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Title:

Sharp-Interface Limit of a Ginzburg–Landau Functional with a Random External Field

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We add a random bulk term, modeling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double-well potential. For the resulting functional we study the asymptotic properties of minimizers and minimal energy under a rescaling in space, i.e., ...

We add a random bulk term, modeling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double-well potential. For the resulting functional we study the asymptotic properties of minimizers and minimal energy under a rescaling in space, i.e., on the macroscopic scale. By bounding the energy from below by a coarse-grained, discrete functional, we show that for a suitable strength of the random field the random energy functional has two types of random global minimizers, corresponding to two phases. Then we derive the macroscopic cost of low energy "excited" states that correspond to a bubble of one phase surrounded by the opposite phase. Minimize

Year of Publication:

2009

Document Type:

Articles ; PeerReviewed

Relations:

Dirr, N. and Orlandi, E., 2009. Sharp-Interface Limit of a Ginzburg–Landau Functional with a Random External Field. SIAM Journal on Mathematical Analysis (SIMA), 41 (2), pp. 781-824.

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Title:

Unique minimizer for a random functional with double-well potential in dimension 1 and 2

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We add a random bulk term, modelling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double well potential. We show that in d >= 2 there exists, for almost all the realizations of the random bulk term, a unique random macroscopic minimize...

We add a random bulk term, modelling the interaction with the impurities of the medium, to a standard functional in the gradient theory of phase transitions consisting of a gradient term with a double well potential. We show that in d >= 2 there exists, for almost all the realizations of the random bulk term, a unique random macroscopic minimizer. This result is in sharp contrast to the case when the random bulk term is absent. In the latter case there are two minimizers which are (in law) invariant under translations in space. Minimize

Year of Publication:

2011-06

Document Type:

Articles ; PeerReviewed

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Dirr, N. and Orlandi, E., 2011. Unique minimizer for a random functional with double-well potential in dimension 1 and 2. Communications in Mathematical Sciences, 9 (2), pp. 331-351.

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Title:

Large-time behavior for viscous and nonviscous Hamilton-Jacobi equations forced by additive noise

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We study the large-time behavior of the solutions to viscous and nonviscous Hamilton-Jacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants, global-in-time solutions, which attract any other solution.

We study the large-time behavior of the solutions to viscous and nonviscous Hamilton-Jacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants, global-in-time solutions, which attract any other solution. Minimize

Year of Publication:

2005

Document Type:

Articles ; PeerReviewed

Relations:

Dirr, N. and Souganidis, P. E., 2005. Large-time behavior for viscous and nonviscous Hamilton-Jacobi equations forced by additive noise. SIAM Journal on Mathematical Analysis (SIMA), 37 (3), pp. 777-796.

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Large-time behavior for viscous and nonviscous Hamilton-Jacobi equations forced by additive noise

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We study the large-time behavior of the solutions to viscous and nonviscous Hamilton--Jacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants, global-in-time solutions, which attract any other solution.

We study the large-time behavior of the solutions to viscous and nonviscous Hamilton--Jacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants, global-in-time solutions, which attract any other solution. Minimize

Publisher:

Society for Industrial and Applied Mathematics

Year of Publication:

2005

Document Type:

Article ; PeerReviewed

Subjects:

QA Mathematics

QA Mathematics Minimize

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http://orca.cf.ac.uk/13069/1/Dirr%202005.pdf ; Dirr, Nicolas <http://orca.cf.ac.uk/view/cardiffauthors/A2680115.html> and Souganidis, Panagiotis E. 2005. Large-time behavior for viscous and nonviscous Hamilton-Jacobi equations forced by additive noise. SIAM Journal on Mathematical Analysis 37 (3) , pp. 777-796. 10.1137/040611896...

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Title:

Induction of nitrate reductase in pumpkin seedlings

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Nitrate reductase activity (NRA) was found to be induced in 9-day-old pumpkin seedlings by nitrate and light. NRA was greatest in leaves and cotyledons and in vitro measurements gave higher values than in vitro measurements. NRA was found in roots by the in vivo method but not by the in vitro method. NRA changed with the age of the seedling with...

Nitrate reductase activity (NRA) was found to be induced in 9-day-old pumpkin seedlings by nitrate and light. NRA was greatest in leaves and cotyledons and in vitro measurements gave higher values than in vitro measurements. NRA was found in roots by the in vivo method but not by the in vitro method. NRA changed with the age of the seedling with maximum activity in 7-day-old cotyledons and 9-day-old roots of light grown plants; and roots of 7-day-old etiolated plants. Little activity was found in etiolated cotyledons. Minimize

Publisher:

Oxford University Press

Year of Publication:

1978-04-01 00:00:00.0

Document Type:

TEXT

Language:

en

Subjects:

research-article

research-article Minimize

Rights:

Copyright (C) 1978, The Japanese Society of Plant Physiologists

Copyright (C) 1978, The Japanese Society of Plant Physiologists Minimize

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Title:

Interface instability under forced displacements

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By applying linear response theory and the Onsager principle, the power (per unit area) needed to make a planar interface move with velocity V is found to be equal to V-2/ mu, mu a mobility coefficient. To verify such a law, we study a one dimensional model where the interface is the stationary solution of a non local evolution equation, called ...

