scholarly journals Surface energies emerging in a microscopic, two-dimensional two-well problem

2017 ◽  
Vol 147 (5) ◽  
pp. 1041-1089 ◽  
Author(s):  
Georgy Kitavtsev ◽  
Stephan Luckhaus ◽  
Angkana Rüland
Keyword(s):  
Surface Energy ◽  
Two Dimensional ◽  
Direct Control ◽  
First Order ◽  
Surface Energies ◽  
Energy Scaling ◽  
Continuous Analogue ◽  
Dimensional Shape ◽  
Set Up ◽  
Microscopic Modelling

In this paper we are interested in the microscopic modelling of a two-dimensional two-well problem that arises from the square-to-rectangular transformation in (two-dimensional) shape-memory materials. In this discrete set-up, we focus on the surface energy scaling regime and further analyse the Hamiltonian that was introduced by Kitavtsev et al. in 2015. It turns out that this class of Hamiltonians allows for a direct control of the discrete second-order gradients and for a one-sided comparison with a two-dimensional spin system. Using this and relying on the ideas of Conti and Schweizer, which were developed for a continuous analogue of the model under consideration, we derive a (first-order) continuum limit. This shows the emergence of surface energy in the form of a sharp-interface limiting model as well the explicit structure of the minimizers to the latter.

Correlation of Surface and Interfacial Energies on Enhanced Pool Boiling Heat Transfer

Volume 3 ◽  
2004 ◽  
Author(s):  
Elva Mele´ndez ◽  
Rene´ Reyes
Keyword(s):  
Heat Transfer ◽  
Contact Angle ◽  
Surface Energy ◽  
Interfacial Energy ◽  
Boiling Heat Transfer ◽  
Contact Angles ◽  
Lauryl Sulfate ◽  
Surface Energies ◽  
Interfacial Energies ◽  
Set Up

The surface energy of the material used in the construction of capillary covers is an important element to increase the boiling heat transfer on the coverings. There are a variety of methodologies for measuring the surface energy of solids, but few could be used with the construction materials tested. The sessile drop methodology allows the evaluation of either the surface energy of solids or the interfacial energy of liquids. The methodology uses an image digitalization system for measuring the contact angle of liquids on the solid’s surface. The contact angles thus measured are used to calculate the superficial and interfacial energies. This methodology was tested with an experimental set up built for this study. The accuracy of the set up was obtained with clean and greased surfaces of high heat conductivity metals. The surface energies calculated were in accordance with previous experimental results. The surface energies of metal foils used for construction of capillary coverings were similar to the values calculated for the parental solid metal. The surfaces with different grease thickness get values of surface energy close to the value for the adhered hydrocarbons. The same methodology is used for measuring interfacial energies of pure and mixtures of liquids. The liquids studied include those used for increasing boiling heat transfer. Ethanol-water mixtures were analyzed. The mixture with 16% ethanol by weight had the lowest contact angle (associated to the lowest interfacial energy) and produced the highest convective heat transfer coefficient, h. A minimum in the value of the contact angle around the 16% weight ethanol mixtures follows the maximum in the value of h around this composition, and a maximum in the wettability. Similarly, the surfactant sodium-lauryl-sulfate (SLS) produced an increment of the wettability of the mixture on the solid surface. The reduction of the contact angle is obtained with the addition of 100 ppm of SLS or less, depending on the base metal, but above this concentration, the surfactant does not modify the value of the contact angle. The h values increased with the addition of surfactant up to 100 ppm but do not change if the concentration of surfactant is higher than that value.

scholarly journals Solving puzzles in deformed JT gravity: phase transitions and non-perturbative effects

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Clifford V. Johnson ◽  
Felipe Rosso
Keyword(s):  
Phase Structure ◽  
Scalar Potential ◽  
String Equation ◽  
Two Dimensional ◽  
Leading Order ◽  
Classical Analysis ◽  
First Order ◽  
First Order Phase Transition ◽  
Definition Of ◽  
First Order Phase

