Adhesion of lipid tubules in an assembly

1998 ◽  
Vol 9 (5) ◽  
pp. 485-506 ◽  
Author(s):  
RICCARDO ROSSO ◽  
EPIFIANO G. VIRGA
Keyword(s):  
Surface Tension ◽  
External Field ◽  
Equilibrium Problem ◽  
Biological Systems ◽  
Critical Value ◽  
Stability Diagram ◽  
Energy Functional ◽  
Highly Nonlinear ◽  
The Stability ◽  
Lipid Tubules

We study a unilateral equilibrium problem for the energy functional of a lipid tubule subject to an external field. These tubules, which constitute many biological systems, may form assemblies when they are brought in contact, and so made to adhere to one another along at interstices. The contact energy is taken to be proportional to the area of contact through a constant, which is called the adhesion potential. This competes against the external field in determining the stability of patterns with flat interstices. Though the equilibrium problem is highly nonlinear, we determine explicitly the stability diagram for the adhesion between tubules. We conclude that the higher the field, the lower the adhesion potential needed to make at interstices energetically favourable, though its critical value depends also on the surface tension of the interface between the tubules and the isotropic fluid around them.

The stability of a strut under thrust, when buckling is resisted by a force proportional to the displacement

1926 ◽  
Vol 23 (2) ◽  
pp. 120-129 ◽  
Author(s):  
S. Goldstein
Keyword(s):  
Surface Tension ◽  
Solid Surface ◽  
Wave Length ◽  
Critical Value ◽  
Breaking Stress ◽  
Surface Films ◽  
The Earth ◽  
Solid Film ◽  
Rough Calculation ◽  
The Stability

For a strut under thrust when buckling is resisted by a force proportional to the displacement, it is shown that for both a clamped and a pinned strut there is stability for any length when the thrust is less than a certain critical value; and the relation is found between the length and the first value of the thrust above this that will give buckling. A notion of the wave-length and number of nodes after buckling is obtained.The results are applied to the theory of the formation of mountains by horizontal compression, and it is shown that the crust of the earth would be able to transmit, without buckling, stresses right up to the breaking stress across regions of continental extent, unless the depth down to the level of no strain were less than 16 metres.An attempt is made to employ the results also to consider the stability of solid surface films under compression, and it is seen that other factors, making for stability, must enter besides rigidity and gravity. This is supplied by surface tension, and it then appears that collapse due to a weakness in the film must precede buckling.A rough calculation is given of the frequency of vibration of an atom in a solid film.

Viscous potential flow analysis of Kelvin–Helmholtz instability in a channel

2001 ◽  
Vol 445 ◽  
pp. 263-283 ◽  
Author(s):  
T. FUNADA ◽  
D. D. JOSEPH
Keyword(s):  
Surface Tension ◽  
Critical Velocity ◽  
Potential Flow ◽  
Critical Value ◽  
Neutral Curve ◽  
Shear Stresses ◽  
Inviscid Fluid ◽  
Neutral Stability ◽  
Viscous Potential Flow ◽  
The Stability

We study the stability of stratified gas–liquid flow in a horizontal rectangular channel using viscous potential flow. The analysis leads to an explicit dispersion relation in which the effects of surface tension and viscosity on the normal stress are not neglected but the effect of shear stresses is. Formulas for the growth rates, wave speeds and neutral stability curve are given in general and applied to experiments in air–water flows. The effects of surface tension are always important and determine the stability limits for the cases in which the volume fraction of gas is not too small. The stability criterion for viscous potential flow is expressed by a critical value of the relative velocity. The maximum critical value is when the viscosity ratio is equal to the density ratio; surprisingly the neutral curve for this viscous fluid is the same as the neutral curve for inviscid fluids. The maximum critical value of the velocity of all viscous fluids is given by that for inviscid fluid. For air at 20°C and liquids with density ρ = 1 g cm−3 the liquid viscosity for the critical conditions is 15 cP: the critical velocity for liquids with viscosities larger than 15 cP is only slightly smaller but the critical velocity for liquids with viscosities smaller than 15 cP, like water, can be much lower. The viscosity of the liquid has a strong effect on the growth rate. The viscous potential flow theory fits the experimental data for air and water well when the gas fraction is greater than about 70%.

