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Enrico Valdinoci - One of the best experts on this subject based on the ideXlab platform.
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a three dimensional symmetry result for a phase Transition Equation in the genuinely nonlocal regime
Calculus of Variations and Partial Differential Equations, 2018Co-Authors: Serena Dipierro, Enrico Valdinoci, Alberto FarinaAbstract:We consider bounded solutions of the nonlocal Allen–Cahn Equation $$\begin{aligned} (-\Delta )^s u=u-u^3\qquad { \text{ in } }\mathbb {R}^3, \end{aligned}$$ under the monotonicity condition $$\partial _{x_3}u>0$$ and in the genuinely nonlocal regime in which $$s\in \left( 0,\frac{1}{2}\right) $$ . Under the limit assumptions $$\begin{aligned} \lim _{x_n\rightarrow -\infty } u(x',x_n)=-1\quad { \text{ and } }\quad \lim _{x_n\rightarrow +\infty } u(x',x_n)=1, \end{aligned}$$ it has been recently shown in Dipierro et al. (Improvement of flatness for nonlocal phase Transitions, 2016) that u is necessarily 1D, i.e. it depends only on one Euclidean variable. The goal of this paper is to obtain a similar result without assuming such limit conditions. This type of results can be seen as nonlocal counterparts of the celebrated conjecture formulated by De Giorgi (Proceedings of the international meeting on recent methods in nonlinear analysis (Rome, 1978), Pitagora, Bologna, pp 131–188, 1979).
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a three dimensional symmetry result for a phase Transition Equation in the genuinely nonlocal regime
arXiv: Analysis of PDEs, 2017Co-Authors: Serena Dipierro, Enrico Valdinoci, Alberto FarinaAbstract:We consider bounded solutions of the nonlocal Allen-Cahn Equation $$ (-\Delta)^s u=u-u^3\qquad{\mbox{ in }}{\mathbb{R}}^3,$$ under the monotonicity condition $\partial_{x_3}u>0$ and in the genuinely nonlocal regime in which~$s\in\left(0,\frac12\right)$. Under the limit assumptions $$ \lim_{x_n\to-\infty} u(x',x_n)=-1\quad{\mbox{ and }}\quad \lim_{x_n\to+\infty} u(x',x_n)=1,$$ it has been recently shown that~$u$ is necessarily $1$D, i.e. it depends only on one Euclidean variable. The goal of this paper is to obtain a similar result without assuming such limit conditions. This type of results can be seen as nonlocal counterparts of the celebrated conjecture formulated by Ennio De Giorgi.
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plane like minimizers for a non local ginzburg landau type energy in a periodic medium
arXiv: Analysis of PDEs, 2015Co-Authors: Matteo Cozzi, Enrico ValdinociAbstract:We consider a non-local phase Transition Equation set in a periodic medium and we construct solutions whose interface stays in a slab of prescribed direction and universal width. The solutions constructed also enjoy a local minimality property with respect to a suitable non-local energy functional.
Frank L Lewis - One of the best experts on this subject based on the ideXlab platform.
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Analysis of Deadlock and Circular Waits Using a Matrix Model for Flexible Manufacturing Systems
Automatica, 1998Co-Authors: Frank L Lewis, A. Gurel, Stjepan Bogdan, Alper Doganalp, Octavian PastravanuAbstract:The problem of deadlock in a large class of reentrant flowline systems is analysed based on a Petri net model. The relation between deadlock and circular waits is established by rigorously defining the situation of circular blocking. Deadlock analysis is then performed in terms of circular waits and their associated structures, the so-called critical siphons and critical subsystems. A dynamical system representation obtained by coupling the Petri net marking Transition Equation with the matrix rule-based controller Equations is adopted. The task of computing the Petri net structures of deadlock analysis is largely simplified (operations involved are of polynomial complexity) by using the matrices of this system description. An on-line maximally permissive control policy for deadlock avoidance (MAXWIP) is then devised. This can be efficiently implemented by incorporating the ''outer-loop'' control decisions via certain dispatching control inputs. The result is a dispatching control with deadlock avoidance, which is a generalized kanban scheme.
