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1.
Unique minimizer for a random functional with doublewell potential in dimension 1 and 2
Title:
Unique minimizer for a random functional with doublewell potential in dimension 1 and 2
Author:
Dirr, Nicolas
;
Orlandi, E
Dirr, Nicolas
;
Orlandi, E
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Description:
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.
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Year of Publication:
201106
Document Type:
Articles ; PeerReviewed
Relations:
Dirr, N. and Orlandi, E., 2011. Unique minimizer for a random functional with doublewell potential in dimension 1 and 2. Communications in Mathematical Sciences, 9 (2), pp. 331351.
URL:
http://opus.bath.ac.uk/23000/
http://www.intlpress.com/CMS/2011/issue92/
http://opus.bath.ac.uk/23000/
http://www.intlpress.com/CMS/2011/issue92/
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2.
SharpInterface Limit of a Ginzburg–Landau Functional with a Random External Field
Title:
SharpInterface Limit of a Ginzburg–Landau Functional with a Random External Field
Author:
Dirr, Nicolas
;
Orlandi, E
Dirr, Nicolas
;
Orlandi, E
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Description:
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 doublewell 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 doublewell 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 coarsegrained, 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.
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Year of Publication:
2009
Document Type:
Articles ; PeerReviewed
Relations:
Dirr, N. and Orlandi, E., 2009. SharpInterface Limit of a Ginzburg–Landau Functional with a Random External Field. SIAM Journal on Mathematical Analysis (SIMA), 41 (2), pp. 781824.
URL:
http://opus.bath.ac.uk/14983/
http://dx.doi.org/10.1137/070684100
http://opus.bath.ac.uk/14983/
http://dx.doi.org/10.1137/070684100
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3.
Largetime behavior for viscous and nonviscous HamiltonJacobi equations forced by additive noise
Title:
Largetime behavior for viscous and nonviscous HamiltonJacobi equations forced by additive noise
Author:
Dirr, N
;
Souganidis, P E
Dirr, N
;
Souganidis, P E
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Description:
We study the largetime behavior of the solutions to viscous and nonviscous HamiltonJacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants, globalintime solutions, which attract any other solution.
We study the largetime behavior of the solutions to viscous and nonviscous HamiltonJacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants, globalintime solutions, which attract any other solution.
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Year of Publication:
2005
Document Type:
Articles ; PeerReviewed
Relations:
Dirr, N. and Souganidis, P. E., 2005. Largetime behavior for viscous and nonviscous HamiltonJacobi equations forced by additive noise. SIAM Journal on Mathematical Analysis (SIMA), 37 (3), pp. 777796.
URL:
http://opus.bath.ac.uk/7168/
http://opus.bath.ac.uk/7168/
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4.
Largetime behavior for viscous and nonviscous HamiltonJacobi equations forced by additive noise
Title:
Largetime behavior for viscous and nonviscous HamiltonJacobi equations forced by additive noise
Author:
Dirr, Nicolas
;
Souganidis, Panagiotis E.
Dirr, Nicolas
;
Souganidis, Panagiotis E.
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Description:
We study the largetime behavior of the solutions to viscous and nonviscous HamiltonJacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants, globalintime solutions, which attract any other solution.
We study the largetime behavior of the solutions to viscous and nonviscous HamiltonJacobi equations with additive noise and periodic spatial dependence. Under general structural conditions on the Hamiltonian, we show the existence of unique up to constants, globalintime solutions, which attract any other solution.
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Publisher:
Society for Industrial and Applied Mathematics
Year of Publication:
2005
Document Type:
Article ; PeerReviewed
Subjects:
QA Mathematics
QA Mathematics
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Relations:
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. Largetime behavior for viscous and nonviscous HamiltonJacobi equations forced by additive noise. SIAM Journal on Mathematical Analysis 37 (3) , pp. 777796. 10.1137/040611896...
URL:
http://orca.cf.ac.uk/13069/
http://dx.doi.org/10.1137/040611896
http://orca.cf.ac.uk/13069/
http://dx.doi.org/10.1137/040611896
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Cardiff University: ORCA (Online Research @ Cardiff)
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5.
Induction of nitrate reductase in pumpkin seedlings
Open Access
Title:
Induction of nitrate reductase in pumpkin seedlings
Author:
Amindari, Simin
;
Dirr, Michael A.
;
Splittstoesser, Walter E.
Amindari, Simin
;
Dirr, Michael A.
;
Splittstoesser, Walter E.
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Description:
Nitrate reductase activity (NRA) was found to be induced in 9dayold 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 9dayold 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 7dayold cotyledons and 9dayold roots of light grown plants; and roots of 7dayold etiolated plants. Little activity was found in etiolated cotyledons.
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Publisher:
Oxford University Press
Year of Publication:
19780401 00:00:00.0
Document Type:
TEXT
Language:
en
Subjects:
researcharticle
researcharticle
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Rights:
Copyright (C) 1978, The Japanese Society of Plant Physiologists
Copyright (C) 1978, The Japanese Society of Plant Physiologists
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URL:
http://pcp.oxfordjournals.org/cgi/content/short/19/2/299
http://pcp.oxfordjournals.org/cgi/content/short/19/2/299
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HighWire Press (Stanford University)
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6.