Finite Element Analysis of Fluid-Elastic Instability of Heat Exchanger Array

2014 ◽  
Vol 926-930 ◽  
pp. 789-792
Author(s):  
Peng Wang ◽  
Jian Hu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Heat Exchanger ◽  
Flow Velocity ◽  
Critical Value ◽  
Stability Diagram ◽  
Elastic Instability ◽  
Element Analysis ◽  
Damping Parameter ◽  
The Stability

From the viewpoint of primary theory of Finite Element Analysis, as well as practical application, the present paper sets up a model for the use of analyzing the fluid-elastic instability of heat exchanger array. In accordance with related compared velocity and mass damping parameter, the author obtains the stability diagram and analyzes the diagram of the array displacement when it reaches the critical value of flow velocity. Accordingly, the instability of heat exchanger array in critical value if flow velocity was verified.

scholarly journals A pH-Responsive Foam Formulated with PAA/Gemini 12-2-12 Complexes

2021 ◽  
Vol 5 (3) ◽  
pp. 37
Author(s):  
Hernán Martinelli ◽  
Claudia Domínguez ◽  
Marcos Fernández Leyes ◽  
Sergio Moya ◽  
Hernán Ritacco
Keyword(s):  
Surface Tension ◽  
Dynamic Surface Tension ◽  
Foam Formation ◽  
Ph Responsive ◽  
Dynamic Surface ◽  
X Ray ◽  
Equilibrium Surface Tension ◽  
Potential Applications ◽  
The Stability ◽  
Air Interfaces

In the search for responsive complexes with potential applications in the formulation of smart dispersed systems such as foams, we hypothesized that a pH-responsive system could be formulated with polyacrylic acid (PAA) mixed with a cationic surfactant, Gemini 12-2-12 (G12). We studied PAA-G12 complexes at liquid–air interfaces by equilibrium and dynamic surface tension, surface rheology, and X-ray reflectometry (XRR). We found that complexes adsorb at the interfaces synergistically, lowering the equilibrium surface tension at surfactant concentrations well below the critical micelle concentration (cmc) of the surfactant. We studied the stability of foams formulated with the complexes as a function of pH. The foams respond reversibly to pH changes: at pH 3.5, they are very stable; at pH > 6, the complexes do not form foams at all. The data presented here demonstrate that foam formation and its pH responsiveness are due to interfacial dynamics.

scholarly journals Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field

2005 ◽  
Vol 2005 (23) ◽  
pp. 3727-3737 ◽  
Author(s):  
Jitender Singh ◽  
Renu Bajaj
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Critical Value ◽  
Annular Space ◽  
Rotating Cylinders ◽  
The Stability

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratioΩ∗of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

Electrohydrodynamic stability: Taylor–Melcher theory for a liquid bridge suspended in a dielectric gas

2002 ◽  
Vol 452 ◽  
pp. 163-187 ◽  
Author(s):  
C. L. BURCHAM ◽  
D. A. SAVILLE
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Electric Fields ◽  
Liquid Bridge ◽  
Numerical Solutions ◽  
Specific Conductivity ◽  
Axisymmetric Deformation ◽  
Aspect Ratios ◽  
The Stability ◽  
Theory And Experiment

A liquid bridge is a column of liquid, pinned at each end. Here we analyse the stability of a bridge pinned between planar electrodes held at different potentials and surrounded by a non-conducting, dielectric gas. In the absence of electric fields, surface tension destabilizes bridges with aspect ratios (length/diameter) greater than π. Here we describe how electrical forces counteract surface tension, using a linearized model. When the liquid is treated as an Ohmic conductor, the specific conductivity level is irrelevant and only the dielectric properties of the bridge and the surrounding gas are involved. Fourier series and a biharmonic, biorthogonal set of Papkovich–Fadle functions are used to formulate an eigenvalue problem. Numerical solutions disclose that the most unstable axisymmetric deformation is antisymmetric with respect to the bridge’s midplane. It is shown that whilst a bridge whose length exceeds its circumference may be unstable, a sufficiently strong axial field provides stability if the dielectric constant of the bridge exceeds that of the surrounding fluid. Conversely, a field destabilizes a bridge whose dielectric constant is lower than that of its surroundings, even when its aspect ratio is less than π. Bridge behaviour is sensitive to the presence of conduction along the surface and much higher fields are required for stability when surface transport is present. The theoretical results are compared with experimental work (Burcham & Saville 2000) that demonstrated how a field stabilizes an otherwise unstable configuration. According to the experiments, the bridge undergoes two asymmetric transitions (cylinder-to-amphora and pinch-off) as the field is reduced. Agreement between theory and experiment for the field strength at the pinch-off transition is excellent, but less so for the change from cylinder to amphora. Using surface conductivity as an adjustable parameter brings theory and experiment into agreement.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