By applying linear response theory and the Onsager principle, the power (per unit area) needed to make a planar interface move with velocity V is found to be equal to V-2/ mu, mu a mobility coefficient. To verify such a law, we study a one dimensional model where the interface is the stationary solution of a non local evolution equation, called an instanton. We then assign a penalty functional to orbits which deviate from solutions of the evolution equation and study the optimal way to displace the instanton. We find that the minimal penalty has the expression V-2/ mu only when V is small enough. Past a critical speed, there appear nucleations of the other phase ahead of the front, their number and location are identified in terms of the imposed speed. Minimize

Year of Publication:

2006

Document Type:

Articles ; PeerReviewed

Relations:

De Masi, A., Dirr, N. and Presutti, E., 2006. Interface instability under forced displacements. Annales Henri Poincare, 7 (3), pp. 471-511.

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Title:

Analysis of the levels of conservation of the J domain among the various types of DnaJ-like proteins

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DnaJ-like proteins are defined by the presence of an approximately 73 amino acid region termed the J domain. This region bears similarity to the initial 73 amino acids of the Escherichia coli protein DnaJ. Although the structures of the J domains of E coli DnaJ and human heat shock protein 40 have been solved using nuclear magnetic resonance, no...

DnaJ-like proteins are defined by the presence of an approximately 73 amino acid region termed the J domain. This region bears similarity to the initial 73 amino acids of the Escherichia coli protein DnaJ. Although the structures of the J domains of E coli DnaJ and human heat shock protein 40 have been solved using nuclear magnetic resonance, no detailed analysis of the amino acid conservation among the J domains of the various DnaJ-like proteins has yet been attempted. A multiple alignment of 223 J domain sequences was performed, and the levels of amino acid conservation at each position were established. It was found that the levels of sequence conservation were particularly high in ‘true’ DnaJ homologues (ie, those that share full domain conservation with DnaJ) and decreased substantially in those J domains in DnaJ-like proteins that contained no additional similarity to DnaJ outside their J domain. Residues were also identified that could be important for stabilizing the J domain and for mediating the interaction with heat shock protein 70. Minimize

Publisher:

Cell Stress Society International

Year of Publication:

2000-10

Document Type:

Text

Language:

en

Subjects:

Original Articles

Original Articles Minimize

DDC:

500 Natural sciences & mathematics *(computed)*

Rights:

Copyright © 2000, Cell Stress Society International

Copyright © 2000, Cell Stress Society International Minimize

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Title:

Lipschitz percolation

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We prove the existence of a (random) Lipschitz function $F : \Z^{d-1}\to\Z^+$ such that, for every $x \in \Z^{d-1}$, the site $(x,F(x))$ is open in a site percolation process on $\Z^{d}$. The Lipschitz constant may be taken to be 1 when the parameter $p$ of the percolation model is sufficiently close to 1. ; Comment: Minor error corrected, and r...

We prove the existence of a (random) Lipschitz function $F : \Z^{d-1}\to\Z^+$ such that, for every $x \in \Z^{d-1}$, the site $(x,F(x))$ is open in a site percolation process on $\Z^{d}$. The Lipschitz constant may be taken to be 1 when the parameter $p$ of the percolation model is sufficiently close to 1. ; Comment: Minor error corrected, and reference updated Minimize

Year of Publication:

2009-11-17

Document Type:

text

Subjects:

Mathematics - Probability ; 60K35 ; 82B20

Mathematics - Probability ; 60K35 ; 82B20 Minimize

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References

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Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients. (English summary) Netw. Heterog. Media 5 (2010), no. 4, 745–763.1556-181X Summary: “We consider a so-called random obstacle model for the motion of a hypersurface through a field of random obstacles, driven by a constant driving field. The re...

Non-existence of positive stationary solutions for a class of semi-linear PDEs with random coefficients. (English summary) Netw. Heterog. Media 5 (2010), no. 4, 745–763.1556-181X Summary: “We consider a so-called random obstacle model for the motion of a hypersurface through a field of random obstacles, driven by a constant driving field. The resulting semi-linear parabolic PDE with random coefficients does not admit a global nonnegative stationary solution, which implies that an interface that was flat originally cannot get stationary. The absence of global stationary solutions is shown by proving lower bounds on the growth of stationary solutions on large domains with Dirichlet boundary conditions. Difficulties arise because the random lower order part of the equation cannot be bounded uniformly.” Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-10-01

Document Type:

text

Language:

en

Subjects:

media ; Interfaces and Free Boundaries ; 8 (2006 ; 79–109. MR2231253 (2007d ; 35144

media ; Interfaces and Free Boundaries ; 8 (2006 ; 79–109. MR2231253 (2007d ; 35144 Minimize

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Lipschitz percolation

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Abstract. We prove the existence of a (random) Lipschitz function F: Z d−1 → Z + such that, for every x ∈ Z d−1, the site (x, F (x)) is open in a site percolation process on Z d. The Lipschitz constant may be taken to be 1 when the parameter p of the percolation model is sufficiently close to 1. 1.

Abstract. We prove the existence of a (random) Lipschitz function F: Z d−1 → Z + such that, for every x ∈ Z d−1, the site (x, F (x)) is open in a site percolation process on Z d. The Lipschitz constant may be taken to be 1 when the parameter p of the percolation model is sufficiently close to 1. 1. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-04-29

Source:

http://research.microsoft.com/%7Eholroyd/papers/lip-perc.pdf

http://research.microsoft.com/%7Eholroyd/papers/lip-perc.pdf Minimize

Document Type:

text

Language:

en

Rights:

Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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