The Experts below are selected from a list of 4407 Experts worldwide ranked by ideXlab platform
Anna Rozanova-pierrat - One of the best experts on this subject based on the ideXlab platform.
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Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions
Mathematical Models and Methods in Applied Sciences, 2015Co-Authors: Claude Bardos, Denis S. Grebenkov, Anna Rozanova-pierratAbstract:We consider a heat problem with discontinuous diffusion coefficients and discontinuous transmission boundary conditions with a Resistance coefficient. For all bounded (ϵ, δ)-domains Ω ⊂ ℝn with a d-set boundary (for instance, a self-similar fractal), we find the first term of the small-time asymptotic expansion of the heat content in the complement of Ω, and also the second-order term in the case of a regular boundary. The asymptotic expansion is different for the cases of finite and Infinite Resistance of the boundary. The derived formulas relate the heat content to the volume of the interior Minkowski sausage and present a mathematical justification to the de Gennes' approach. The accuracy of the analytical results is illustrated by solving the heat problem on prefractal domains by a finite elements method.
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Short time heat diffusion in compact domains with discontinuous transmission boundary conditions
arXiv: Analysis of PDEs, 2015Co-Authors: Claude Bardos, Denis S. Grebenkov, Anna Rozanova-pierratAbstract:We consider a heat problem with discontinuous diffusion coefficientsand discontinuous transmission boundary conditions with a Resistancecoefficient. For all compact $(\epsilon,\delta)$-domains $\Omega\subset\mathbb{R}^n$ with a $d$-set boundary (for instance, aself-similar fractal), we find the first term of the small-timeasymptotic expansion of the heat content in the complement of$\Omega$, and also the second-order term in the case of a regularboundary. The asymptotic expansion is different for the cases offinite and Infinite Resistance of the boundary. The derived formulasrelate the heat content to the volume of the interior Minkowskisausage and present a mathematical justification to the de Gennes'approach. The accuracy of the analytical results is illustrated bysolving the heat problem on prefractal domains by a finite elementsmethod.
Claude Bardos - One of the best experts on this subject based on the ideXlab platform.
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Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions
Mathematical Models and Methods in Applied Sciences, 2015Co-Authors: Claude Bardos, Denis S. Grebenkov, Anna Rozanova-pierratAbstract:We consider a heat problem with discontinuous diffusion coefficients and discontinuous transmission boundary conditions with a Resistance coefficient. For all bounded (ϵ, δ)-domains Ω ⊂ ℝn with a d-set boundary (for instance, a self-similar fractal), we find the first term of the small-time asymptotic expansion of the heat content in the complement of Ω, and also the second-order term in the case of a regular boundary. The asymptotic expansion is different for the cases of finite and Infinite Resistance of the boundary. The derived formulas relate the heat content to the volume of the interior Minkowski sausage and present a mathematical justification to the de Gennes' approach. The accuracy of the analytical results is illustrated by solving the heat problem on prefractal domains by a finite elements method.
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Short time heat diffusion in compact domains with discontinuous transmission boundary conditions
arXiv: Analysis of PDEs, 2015Co-Authors: Claude Bardos, Denis S. Grebenkov, Anna Rozanova-pierratAbstract:We consider a heat problem with discontinuous diffusion coefficientsand discontinuous transmission boundary conditions with a Resistancecoefficient. For all compact $(\epsilon,\delta)$-domains $\Omega\subset\mathbb{R}^n$ with a $d$-set boundary (for instance, aself-similar fractal), we find the first term of the small-timeasymptotic expansion of the heat content in the complement of$\Omega$, and also the second-order term in the case of a regularboundary. The asymptotic expansion is different for the cases offinite and Infinite Resistance of the boundary. The derived formulasrelate the heat content to the volume of the interior Minkowskisausage and present a mathematical justification to the de Gennes'approach. The accuracy of the analytical results is illustrated bysolving the heat problem on prefractal domains by a finite elementsmethod.
