  
Stokes Equations ◽  
Travelling Waves ◽  
Film Surface ◽  
Wave Model ◽  
Bound State ◽  
Long Wave ◽  
Finite Set ◽  
Solitary Pulse

The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.

scholarly journals Comment on: “Some quantum aspects of a particle with electric quadrupole moment interacting with an electric field subject to confining potentials”

2020 ◽  
Vol 35 (25) ◽  
pp. 2075002
Author(s):  
Francisco M. Fernández
Keyword(s):  
Electric Field ◽  
Quadrupole Moment ◽  
Bound States ◽  
Electric Quadrupole ◽  
Bound State ◽  
Electric Quadrupole Moment ◽  
Bound State Spectrum ◽  
Moving Particle ◽  
Quantum Aspects

We analyze the results obtained from a model consisting of the interaction between the electric quadrupole moment of a moving particle and an electric field. We argue that the system does not support bound states because the motion along the [Formula: see text] axis is unbounded. It is shown that the author obtains a wrong bound-state spectrum for the motion in the [Formula: see text] plane and that the existence of allowed cyclotron frequencies is an artifact of the approach.

Periodic travelling waves for a generalized long wave model

2015 ◽  
Vol 9 ◽  
pp. 6747-6756
Author(s):  
Alex M. Montes ◽  
Ricardo Cordoba
Keyword(s):  
Travelling Waves ◽  
Wave Model ◽  
Long Wave

scholarly journals Internal waves in marginally stable abyssal stratified flows

2018 ◽  
Author(s):  
Nikolay I. Makarenko ◽  
Janna L. Maltseva ◽  
Eugene G. Morozov ◽  
Roman Y. Tarakanov ◽  
Kseniya A. Ivanova
Keyword(s):  
Internal Waves ◽  
Travelling Waves ◽  
Fluid Flows ◽  
Wave Model ◽  
Velocity Shear ◽  
Interfacial Velocity ◽  
Long Wave ◽  
Scaling Procedure ◽  
Upstream Flow ◽  
Exponential Stratification

Abstract. The problem on internal waves in a weakly stratified two-layered fluid is studied semi-analytically. We discuss the 2.5-layer fluid flows with exponential stratification of both layers. The long-wave model describing travelling waves is constructed by means of scaling procedure with a small Boussinesq parameter. It is demonstrated that solitary wave regimes can be affected by the Kelvin–Helmholtz instability arising due to interfacial velocity shear in upstream flow.

scholarly journals Internal waves in marginally stable abyssal stratified flows

2018 ◽  
Vol 25 (3) ◽  
pp. 659-669 ◽  
Author(s):  
Nikolay Makarenko ◽  
Janna Maltseva ◽  
Eugene Morozov ◽  
Roman Tarakanov ◽  
Kseniya Ivanova
Keyword(s):  
Internal Waves ◽  
Travelling Waves ◽  
Fluid Flows ◽  
Wave Model ◽  
Velocity Shear ◽  
Interfacial Velocity ◽  
Long Wave ◽  
Scaling Procedure ◽  
Upstream Flow ◽  
Exponential Stratification

Abstract. The problem on internal waves in a weakly stratified two-layer fluid is studied semi-analytically. We discuss the 2.5-layer fluid flows with exponential stratification of both layers. The long-wave model describing travelling waves is constructed by means of a scaling procedure with a small Boussinesq parameter. It is demonstrated that solitary-wave regimes can be affected by the Kelvin–Helmholtz instability arising due to interfacial velocity shear in upstream flow.

scholarly journals The Morbid Equation of Quantum Numbers

2021 ◽  
Author(s):  
XD Dongfang
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Bound States ◽  
Valence Electron ◽  
Coulomb Field ◽  
Bound State ◽  
Quantum Model ◽  
Conservation Of Energy ◽  
Quantum Numbers ◽  
The Law

The quantum model of valence electron generation orbital penetration of alkali metal elements with unique stable structure is investigated. The electric field outside the atomic kernel is usually expressed by the Coulomb field of the point charge mode, and the composite electric field in atomic kernel can be equivalent to the electric field inside the sphere with uniform charge distribution or other electric fields without divergence point. The exact solutions of two Schrödinger equations for the bound state of the Coulomb field outside the atom and the binding state of the equivalent field inside the atom determine two different quantization energy formulas respectively. Here we show that the atomic kernel surface is the only common zero potential surface that can be selected. When the orbital penetration occurs, the law of conservation of energy requires that the energy level formulas of the two bound states must have corresponding quantum numbers to make them equal. As a result, there is no solution to the quantum number equation, indicating that the two quantum states of the valence electron are incompatible. This irreconcilable contradiction shows that the quantized energy of quantum mechanics cannot absolutely satisfy the law of conservation of energy.

