90,364 research outputs found
Triviality of the 2D stochastic Allen-Cahn equation
No full textWe consider the stochastic Allen-Cahn equation driven by mollified space-time white noise. We show that, as the mollifier is removed, the solutions converge weakly to
0, independently of the initial condition. If the intensity of the noise simultaneously converges to 0 at a sufficiently fast rate, then the solutions converge to those of the
deterministic equation. At the critical rate, the limiting solution is still deterministic, but it exhibits an additional damping term
Solutions for the Cahn-Hilliard Equation With Many Boundary Spike Layers
No full textIn this paper we
construct new classes of stationary solutions for the Cahn-Hilliard
equation
by a novel approach.
One of the results is as follows:
Given a positive integer K and a (not necessarily nondegenerate) local
minimum point of the mean curvature of the boundary then there are
boundary
K-spike solutions
whose peaks all approach this point.
This implies that for any smooth and bounded domain there
exist boundary K-spike solutions.
The central ingredient of our analysis is the novel derivation and
exploitation of a reduction of the energy to finite dimensions (Lemma 3.5),
where the variables are closely related to the peak loations
Numerical analysis of a coupled pair of Cahn-Hilliard equations
No full textA mathematical analysis has been carried out for a coupled pair of Cahn-Hilliard equations, which appear in modelling a phase separation on a thin film of binary liquid mixture coating substrate, which is wet by one component. Existence and uniqueness are proved for a weak formulation of the problem, which possesses a Lyapunov functional. Regularity results are presented for the weak formulation. A fully practical piecewise linear finite element approximation is proposed where existence and uniqueness of the numerical solution, and its convergence to the solution of the continuous problem are proven. An error bound between the discrete and continuous solutions is given in three space dimensions. A practical algorithm for solving the resulting algebraic problem at each time step is suggested and its convergence is proven. Finally, linear stability analysis for one space dimension is presented, and some numerical simulations in one and two spaces dimension are exhibited
Numerical analysis of a coupled pair of Cahn-Hilliard equations with non-smooth free energy
No full textA mathematical analysis has been carried out for a coupled pair of Cahn-Hilliard equations with a double well potential function with infinite walled free energy, which appears in modelling a phase separation on a thin film of binary liquid mixture coating substrate, which is wet by one component. Existence and uniqueness are proved for a weak formulation of the problem, which possesses a Lyapunov functional. Regularity results for the weak formulation are presented. Semi and fully discrete finite element approximations are proposed where existence and uniqueness of their solutions are proven. Their convergence to the solution of the continuous solutions are presented. Error bound between semi-discrete and continuous solutions, between semi-discrete and fully discrete solutions, and between fully discrete and continuous solutions are all investigated. A practical algorithm to solve the fully discrete finite element formulation at each time step is introduced and its convergence is shown. Finally, a linear stability analysis of the equations in one dimension space is presented and some numerical simulations in one and two dimension spaces are preformed
Mathematical and Numerical Analysis of a Pair of Coupled Cahn-Hilliard Equations with a Logarithmic Potential
No full textMathematical and numerical analysis has been undertaken for a pair of coupled Cahn-Hilliard equations with a logarithmic potential and with homogeneous Neumann boundary conditions. This pair of coupled equations arises in a phase separation model of thin film of binary liquid mixture. Global existence and uniqueness of a weak solution to the problem is proved using Faedo-Galerkin method. Higher regularity results of the weak solution are established under further regular requirements on the initial data. Further, continuous dependence on the initial data is presented.
Numerically, semi-discrete and fully-discrete piecewise linear finite element approximations to the continuous problem are proposed for which existence, uniqueness and various stability estimates of the approximate solutions are proved. Semi-discrete and fully-discrete error bounds are derived where the time discretisation error is optimal. An iterative method for solving the resulting nonlinear algebraic system is introduced and linear stability analysis in one space dimension is studied. Finally, numerical experiments illustrating some of the theoretical results are performed in one and two space dimensions
Optimal energy growth lower bounds for a class of solutions to the vectorial Allen-Cahn equation
No full textWe prove optimal lower bounds for the growth of the energy over balls of minimizers to the vectorial Allen-Cahn energy in two spatial dimensions, as the radius tends to infinity. In the case of radially symmetric solutions, we can prove a stronger result in all dimensions
Finite Element Approximations for a linear Cahn-Hilliard-Cook equation driven by the space derivative of a space-time white noise
No full textWe consider an initial- and Dirichlet boundary- value problem for
a linear Cahn-Hilliard-Cook equation, in one space dimension,
forced by the space derivative of a space-time white noise.
First, we propose an approximate regularized stochastic parabolic
problem discretizing the noise using linear splines. Then
fully-discrete approximations to the solution of the
regularized problem are constructed using, for the discretization
in space, a Galerkin finite element method based on
piecewise polynomials, and, for time-stepping, the Backward
Euler method.
Finally, we derive strong a priori estimates for the modeling error and
for the numerical approximation error to the solution of the regularized problem
George F. Patrick, Desenvolvimento agricola do Nordeste
No full textCahn Roger H. George F. Patrick, Desenvolvimento agricola do Nordeste. In: Tiers-Monde, tome 14, n°54, 1973. Le développement rural. pp. 448-449
Travelling waves for the spatially discretized bistable Allen-Cahn equation
No full textWe analyze the spatially discretized version of the Allen-Cahn partial differential equation. The second order derivative is numerically approximated by a weighted infinite sum. The coefficients of this sum as well as the function f in the differential equation have got freedom inside determined restrictions. For this spatially discretized variation of the Allen-Cahn partial differential equation, we prove the existence of a travelling wave solution.Applied Mathematic
Coadministration of Anti-Viral Monoclonal Antibodies With Routine Pediatric Vaccines and Implications for Nirsevimab Use: A White Paper
No full textRoutine childhood vaccinations are key for the protection of children from a variety of serious and potentially fatal diseases. Current pediatric vaccine schedules mainly cover active vaccines. Active vaccination in infants is a highly effective approach against several infectious diseases; however, thus far, for some important viral pathogens, including respiratory syncytial virus (RSV), vaccine development and license by healthcare authorities have not been accomplished. Nirsevimab is a human-derived, highly potent monoclonal antibody (mAb) with an extended half-life for RSV prophylaxis in all infants. In this manuscript, we consider the potential implications for the introduction of an anti-viral mAb, such as nirsevimab, into the routine pediatric vaccine schedule, as well as considerations for coadministration. Specifically, we present evidence on the general mechanism of action of anti-viral mAbs and experience with palivizumab, the only approved mAb for the prevention of RSV infection in preterm infants, infants with chronic lung disease of prematurity and certain infants with hemodynamically significant heart disease. Palivizumab has been used for over two decades in infants who also receive routine vaccinations without any alerts concerning the safety and efficacy of coadministration. Immunization guidelines (Advisory Committee on Immunization Practices, Joint Committee on Vaccination and Immunization, National Advisory Committee on Immunization, Centers for Disease Control and Prevention, American Academy of Pediatrics, The Association of the Scientific Medical Societies in Germany) support coadministration of palivizumab with routine pediatric vaccines, noting that immunobiologics, such as palivizumab, do not interfere with the immune response to licensed live or inactivated active vaccines. Based on the mechanism of action of the new generation of anti-viral mAbs, such as nirsevimab, which is highly specific targeting viral antigenic sites, it is unlikely that it could interfere with the immune response to other vaccines. Taken together, we anticipate that nirsevimab could be concomitantly administered to infants with routine pediatric vaccines during the same clinic visit
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