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a new matrix model for discrete event systems application to simulation
IEEE Control Systems Magazine, 1997Co-Authors: D A Tacconi, Frank L LewisAbstract:Simulation schemes for discrete event (DE) systems based on a new DE matrix formulation are presented. This new formulation is a hybrid system with logical and algebraic components that allows fast, direct design and reconfiguration of rule-based controllers for manufacturing systems. It applies to general DE systems that include shared resources, dispatching, circular waits, and variable part routing. A certain DE matrix state Equation together with the familiar Petri net marking Transition Equation yield a complete dynamical description of a DE system. Our goal in this article is to show that this provides a simplified computer tool that allows efficient simulation and modeling for DE systems.
D S Sanditov - One of the best experts on this subject based on the ideXlab platform.
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On relaxation nature of glass Transition in amorphous materials
'Elsevier BV', 2017Co-Authors: D S Sanditov, Ojovan MAbstract:A short review on relaxation theories of glass Transition is presented. The main attention is paid to modern aspects of the glass Transition Equation qτg = C, suggested by Bartenev in 1951 (q – cooling rate of the melt, τg – structural relaxation time at the glass Transition temperature Tg). This Equation represents a criterion of structural relaxation at Transition from liquid to glass at T = Tg (analogous to the condition of mechanical relaxation ωτ = 1, where the maximum of mechanical loss is observed). The empirical parameter С = δTg has the meaning of temperature range δTg that characterizes the liquid-glass Transition. Different approaches of δTg calculation are reviewed. In the framework of the model of delocalized atoms a modified kinetic criterion of glass Transition is proposed (q/Tg)τg = Cg, where Cg ≅ 7·10−3 is a practically universal dimensionless constant. It depends on fraction of fluctuation volume fg, which is frozen at the glass Transition temperature Cg = fg/ln(1/fg). The value of fg is approximately constant fg ≅ 0.025. At Tg the process of atom delocalization, i.e. its displacement from the equilibrium position, is frozen. In silicate glasses atom delocalization is reduced to critical displacement of bridge oxygen atom in Si-O-Si bridge necessary to switch a valence bond according to Muller and Nemilov. An Equation is derived for the temperature dependence of viscosity of glass-forming liquids in the wide temperature range, including the liquid-glass Transition and the region of higher temperatures. Notion of (bridge) atom delocalization is developed, which is related to necessity of local low activation deformation of structural network for realization of elementary act of viscous flow – activated switch of a valence (bridge) bond. Without atom delocalization (“trigger mechanism”) a switch of the valence bond is impossible and, consequently, the viscous flow. Thus the freezing of atom delocalization process at low temperatures, around Tg, leads to the cease of the viscous flow and Transition of a melt to a glassy state. This occurs when the energy of disordered lattice thermal vibrations averaged to one atom becomes equal or less than the energy of atom delocalization. The Bartenev Equation for cooling rate dependence of glass Transition temperature Tg = Tg(q) is discussed. The value of fg calculated from the data on the Tg(q) dependence coincides with result of the fg calculation using the data on viscosity near the glass Transition. Derivation of the Bartenev Equation with the account of temperature dependence of activation energy of glass Transition process is considered. The obtained generalized relation describes the Tg(q) dependence in a wider interval of the cooling rate compared Bartenev Equation. Experimental data related to standard cooling rate q = 3 K/min were used in this work
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on the nature of the liquid to glass Transition Equation