Valerii M. Vinokur - One of the best experts on this subject based on the ideXlab platform.
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Magnetic Monopoles and Superinsulation in Josephson Junction Arrays
Quantum Reports, 2020Co-Authors: Carlo A. Trugenberger, M. Cristina Diamantini, Nicola Poccia, Flavio S. Nogueira, Valerii M. VinokurAbstract:Electric-magnetic duality or S-duality, extending the symmetry of Maxwell’s equations by including the symmetry between Noether electric charges and topological magnetic monopoles, is one of the most fundamental concepts of modern physics. In two-dimensional systems harboring Cooper pairs, S-duality manifests in the emergence of superinsulation, a state dual to superconductivity, which exhibits an Infinite Resistance at finite temperatures. The mechanism behind this Infinite Resistance is the linear charge confinement by a magnetic monopole plasma. This plasma constricts electric field lines connecting the charge–anti-charge pairs into electric strings, in analogy to quarks within hadrons. However, the origin of the monopole plasma remains an open question. Here, we consider a two-dimensional Josephson junction array (JJA) and reveal that the magnetic monopole plasma arises as quantum instantons, thus establishing the underlying mechanism of superinsulation as two-dimensional quantum tunneling events. We calculate the string tension and the dimension of an electric pion determining the minimal size of a system capable of hosting superinsulation. Our findings pave the way for study of fundamental S-duality in desktop experiments on JJA and superconducting films.
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The Superconductor-Superinsulator Transition: S-duality and the QCD on the Desktop
Journal of Superconductivity and Novel Magnetism, 2019Co-Authors: M. Cristina Diamantini, Carlo A. Trugenberger, Luca Gammaitoni, Valerii M. VinokurAbstract:We show that the nature of quantum phases around the superconductor-insulator transition (SIT) is controlled by charge-vortex topological interactions, and does not depend on the details of material parameters and disorder. We find three distinct phases, superconductor, superinsulator, and bosonic topological insulator. The superinsulator is a state of matter with Infinite Resistance in a finite temperature range, which is the S-dual of the superconductor and in which charge transport is prevented by electric strings binding charges of opposite sign. The electric strings ensuring linear confinement of charges are generated by instantons and are dual to superconducting Abrikosov vortices. Material parameters and disorder enter the London penetration depth of the superconductor, the string tension of the superinsulator and the quantum fluctuation parameter driving the transition between them. They are entirely encoded in four phenomenological parameters of a topological gauge theory of the SIT. Finally, we point out that, in the context of strong coupling gauge theories, the many-body localization phenomenon that is often referred to as an underlying mechanism for superinsulation is a mere transcription of the well-known phenomenon of confinement into solid-state physics language and is entirely driven by endogenous disorder embodied by instantons with no need of exogenous disorder.
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Confinement and asymptotic freedom with Cooper pairs
Communications Physics, 2018Co-Authors: M. C. Diamantini, Carlo A. Trugenberger, Valerii M. VinokurAbstract:One of the most profound aspects of the standard model of particle physics, the mechanism of confinement binding quarks into hadrons, is not sufficiently understood. The only known semiclassical mechanism of confinement, mediated by chromo-electric strings in a condensate of magnetic monopoles still lacks experimental evidence. Here we show that the Infinite Resistance superinsulating state, which emerges on the insulating side of the superconductor-insulator transition in superconducting films offers a realization of confinement that allows for a direct experimental access. We find that superinsulators realize a single-color version of quantum chromodynamics and establish the mapping of quarks onto Cooper pairs. We reveal that the mechanism of superinsulation is the linear binding of Cooper pairs into neutral “mesons” by electric strings. Our findings offer a powerful laboratory for exploring and testing the fundamental implications of confinement, asymptotic freedom, and related quantum chromodynamics phenomena via desktop experiments on superconductors. The standard model describes many aspects of particle physics but mechanisms such as the binding of quarks into hadrons, still remain a mystery. The authors theoretically outline an analogy with the Cooper pairs of a superinsulator to demonstrate that the mechanisms behind the Infinite Resistance of a superinsulator are analogous to that which confine quarks into hadrons.
