scholarly journals On the heteroclinic connection problem for multi-well gradient systems

2016 ◽  
Vol 261 (7) ◽  
pp. 3987-4007 ◽  
Author(s):  
Andres Zuniga ◽  
Peter Sternberg
Keyword(s):  
Gradient Systems ◽  
Connection Problem ◽  
Heteroclinic Connection

scholarly journals On the loss of compactness in the vectorial heteroclinic connection problem

2016 ◽  
Vol 146 (3) ◽  
pp. 595-608 ◽  
Author(s):  
Nikos Katzourakis
Keyword(s):  
A Priori ◽  
Functional Space ◽  
Alternative Proof ◽  
Local Minima ◽  
Minimizing Sequences ◽  
Connection Problem ◽  
Heteroclinic Connection ◽  
Image Position ◽  
Constraint Method ◽  
Loss Of Compactness

We give an alternative proof of the theorem of Alikakos and Fusco concerning existence of heteroclinic solutions U : ℝ → ℝN to the systemHere a± are local minima of a potential W ∈ C2(ℝN) with W(a±) = 0. This system arises in the theory of phase transitions. Our method is variational but differs from the original artificial constraint method of Alikakos and Fusco and establishes existence by analysing the loss of compactness in minimizing sequences of the action in the appropriate functional space. Our assumptions are slightly different from those considered previously and also imply a priori estimates for the solution.

STARCH GEL ELECTROPHORESIS OF MYOGEN FROM CHICKEN BREAST MUSCLE IN CONSTANT AND GRADIENT BUFFER SYSTEMS

1963 ◽  
Vol 41 (1) ◽  
pp. 369-387 ◽  
Author(s):  
J. M. Neelin
Keyword(s):  
Gel Electrophoresis ◽  
Protein Concentration ◽  
Breast Muscle ◽  
Chicken Breast ◽  
Starch Gel Electrophoresis ◽  
Two Dimensional ◽  
Sodium Cacodylate ◽  
Gradient Systems ◽  
Optimal Separation ◽  
Starch Gel

By varying conditions of starch gel electrophoresis, factors contributing to the resolution of myogen proteins from chicken breast muscle have been studied. Variables examined included composition of the myogen extractant, protein concentration, ionic strength of electrophoretic media, pH of gel media, plane and direction of electrophoresis, and the nature of cations and anions in gel media and bridge solutions. The significance of anions was more closely studied with constant buffer systems, and gradient systems in which bridge electrolyte differed from, and gradually altered, the gel medium. Optimal separation was obtained in gradient systems with 0.10 M sodium chloride bridge solutions, and gel media of sodium cacodylate, pH 6.9, μ 0.010, which resolved 12 cationic zones, and sodium veronal, pH 7.4, μ 0.010, which resolved 10 anionic zones. These buffers in two-dimensional sequence revealed a total of about 24 components in this myogen.

Reference-free, depth-dependent characterization of nanolayers and gradient systems with advanced grazing incidence X-ray fluorescence analysis

2015 ◽  
Vol 212 (3) ◽  
pp. 523-528 ◽  
Author(s):  
Philipp Hönicke ◽  
Blanka Detlefs ◽  
Matthias Müller ◽  
Erik Darlatt ◽  
Emmanuel Nolot ◽  
...  
Keyword(s):  
Fluorescence Analysis ◽  
Grazing Incidence ◽  
X Ray ◽  
Gradient Systems

Improving the extraction of tetrachloroethylene from soil columns using surfactant gradient systems

2004 ◽  
Vol 71 (1-4) ◽  
pp. 27-45 ◽  
Author(s):  
Jeffrey D Childs ◽  
Edgar Acosta ◽  
Robert Knox ◽  
Jeffrey H Harwell ◽  
David A Sabatini
Keyword(s):  
Soil Columns ◽  
Gradient Systems

Travelling fronts in a food-limited population model with time delay

2002 ◽  
Vol 132 (1) ◽  
pp. 75-89 ◽  
Author(s):  
S. A. Gourley ◽  
M. A. J. Chaplain
Keyword(s):  
Population Model ◽  
Time Delays ◽  
Front Solutions ◽  
Heteroclinic Connection ◽  
Non Local ◽  
Spatial Terms ◽  
Travelling Fronts ◽  
Manifold Theory ◽  
And Diffusion ◽  
Existence Question

In this paper we study travelling front solutions of a certain food-limited population model incorporating time-delays and diffusion. Special attention is paid to the modelling of the time delays to incorporate associated non-local spatial terms which account for the drift of individuals to their present position from their possible positions at previous times. For a particular class of delay kernels, existence of travelling front solutions connecting the two spatially uniform steady states is established for sufficiently small delays. The approach is to reformulate the problem as an existence question for a heteroclinic connection in R4. The problem is then tackled using dynamical systems techniques, in particular, Fenichel's invariant manifold theory. For larger delays, numerical simulations reveal changes in the front's profile which develops a prominent hump.

scholarly journals Reconfiguring Smart Structures Using Approximate Heteroclinic Connections in a Spring-Mass Model

2015 ◽  
Author(s):  
Jiaying Zhang ◽  
Colin R. McInnes
Keyword(s):  
Optimal Control ◽  
Control Method ◽  
Smart Structures ◽  
Polynomial Method ◽  
Reference Trajectory ◽  
Sensors And Actuators ◽  
Embedded Computing ◽  
Equal Energy ◽  
Optimal Control Method ◽  
Heteroclinic Connection

Several new methods are proposed to reconfigure smart structures with embedded computing, sensors and actuators. These methods are based on heteroclinic connections between equal-energy unstable equilibria in an idealised spring-mass smart structure model. Transitions between equal-energy unstable (but actively controlled) equilibria are considered since in an ideal model zero net energy input is required, compared to transitions between stable equilibria across a potential barrier. Dynamical system theory is used firstly to identify sets of equal-energy unstable configurations in the model, and then to connect them through heteroclinic connection in the phase space numerically. However, it is difficult to obtain such heteroclinic connections numerically in complex dynamical systems, so an optimal control method is investigated to seek transitions between unstable equilibria, which approximate the ideal heteroclinic connection. The optimal control method is verified to be effective through comparison with the results of the exact heteroclinic connection. In addition, we explore the use of polynomials of varying order to approximate the heteroclinic connection, and then develop an inverse method to control the dynamics of the system to track the polynomial reference trajectory. It is found that high order polynomials can provide a good approximation to true heteroclinic connections and provide an efficient means of generating such trajectories. The polynomial method is envisaged as being computationally efficient to form the basis for real-time reconfiguration of real, complex smart structures with embedded computing, sensors and actuators.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

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