Abstract Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

scholarly journals Vertical Orientation of Liquid Crystal on 4-n-Alkyloxyphenoxymethyl-Substituted Polystyrene Containing Liquid Crystal Precursor

Polymers ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 736
Author(s):  
Kyutae Seo ◽  
Hyo Kang
Keyword(s):  
Molecular Structure ◽  
Liquid Crystal ◽  
Surface Energy ◽  
Polymer Films ◽  
Ultraviolet Irradiation ◽  
Molar Fraction ◽  
Side Chain ◽  
Polymer Modification ◽  
Vertical Orientation ◽  
Surface Energies

We synthesized a series of polystyrene derivatives that were modified with precursors of liquid crystal (LC) molecules, such as 4-ethyloxyphenol (homopolymer PEOP and copolymer PEOP#; # = 20, 40, 60, and 80, where # indicates the molar fraction of 4-ethyloxyphenoxymethyl in the side chain), 4-n-butyloxyphenol (PBOP), 4-n-hexyloxyphenol (PHOP), and 4-n-octyloxyphenol (POOP), via polymer modification reaction to investigate the orientation of LC molecules on polymer films, exhibiting part of the LC molecular structure. LC molecules showed a stable and uniform vertical orientation in LC cells fabricated with polymers that have 4-ethyloxyphenoxymethyl in the range of 40–100 mol%. In addition, similar results were obtained in LC cells fabricated with homopolymers of PEOP, PBOP, PHOP, and POOP. The vertical orientation of LC molecules in LC cells fabricated with polymer films correlated to the surface energy of polymer films. For example, vertical LC orientation was observed when the total surface energies of the polymer films were lower than approximately 43.2 mJ/m2. Good alignment stabilities were observed at 150 °C and 20 J/cm2 of ultraviolet irradiation for LC cells fabricated with PEOP film.

Partially Invariant Solutions for Two-dimensional Ideal MHD Equations

1990 ◽  
Vol 45 (11-12) ◽  
pp. 1219-1229 ◽  
Author(s):  
D.-A. Becker ◽  
E. W. Richter
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Mhd Equations ◽  
Two Dimensional ◽  
Invariant Solutions ◽  
First Order ◽  
Partially Invariant Solutions ◽  
Quasilinear Systems ◽  
Ideal Mhd ◽  
Non Linear Equations

AbstractA generalization of the usual method of similarity analysis of differential equations, the method of partially invariant solutions, was introduced by Ovsiannikov. The degree of non-invariance of these solutions is characterized by the defect of invariance d. We develop an algorithm leading to partially invariant solutions of quasilinear systems of first-order partial differential equations. We apply the algorithm to the non-linear equations of the two-dimensional non-stationary ideal MHD with a magnetic field perpendicular to the plane of motion.

scholarly journals Energy budget in internal wave attractor experiments

2019 ◽  
Vol 880 ◽  
pp. 743-763 ◽  
Author(s):  
Géraldine Davis ◽  
Thierry Dauxois ◽  
Timothée Jamin ◽  
Sylvain Joubaud
Keyword(s):  
Velocity Field ◽  
Internal Wave ◽  
Boundary Layers ◽  
Energy Budget ◽  
Dissipation Rate ◽  
Theoretical Expression ◽  
Two Dimensional ◽  
Energy Sink ◽  
Set Up ◽  
Different Sources

The current paper presents an experimental study of the energy budget of a two-dimensional internal wave attractor in a trapezoidal domain filled with uniformly stratified fluid. The injected energy flux and the dissipation rate are simultaneously measured from a two-dimensional, two-component, experimental velocity field. The pressure perturbation field needed to quantify the injected energy is determined from the linear inviscid theory. The dissipation rate in the bulk of the domain is directly computed from the measurements, while the energy sink occurring in the boundary layers is estimated using the theoretical expression for the velocity field in the boundary layers, derived recently by Beckebanze et al. (J. Fluid Mech., vol. 841, 2018, pp. 614–635). In the linear regime, we show that the energy budget is closed, in the steady state and also in the transient regime, by taking into account the bulk dissipation and, more importantly, the dissipation in the boundary layers, without any adjustable parameters. The dependence of the different sources on the thickness of the experimental set-up is also discussed. In the nonlinear regime, the analysis is extended by estimating the dissipation due to the secondary waves generated by triadic resonant instabilities, showing the importance of the energy transfer from large scales to small scales. The method tested here on internal wave attractors can be generalized straightforwardly to any quasi-two-dimensional stratified flow.