Hydrodynamic bound states of a low-Reynolds-number swimmer near a gap in a wall

2010 ◽  
Vol 667 ◽  
pp. 309-335 ◽  
Author(s):  
DARREN CROWDY ◽  
OPHIR SAMSON
Keyword(s):  
Dynamical System ◽  
Reynolds Number ◽  
Bound States ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Equilibrium Points ◽  
Analytical Form ◽  
Bound State ◽  
Theoretical Predictions ◽  
Low Reynolds

The motion of an organism swimming at low Reynolds number near an infinite straight wall with a finite-length gap is studied theoretically within the framework of a two-dimensional model. The swimmer is modelled as a point singularity of the Stokes equations dependent on a single real parameter. A dynamical system governing the position and orientation of the model swimmer is derived in analytical form. The dynamical system is studied in detail and a bifurcation analysis performed. The analysis reveals,inter alia, the presence of stable equilibrium points in the gap region as well as Hopf bifurcations to periodic bound states. The reduced-model system also exhibits a global gluing bifurcation in which two symmetric periodic orbits merge at a saddle point into symmetric ‘figure-of-eight’ bound states having more complex spatiotemporal structure. The additional effect of a background shear is also studied and is found to introduce new types of bound state. The analysis allows us to make theoretical predictions as to the possible behaviour of a low-Reynolds-number swimmer near a gap in a wall. It offers insights into the use of gaps or orifices as possible control devices for such swimmers in confined environments.

scholarly journals Revisiting Surface-Subsurface Exchange at Intertidal Zone with a Coupled 2D Hydrodynamic and 3D Variably-Saturated Groundwater Model

Water ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 902
Author(s):  
Zhi Li ◽  
Ben R. Hodges
Keyword(s):  
Intertidal Zone ◽  
Coastal Wetlands ◽  
High Performance ◽  
Stokes Equations ◽  
Wave Model ◽  
Surface Flow ◽  
Richards Equation ◽  
Navier Stokes ◽  
Dynamic Surface ◽  
Flow Equations

A new high-performance numerical model (Frehg) is developed to simulate water flow in shallow coastal wetlands. Frehg solves the 2D depth-integrated, hydrostatic, Navier–Stokes equations (i.e., shallow-water equations) in the surface domain and the 3D variably-saturated Richards equation in the subsurface domain. The two domains are asynchronously coupled to model surface-subsurface exchange. The Frehg model is applied to evaluate model sensitivity to a variety of simplifications that are commonly adopted for shallow wetland models, especially the use of the diffusive wave approximation in place of the traditional Saint-Venant equations for surface flow. The results suggest that a dynamic model for momentum is preferred over diffusive wave model for shallow coastal wetlands and marshes because the latter fails to capture flow unsteadiness. Under the combined effects of evaporation and wetting/drying, using diffusive wave model leads to discrepancies in modeled surface-subsurface exchange flux in the intertidal zone where strong exchange processes occur. It indicates shallow wetland models should be built with (i) dynamic surface flow equations that capture the timing of inundation, (ii) complex topographic features that render accurate spatial extent of inundation, and (iii) variably-saturated subsurface flow solver that is capable of modeling moisture change in the subsurface due to evaporation and infiltration.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

Numerical Investigation of the Coulter Principle in a Microfluidic Device

2013 ◽  
Author(s):  
Muheng Zhang ◽  
Yongsheng Lian
Keyword(s):  
Electric Field ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Working Mechanism ◽  
Navier Stokes Equations ◽  
Sheath Flow ◽  
Coulter Counters ◽  
Pass Through ◽  
Cell Motion

Coulter counters are analytical microfluidic instrument used to measure the size and concentration of biological cells or colloid particles suspended in electrolyte. The underlying working mechanism of Coulter counters is the Coulter principle which relies on the fact that when low-conductive cells pass through an electric field these cells cause disturbances in the measurement (current or voltage). Useful information about these cells can be obtained by analyzing these disturbances if an accurate correlation between the measured disturbances and cell characteristics. In this paper we use computational fluid dynamics method to investigate this correlation. The flow field is described by solving the Navier-Stokes equations, the electric field is represented by a Laplace’s equation in which the conductivity is calculated from the Navier-Stokes equations, and the cell motion is calculated by solving the equations of motion. The accuracy of the code is validated by comparing with analytical solutions. The study is based on a coplanar Coulter counter with three inlets that consist of two sheath flow inlet and one conductive flow inlet. The effects of diffusivity, cell size, sheath flow rate, and cell geometry are discussed in details. The impacts of electrode size, gap between electrodes and electrode location on the measured distribution are also studied.

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