Journal of Experimental and Theoretical Physics, 2016Co-Authors: D S SanditovAbstract:Within the model of delocalized atoms, it is shown that the parameter δTg, which enters the glassTransition Equation qτg = δTg and characterizes the temperature interval in which the structure of a liquid is frozen, is determined by the fluctuation volume fraction \({f_g} = {\left( {{{\Delta {V_e}} \mathord{\left/ {\vphantom {{\Delta {V_e}} V}} \right. \kern-\nulldelimiterspace} V}} \right)_{T = {T_g}}}\) frozen at the glass-Transition temperature Tg and the temperature Tg itself. The parameter δTg is estimated by data on fg and Tg. The results obtained are in agreement with the values of δTg calculated by the Williams–Landel–Ferry (WLF) Equation, as well as with the product qτg—the left-hand side of the glass-Transition Equation (q is the cooling rate of the melt, and τg is the structural relaxation time at the glass-Transition temperature). Glasses of the same class with fg ≈ const exhibit a linear correlation between δTg and Tg. It is established that the currently used methods of Bartenev and Nemilov for calculating δTg yield overestimated values, which is associated with the assumption, made during deriving the calculation formulas, that the activation energy of the glass-Transition process is constant. A generalized Bartenev Equation is derived for the dependence of the glass-Transition temperature on the cooling rate of the melt with regard to the temperature dependence of the activation energy of the glassTransition process. A modified version of the kinetic glass-Transition criterion is proposed. A conception is developed that the fluctuation volume fraction f = ΔVe/V can be interpreted as an internal structural parameter analogous to the parameter ξ in the Mandelstam–Leontovich theory, and a conjecture is put forward that the delocalization of an active atom—its critical displacement from the equilibrium position—can be considered as one of possible variants of excitation of a particle in the Vol’kenshtein–Ptitsyn theory. The experimental data used in the study refer to a constant cooling rate of q = 0.05 K/s (3 K/min).
Miaozhi Zhao - One of the best experts on this subject based on the ideXlab platform.
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thermodynamics of size effect on phase Transition temperatures of dispersed phases
Journal of Physical Chemistry C, 2011Co-Authors: Miaozhi ZhaoAbstract:An Equation for a phase Transition in a dispersed system has been proposed, and the applications of the Equation in various kinds of phase Transitions have been discussed. The determinate relation between the interfacial tension and the radius of a droplet has been derived by the monolayer model. Applying the fusion Transition Equation and the interfacial tension relation, the melting temperatures of Au and Sn nanoparticles have been calculated, and the predicted melting temperatures are in good agreement with the available experimental data. The research results show that the phase Transition Equations can be applied to predict the temperatures of phase Transitions of dispersed systems and to explain the phenomenon of metastable states; that the size of a dispersed phase has a remarkable effect on the phase Transition temperatures, and the phase Transition temperatures decrease with the radius of the dispersed phase decreasing; and that the depression of the melting temperature for a nanowire is half of ...
F.l. Lewis - One of the best experts on this subject based on the ideXlab platform.
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Intelligent material handling: development and implementation of a matrix-based discrete-event controller
IEEE Transactions on Industrial Electronics, 2001Co-Authors: Jorge Mireles, F.l. LewisAbstract:A supervisory controller for discrete-event (DE) systems is presented that uses a novel matrix formulation. This matrix formulation makes it possible to directly write down the DE controller from standard manufacturing tools such as the bill of materials or the assembly tree. The matrices also make it straightforward to actually implement the DE controller on a manufacturing workcell for sequencing the jobs and assigning the resources. It is shown that the DE controller Equations plus the Petri net marking Transition Equation together provide a complete dynamical description of a DE system. This means that a computer simulation can be performed to check the DE performance of the controller before it is implemented. In this paper, the authors implement the DE controller on an actual three-robot intelligent material handling cell at the Automation and Robotics Research Institute, University of Texas at Arlington, USA. Then, they show that the actual implementation and the simulated system give commensurate results. The versatility of the system developed with this DE controller permits implementing different methodologies for conflict resolution, as well as optimization of the resource assignment and part throughput. Technical information given includes the development of the controller in LabVIEW and its simulation using MATLAB.