CHARGE STABILITY AND CONDUCTANCE ANALYSIS OF ANTHRACENE-BASED SINGLE ELECTRON TRANSISTOR

2013 ◽  
Vol 12 (06) ◽  
pp. 1350045 ◽  
Author(s):  
ANURAG SRIVASTAVA ◽  
BODDEPALLI SANTHIBHUSHAN ◽  
PANKAJ DOBWAL
Keyword(s):  
Coulomb Blockade ◽  
Density Functional ◽  
Stability Diagram ◽  
Single Electron ◽  
Single Electron Transistor ◽  
Functional Theory ◽  
Charge Stability ◽  
Anthracene Molecule ◽  
The Stability ◽  
Experimental Values

The present paper discusses the investigation of electronic properties of anthracene-based single electron transistor (SET) operating in coulomb blockade region using Density Functional Theory (DFT) based Atomistix toolkit-Virtual nanolab. The charging energies of anthracene molecule in isolated as well as electrostatic SET environments have been calculated for analyzing the stability of the molecule for different charge states. Study also includes the analysis of SET conductance dependence on source/drain and gate potentials in reference to the charge stability diagram. Our computed charging energies for anthracene in isolated environment are in good agreement with the experimental values and the proposed anthracene SET shows good switching properties in comparison to other acene series SETs.

Evaluation of Non-Vibrating Utility Burner/Furnace Systems for Resistance to Thermoacoustic Oscillations

2006 ◽  
Author(s):  
Frantisek L. Eisinger ◽  
Robert E. Sullivan
Keyword(s):  
Design Process ◽  
Axial Direction ◽  
Stability Diagram ◽  
Stable Range ◽  
Design Engineers ◽  
Secondary Role ◽  
The Stability ◽  
Thermoacoustic Oscillations

Six burner/furnace systems which operated successfully without vibration are evaluated for resistance to thermoacoustic oscillations. The evaluation is based on the Rijke and Sondhauss models representing the combined burner/furnace (cold/hot) thermoacoustic systems. Frequency differences between the lowest vulnerable furnace acoustic frequencies in the burner axial direction and those of the systems’ Rijke and Sondhauss frequencies are evaluated to check for resonances. Most importantly, the stability of the Rijke and Sondhauss models is checked against the published design stability diagram of Eisinger [1] and Eisinger and Sullivan [2]. It is shown that the resistance to thermoacoustic oscillations is adequately defined by the published design stability diagram to which the evaluated cases generally adhere. Once the system falls into the stable range, the frequency differences or resonances appear to play only a secondary role. It is concluded, however, that in conjunction with stability, the primary criterion, sufficient frequency separations shall also be maintained in the design process to preclude resonances. The paper provides sufficient details to aid the design engineers.

Robust active disturbance attenuation control of an uncertain quadrotor

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Nigar Ahmed ◽  
Ajeet kumar Bhatia ◽  
Syed Awais Ali Shah
Keyword(s):  
Control Algorithm ◽  
Sliding Mode ◽  
The State ◽  
Disturbance Attenuation ◽  
State Variables ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Content Type ◽  
Highly Nonlinear ◽  
The Stability

PurposeThe aim of this research is to design a robust active disturbance attenuation control (RADAC) technique combined with an extended high gain observer (EHGO) and low pass filter (LPF).Design/methodology/approachFor designing a RADAC technique, the sliding mode control (SMC) method is used. Since the standard method of SMC exhibits a chattering phenomenon in the controller, a multilayer sliding mode surface is designed for avoiding the chattering. In addition, to attenuate the unwanted uncertainties and disturbances (UUDs), the techniques of EHGO and LPF are deployed. Besides acting as a patch for disturbance attenuation, the EHGO design estimates the state variables. To investigate the stability and effectiveness of the designed control algorithm, the stability analysis followed by the simulation study is presented.FindingsThe major findings include the design of a chattering-free RADAC controller based on the multilayer sliding mode surface. Furthermore, a criterion of integrating the LPF scheme within the EHGO scheme is also developed to attenuate matched and mismatched UUDs.Practical implicationsIn practice, the quadrotor flight is opposed by different kinds of the UUDs. And, the model of the quadrotor is a highly nonlinear underactuated model. Thus, the dynamics of the quadrotor model become more complex and uncertain due to the additional UUDs. Hence, it is necessary to design a robust disturbance attenuation technique with the ability to estimate the state variables and attenuate the UUDs and also achieve the desired control objectives.Originality/valueDesigning control methods to attenuate the disturbances while assuming that the state variables are known is a common practice. However, investigating the uncertain plants with unknown states along with the disturbances is rarely taken in consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the UUDs as well as investigate a criterion to reduce the chattering incurred in the controller due to the standard SMC algorithm.

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