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The superconductor-superinsulator transition: S-duality and QCD on the desktop
arXiv: Superconductivity, 2018Co-Authors: M. Cristina Diamantini, Carlo A. Trugenberger, Luca Gammaitoni, Valerii M. VinokurAbstract:We show that the nature of quantum phases around the superconductor-insulator transition (SIT) is controlled by charge-vortex topological interactions and does not depend on the details of material parameters and disorder. We find three distinct phases, superconductor, superinsulator and bosonic topological insulator. The superinsulator is a state of matter with Infinite Resistance in a finite temperature range, which is the S-dual of the superconductor and in which charge transport is prevented by electric strings binding charges of opposite sign. The electric strings ensuring linear confinement of charges are generated by instantons and are dual to superconducting Abrikosov vortices. Material parameters and disorder enter the London penetration depth of the superconductor, the string tension of the superinsulator and the quantum fluctuation parameter driving the transition between them. They are entirely encoded in four phenomenological parameters of a topological gauge theory of the SIT. Finally, we point out that, in the context of strong coupling gauge theories, the many-body localization phenomenon that is often referred to as an underlying mechanism for superinsulation is a mere transcription of the well-known phenomenon of confinement into solid state physics language and is entirely driven by endogenous disorder embodied by instantons with no need of exogenous disorder.
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arXiv : Gauge Topological Nature of the Superconductor-Insulator Transition
arXiv: Superconductivity, 2017Co-Authors: M. C. Diamantini, Valerii M. Vinokur, I. Lukyanchuk, Carlo A. TrugenbergerAbstract:It has long been believed that, at absolute zero, electrons can form only one quantum coherent state, a superconductor. Yet, several two dimensional superconducting systems were found to harbor the superinsulating state with Infinite Resistance, a mirror image of superconductivity, and a metallic state often referred to as Bose metal, characterized by finite longitudinal and vanishing Hall Resistances. The nature of these novel and mysterious quantum coherent states is the subject of intense study.Here, we propose a topological gauge description of the superconductor-insulator transition (SIT) that enables us to identify the underlying mechanism of superinsulation as Polyakov's linear confinement of Cooper pairs via instantons. We find a criterion defining conditions for either a direct SIT or for the SIT via the intermediate Bose metal and demonstrate that this Bose metal phase is a Mott topological insulator in which the Cooper pair-vortex liquid is frozen by Aharonov-Bohm interactions.
Denis S. Grebenkov - One of the best experts on this subject based on the ideXlab platform.
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Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions
Mathematical Models and Methods in Applied Sciences, 2015Co-Authors: Claude Bardos, Denis S. Grebenkov, Anna Rozanova-pierratAbstract:We consider a heat problem with discontinuous diffusion coefficients and discontinuous transmission boundary conditions with a Resistance coefficient. For all bounded (ϵ, δ)-domains Ω ⊂ ℝn with a d-set boundary (for instance, a self-similar fractal), we find the first term of the small-time asymptotic expansion of the heat content in the complement of Ω, and also the second-order term in the case of a regular boundary. The asymptotic expansion is different for the cases of finite and Infinite Resistance of the boundary. The derived formulas relate the heat content to the volume of the interior Minkowski sausage and present a mathematical justification to the de Gennes' approach. The accuracy of the analytical results is illustrated by solving the heat problem on prefractal domains by a finite elements method.
