Slip Line Growth as a Critical Phenomenon
Physical Review Letters, 2009 We study the growth of slip line in a plastically deforming crystal by numerical simulation of a double-ended pile-up model with a dislocation source at one end, and an absorbing wall at the other end. In presence of defects, the pile-up undergoes a second order non-equilibrium phase transition as a function of stress, which can be characterized by ...
Leoni, Fabio, Zapperi, Stefano
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Ground states for a fractional scalar field problem with critical growth [PDF]
Differential and Integral Equations, 2016 We prove the existence of a ground state solution for the following fractional scalar field equation $(-\Delta)^{s} u= g(u)$ in $\mathbb{R}^{N}$ where $s\in (0,1), N> 2s$,$ (-\Delta)^{s}$ is the fractional Laplacian, and $g\in C^{1, \beta}(\mathbb{R ...
Ambrosio, Vincenzo
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Normalized Ground State Solutions of Nonlinear Schrödinger Equations Involving Exponential Critical Growth [PDF]
Journal of Geometric Analysis, 2022 We are concerned with the following nonlinear Schrödinger equation: $$\begin{aligned} \begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+\lambda u=f(u) \ \ \textrm{in}\ \mathbb {R}^{2},\\ u\in H^{1}(\mathbb {R}^{2}),~~~ \int _{\mathbb {R}^2}u^2dx=\rho ,
Xiaojun Chang, Man Liu, Duokui Yan
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Parametric superlinear double phase problems with singular term and critical growth on the boundary [PDF]
Mathematical methods in the applied sciences, 2021 In this paper, we study quasilinear elliptic equations driven by the double phase operator along with a reaction that has a singular and a parametric superlinear term and with a nonlinear Neumann boundary condition of critical growth.
Ángel Crespo-Blanco +2 more
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Automated Method to Determine Two Critical Growth Stages of Wheat: Heading and Flowering. [PDF]
Front Plant Sci, 2017 Recording growth stage information is an important aspect of precision agriculture, crop breeding and phenotyping. In practice, crop growth stage is still primarily monitored by-eye, which is not only laborious and time-consuming, but also subjective and
Sadeghi-Tehran P +3 more
europepmc +2 more sources
A planar Schrödinger–Newton system with Trudinger–Moser critical growth
Calculus of Variations and Partial Differential Equations, 2023 In this paper, we focus on the existence of positive solutions to the following planar Schrödinger–Newton system with general critical exponential growth $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta {u}+u+\phi u =f(u)&{} \text{ in }\,\,\mathbb {R}^
Zhisu Liu, V. Rǎdulescu, Jianjun Zhang
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Drought-Tolerant Bacteria and Arbuscular Mycorrhizal Fungi Mitigate the Detrimental Effects of Drought Stress Induced by Withholding Irrigation at Critical Growth Stages of Soybean (Glycine max, L.) [PDF]
MicroorganismsConsidering current global climate change, drought stress is regarded as a major problem negatively impacting the growth of soybeans, particularly at the critical stages R3 (early pod) and R5 (seed development).
Aya Ahmed Nader +3 more
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Probabilistic aspects of critical growth-fragmentation equations [PDF]
, 2015 The self-similar growth-fragmentation equation describes the evolution of a medium in which particles grow and divide as time proceeds, with the growth and splitting of each particle depending only upon its size.
Bertoin, Jean, Watson, Alexander R.
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Fractional NLS equations with magnetic field, critical frequency and critical growth [PDF]
Manuscripta mathematica, 2016 The paper is devoted to the study of singularly perturbed fractional Schrödinger equations involving critical frequency and critical growth in the presence of a magnetic field.
Binlin Zhang, M. Squassina, Zhang Xia
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Advances in Nonlinear Analysis, 2016 In this paper, we concern ourselves with the following Kirchhoff-type equations: { - ( a + b ∫ ℝ 3 | ∇ u | 2 𝑑 x ) △ u + V u = f ( u ) in ℝ 3 , u ∈ H 1 ( ℝ 3 ) , \left\{\begin{aligned} \displaystyle-\biggl{(}a+b\int_{\mathbb{R}^{3 ...
Liping Xu, Haibo Chen
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