Interface instability under forced displacements
Title:
Interface instability under forced displacements
Author:
De Masi, A
;
Dirr, N
;
Presutti, E
De Masi, A
;
Dirr, N
;
Presutti, E
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Description:
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 V2/ 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 V2/ 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 V2/ 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.
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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. 471511.
URL:
http://opus.bath.ac.uk/7079/
http://opus.bath.ac.uk/7079/
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7.
Analysis of the levels of conservation of the J domain among the various types of DnaJlike proteins
Open Access
Title:
Analysis of the levels of conservation of the J domain among the various types of DnaJlike proteins
Author:
Hennessy, Fritha
;
Cheetham, Michael E.
;
Dirr, Heini W.
;
Blatch, Gregory L.
Hennessy, Fritha
;
Cheetham, Michael E.
;
Dirr, Heini W.
;
Blatch, Gregory L.
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Description:
DnaJlike 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...
DnaJlike 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 DnaJlike 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 DnaJlike 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.
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Publisher:
Cell Stress Society International
Year of Publication:
200010
Document Type:
Text
Language:
en
Subjects:
Original Articles
Original Articles
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DDC:
500 Natural sciences & mathematics
(computed)
Rights:
Copyright © 2000, Cell Stress Society International
Copyright © 2000, Cell Stress Society International
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URL:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC312864
http://www.ncbi.nlm.nih.gov/pubmed/11048657
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC312864
http://www.ncbi.nlm.nih.gov/pubmed/11048657
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8.
Mathematical Physics Tunneling in Two Dimensions
Open Access
Title:
Mathematical Physics Tunneling in Two Dimensions
Author:
G. Bellettini
;
A. De Masi
;
N. Dirr
;
E. Presutti
G. Bellettini
;
A. De Masi
;
N. Dirr
;
E. Presutti
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Description:
Abstract: Tunneling is studied here as a variational problem formulated in terms of a functional which approximates the rate function for large deviations in Ising systems with Glauber dynamics and Kac potentials, [9]. The spatial domain is a twodimensional square of side L with reflecting boundary conditions. For L large enough the penalty for...
Abstract: Tunneling is studied here as a variational problem formulated in terms of a functional which approximates the rate function for large deviations in Ising systems with Glauber dynamics and Kac potentials, [9]. The spatial domain is a twodimensional square of side L with reflecting boundary conditions. For L large enough the penalty for tunneling from the minus to the plus equilibrium states is determined. Minimizing sequences are fully characterized and shown to have approximately a planar symmetry at all times, thus departing from the Wulff shape in the initial and final stages of the tunneling. In a final section (Sect. 11), we extend the results to d = 3 but their validity in d> 3 is still open. 1.
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Contributors:
The Pennsylvania State University CiteSeerX Archives
Year of Publication:
20150130
Source:
http://webhost.ua.ac.be/multimat/publ/BellettiniPresuttiCommMatPhys06.pdf
http://webhost.ua.ac.be/multimat/publ/BellettiniPresuttiCommMatPhys06.pdf
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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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.544.4899
http://webhost.ua.ac.be/multimat/publ/BellettiniPresuttiCommMatPhys06.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.544.4899
http://webhost.ua.ac.be/multimat/publ/BellettiniPresuttiCommMatPhys06.pdf
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9.
Lipschitz percolation
Open Access
Title:
Lipschitz percolation
Author:
Dirr, N.
;
Dondl, P. W.
;
Grimmett, G. R.
;
Holroyd, A. E.
;
Scheutzow, M.
Dirr, N.
;
Dondl, P. W.
;
Grimmett, G. R.
;
Holroyd, A. E.
;
Scheutzow, M.
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Description:
We prove the existence of a (random) Lipschitz function $F : \Z^{d1}\to\Z^+$ such that, for every $x \in \Z^{d1}$, 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 $F : \Z^{d1}\to\Z^+$ such that, for every $x \in \Z^{d1}$, 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
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Year of Publication:
20091117
Document Type:
text
Subjects:
Mathematics  Probability ; 60K35 ; 82B20
Mathematics  Probability ; 60K35 ; 82B20
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URL:
http://arxiv.org/abs/0911.3384
http://arxiv.org/abs/0911.3384
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ArXiv.org (Cornell University Library)
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10.
LIPSCHITZ PERCOLATION
Open Access
Title:
LIPSCHITZ PERCOLATION
Author:
N. Dirr
;
P. W. Dondl
;
G. R. Grimmett
;
A. E. Holroyd
;
M. Scheutzow
N. Dirr
;
P. W. Dondl
;
G. R. Grimmett
;
A. E. Holroyd
;
M. Scheutzow
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Description:
We prove the existence of a (random) Lipschitz function F: � d−1 → � + such that, for every x ∈ � d−1, the site (x, F(x)) is open in a site percolation process on � d. The Lipschitz constant may be taken to be 1 when the parameter p of the percolation model is sufficiently close to 1.
We prove the existence of a (random) Lipschitz function F: � d−1 → � + such that, for every x ∈ � d−1, the site (x, F(x)) is open in a site percolation process on � d. The Lipschitz constant may be taken to be 1 when the parameter p of the percolation model is sufficiently close to 1.
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Contributors:
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Year of Publication:
20120309
Document Type:
text
Language:
en
Subjects:
percolation ; Lipschitz embedding ; random surface
percolation ; Lipschitz embedding ; random surface
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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.
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URL:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.207.686
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.207.686
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