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Short time heat diffusion in compact domains with discontinuous transmission boundary conditions
arXiv: Analysis of PDEs, 2015Co-Authors: Claude Bardos, Denis S. Grebenkov, Anna Rozanova-pierratAbstract:We consider a heat problem with discontinuous diffusion coefficientsand discontinuous transmission boundary conditions with a Resistancecoefficient. For all compact $(\epsilon,\delta)$-domains $\Omega\subset\mathbb{R}^n$ with a $d$-set boundary (for instance, aself-similar fractal), we find the first term of the small-timeasymptotic expansion of the heat content in the complement of$\Omega$, and also the second-order term in the case of a regularboundary. The asymptotic expansion is different for the cases offinite and Infinite Resistance of the boundary. The derived formulasrelate the heat content to the volume of the interior Minkowskisausage and present a mathematical justification to the de Gennes'approach. The accuracy of the analytical results is illustrated bysolving the heat problem on prefractal domains by a finite elementsmethod.
Jianbiao Pan - One of the best experts on this subject based on the ideXlab platform.
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A Control-Chart Based Method for Solder Joint Crack Detection
Journal of Microelectronics and Electronic Packaging, 2014Co-Authors: Jianbiao PanAbstract:Many researchers have used different failure criteria in published solder joint reliability studies. Since the reported time-to-failure would be different if different failure criteria were used, it would be difficult to compare the reported reliability life of solder joints from one study to another. The purpose of this study is to evaluate the effect of failure criteria on the reported thermal fatigue life and determine which failure criterion could detect failure sooner. First, the application of the control-chart-based method in a thermal cycling reliability study is described. The reported time-to-failure data were then compared based on four different failure criteria: a control-chart-based method, a 20% Resistance increase from IPC-9701A, a Resistance threshold of 500 Ω, and an Infinite Resistance. Over 3.5 GB Resistance data measured by data loggers from a low-silver solder joint reliability study were analyzed. The results show that estimated time-to-failure based on the control-chart-based metho...
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A Control-Chart Based Method for Solder Joint Crack Detection - conference proceeding
2014Co-Authors: Jianbiao PanAbstract:Many researchers have used different failure criteria in the published solder joint reliability studies. Since the reported timeto-failure would be different if different failure criteria were used, it would be difficult to compare the reported reliability life of solder joints from one study to another. The purpose of this study is to evaluate the effect of failure criteria on the reported thermal fatigue life and find out which failure criterion can detect failure sooner. First, the application of the control-chart based method in a thermal cycling reliability study is described. The reported time-to-failure data were then compared based on four different failure criteria: a control-chart based method, a 20% Resistance increase from IPC-9701A, a Resistance threshold of 500Ω, and an Infinite Resistance. Over 3.5 GB Resistance data measured by data loggers from a low-silver solder joint reliability study were analyzed. The results show that estimated time-to-failure based on the control-chart method is very similar to that when the IPC-9701A failure criterion is used. Both methods detected failure much earlier than the failure criterion of a Resistance threshold of 500Ω or an Infinite Resistance. A scientific explanation is made of why the 20% increase in IPC-9701A is a reasonable failure criterion and why the IPC-9701A and the control-chart based method produced similar results. Three different stages in Resistance change were identified: stable, crack, and open. It is recommended that the control-chart based method be used as failure criterion because it not only monitors the average of Resistance, but also monitors the dispersion of Resistance in each thermal cycle over time.
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Reliability analysis of low-Ag BGA solder joints using four failure criteria
2012Co-Authors: Erin Kimura, Jianbiao PanAbstract:The appropriate selection of failure criterion for solder joint studies is necessary to correctly estimate reliability life. The objective of this study is to compare the effect of different failure criteria on the reliability life estimation. The four failure criteria in this study are a 20% Resistance increase defined in the IPC-9701A standard, a Resistance beyond 500Ω, an Infinite Resistance (hard open), and a failure criterion based on X and R control charts. Accelerated thermal cycling conditions of a low-silver BGA study included 0°C to 100 °C with ten minute dwell times and −40°C to 125°C with ten minute dwell times. The results show that the life estimation based on X and R failure criterion is very similar to the life estimation when a 20% Resistance increase defined in the IPC-9701A failure criterion is used. The results also show that the reliability life would be overestimated if the failure criterion of a Resistance threshold of 500Ω or an Infinite Resistance (hard open) is used.