scholarly journals Intermittent heat instabilities in an air plume

2016 ◽  
Vol 23 (4) ◽  
pp. 319-330
Author(s):  
Jean-Louis Le Mouël ◽  
Vladimir G. Kossobokov ◽  
Frederic Perrier ◽  
Pierre Morat
Keyword(s):  
Temperature Sensors ◽  
Time Varying ◽  
First Order ◽  
Spatial Function ◽  
Universal Feature ◽  
Classical Models ◽  
Set Up ◽  
Plume Flow ◽  
Temperature Time ◽  
Classical Shape

Abstract. We report the results of heating experiments carried out in an abandoned limestone quarry close to Paris, in an isolated room of a volume of about 400 m3. A heat source made of a metallic resistor of power 100 W was installed on the floor of the room, at distance from the walls. High-quality temperature sensors, with a response time of 20 s, were fixed on a 2 m long bar. In a series of 24 h heating experiments the bar had been set up horizontally at different heights or vertically along the axis of the plume to record changes in temperature distribution with a sampling time varying from 20 to 120 s. When taken in averages over 24 h, the temperatures present the classical shape of steady-state plumes, as described by classical models. On the contrary, the temperature time series show a rich dynamic plume flow with intermittent trains of oscillations, spatially coherent, of large amplitude and a period around 400 s, separated by intervals of relative quiescence whose duration can reach several hours. To our knowledge, no specific theory is available to explain this behavior, which appears to be a chaotic interaction between a turbulent plume and a stratified environment. The observed behavior, with first-order factorization of a smooth spatial function with a global temporal intermittent function, could be a universal feature of some turbulent plumes in geophysical environments.

A Difference Method for Plane Problems in Magnetoelastodynamics

1972 ◽  
Vol 39 (3) ◽  
pp. 689-695 ◽  
Author(s):  
W. W. Recker
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Method ◽  
Difference Method ◽  
Necessary Condition ◽  
Two Dimensional ◽  
Symmetric Hyperbolic System ◽  
Von Neumann ◽  
First Order ◽  
Independent Variables

The two-dimensional equations of magnetoelastodynamics are considered as a symmetric hyperbolic system of linear first-order partial-differential equations in three independent variables. The characteristic properties of the system are determined and a numerical method for obtaining the solution to mixed initial and boundary-value problems in plane magnetoelastodynamics is presented. Results on the von Neumann necessary condition are presented. Application of the method to a problem which has a known solution provides further numerical evidence of the convergence and stability of the method.

Comparative studies of the set up of two-dimensional pneumatic arm systems by muscle and rotational actuators

2007 ◽  
Vol 221 (5) ◽  
pp. 743-748 ◽  
Author(s):  
Y-T Wang ◽  
R-H Wong ◽  
J-T Lu
Keyword(s):  
Control Systems ◽  
Fuzzy Controller ◽  
Control Algorithms ◽  
Two Dimensional ◽  
Pneumatic Control ◽  
Learning Mechanism ◽  
Set Up ◽  
And Control ◽  
Self Learning ◽  
System Characteristics

As opposed to traditional pneumatic linear actuators, muscle and rotational actuators are newly developed actuators in rotational and specified applications. In the current paper, these actuators are used to set up two-dimensional pneumatic arms, which are used mainly to simulate the excavator's motion. Fuzzy control algorithms are typically applied in pneumatic control systems owing to their non-linearities and ill-defined mathematical model. The self-organizing fuzzy controller, which includes a self-learning mechanism to modify fuzzy rules, is applied in these two-dimensional pneumatic arm control systems. Via a variety of trajectory tracking experiments, the present paper provides comparisons of system characteristics and control performances.

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