scholarly journals Convectons, anticonvectons and multiconvectons in binary fluid convection

2010 ◽  
Vol 667 ◽  
pp. 586-606 ◽  
Author(s):  
ISABEL MERCADER ◽  
ORIOL BATISTE ◽  
ARANTXA ALONSO ◽  
EDGAR KNOBLOCH
Keyword(s):  
Boundary Conditions ◽  
Bound States ◽  
Neumann Boundary ◽  
Localized States ◽  
Numerical Continuation ◽  
Binary Fluid ◽  
Flux Boundary Conditions ◽  
New States ◽  
Fluid Convection ◽  
Binary Fluid Mixtures

Binary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. Numerical continuation is used to compute such states in the presence of both Neumann boundary conditions and no-slip no-flux boundary conditions in the horizontal. In addition to the previously identified convectons, new states referred to as anticonvectons with a void in the centre of the domain, and wall-attached convectons attached to one or other wall are identified. Bound states of convectons and anticonvectons called multiconvecton states are also computed. All these states are located in the so-called snaking or pinning region in the Rayleigh number and may be stable. The results are compared with existing results with periodic boundary conditions.

scholarly journals Travelling convectons in binary fluid convection

2013 ◽  
Vol 722 ◽  
pp. 240-266 ◽  
Author(s):  
Isabel Mercader ◽  
Oriol Batiste ◽  
Arantxa Alonso ◽  
Edgar Knobloch
Keyword(s):  
Localized States ◽  
Numerical Continuation ◽  
Fixed Temperature ◽  
Binary Fluid ◽  
Separation Ratio ◽  
Flux Boundary Conditions ◽  
Fluid Convection ◽  
Binary Fluid Mixtures ◽  
Rayleigh Numbers ◽  
Compare And Contrast

AbstractBinary fluid mixtures with a negative separation ratio heated from below exhibit steady spatially localized states called convectons for supercritical Rayleigh numbers. With no-slip, fixed-temperature, no-mass-flux boundary conditions at the top and bottom stationary odd- and even-parity convectons fall on a pair of intertwined branches connected by branches of travelling asymmetric states. In appropriate parameter regimes the stationary convectons may be stable. When the boundary condition on the top is changed to Newton’s law of cooling the odd-parity convectons start to drift and the branch of odd-parity convectons breaks up and reconnects with the branches of asymmetric states. We explore the dependence of these changes and of the resulting drift speed on the associated Biot number using numerical continuation, and compare and contrast the results with a related study of the Swift–Hohenberg equation by Houghton & Knobloch (Phys. Rev.E, vol. 84, 2011, art. 016204). We use the results to identify stable drifting convectons and employ direct numerical simulations to study collisions between them. The collisions are highly inelastic, and result in convectons whose length exceeds the sum of the lengths of the colliding convectons.

scholarly journals Numerical continuation of spiral waves in heteroclinic networks of cyclic dominance

2021 ◽  
Author(s):  
Cris R Hasan ◽  
Hinke M Osinga ◽  
Claire M Postlethwaite ◽  
Alastair M Rucklidge
Keyword(s):  
Boundary Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Spiral Waves ◽  
Numerical Continuation ◽  
Heteroclinic Cycles ◽  
Reaction Diffusion Model ◽  
Inner Radius ◽  
Set Up ◽  
Low Dimensional

Abstract Heteroclinic-induced spiral waves may arise in systems of partial differential equations that exhibit robust heteroclinic cycles between spatially uniform equilibria. Robust heteroclinic cycles arise naturally in systems with invariant subspaces, and their robustness is considered with respect to perturbations that preserve these invariances. We make use of particular symmetries in the system to formulate a relatively low-dimensional spatial two-point boundary-value problem in Fourier space that can be solved efficiently in conjunction with numerical continuation. The standard numerical set-up is formulated on an annulus with small inner radius, and Neumann boundary conditions are used on both inner and outer radial boundaries. We derive and implement alternative boundary conditions that allow for continuing the inner radius to zero and so compute spiral waves on a full disk. As our primary example, we investigate the formation of heteroclinic-induced spiral waves in a reaction–diffusion model that describes the spatiotemporal evolution of three competing populations in a 2D spatial domain—much like the Rock–Paper–Scissors game. We further illustrate the efficiency of our method with the computation of spiral waves in a larger network of cyclic dominance between five competing species, which describes the so-called Rock–Paper–Scissors–Lizard–Spock game.

scholarly journals Three-dimensional spatially localized binary-fluid convection in a porous medium

2013 ◽  
Vol 730 ◽  
Author(s):  
David Lo Jacono ◽  
Alain Bergeon ◽  
Edgar Knobloch
Keyword(s):  
Porous Medium ◽  
Binary Mixture ◽  
Physical Mechanism ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Core Region ◽  
Numerical Continuation ◽  
Binary Fluid ◽  
Fluid Convection ◽  
Convection Patterns

AbstractThree-dimensional convection in a binary mixture in a porous medium heated from below is studied. For negative separation ratios steady spatially localized convection patterns are expected. Such patterns, spatially localized in two dimensions, are computed and numerical continuation is used to examine their growth and proliferation as parameters are varied. The patterns studied have the form of a core region with four extended side-branches and can be stable. A physical mechanism behind the formation of these unusual structures is suggested.

scholarly journals Eigenvalue Bounds for a Class of Schrödinger Operators in a Strip

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Martin Karuhanga
Keyword(s):  
Boundary Conditions ◽  
Bound States ◽  
Schrödinger Operators ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Schrodinger Operators ◽  
Eigenvalue Bounds ◽  
Negative Eigenvalues

This paper is concerned with the estimation of the number of negative eigenvalues (bound states) of Schrödinger operators in a strip subject to Neumann boundary conditions. The estimates involve weighted L1 norms and Lln⁡L norms of the potential. Estimates involving the norms of the potential supported by a curve embedded in a strip are also presented.

Study of fluid flow through a channel deformed by piezoelement

2018 ◽  
Vol 13 (3) ◽  
pp. 1-10 ◽  
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh Nasibullaeva ◽  
O.V. Darintsev
Keyword(s):  
Fluid Flow ◽  
Pressure Drop ◽  
Boundary Conditions ◽  
Flow Rate ◽  
Contact Surface ◽  
Piezoelectric Element ◽  
Neumann Boundary ◽  
Differential Pressure ◽  
Physical Parameters ◽  
Flow Through

The flow of a liquid through a tube deformed by a piezoelectric cell under a harmonic law is studied in this paper. Linear deformations are compared for the Dirichlet and Neumann boundary conditions on the contact surface of the tube and piezoelectric element. The flow of fluid through a deformed channel for two flow regimes is investigated: in a tube with one closed end due to deformation of the tube; for a tube with two open ends due to deformation of the tube and the differential pressure applied to the channel. The flow rate of the liquid is calculated as a function of the frequency of the deformations, the pressure drop and the physical parameters of the liquid.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Sign in / Sign up

Export Citation Format

Share Document