The authors consider the well-posedness in energy space of the critical non-linear system of wave equations with Hamiltonian structure{utt-△u=-F1（｜u｜^2,｜v｜^2）u,utt-△u=-F2（｜u｜^2,｜v｜^2）u where there exists...
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The authors consider the well-posedness in energy space of the critical non-linear system of wave equations with Hamiltonian structure{utt-△u=-F1（｜u｜^2,｜v｜^2）u,utt-△u=-F2（｜u｜^2,｜v｜^2）u where there exists a function F（λ,μ） such that δF（λ,μ）/δλ=F1（λ,μ）.δF（λ,μ）/δμ=F2（λ,μ） By showing that the energy and dilation identities hold for weak solution under some assumptions on the non-linearities, we prove the global well-posedness in energy space by a similar argument to that for global regularity as shown in ＂Shatah and Struwe＇s paper, Ann. of Math. 138, 503-518 （1993）＂.
This book presents a broad survey of models for critical and catastrophic phenomena in the geosciences, with strong emphasis on earthquakes. It assumes the perspective of statistical physics, which provides the theore...
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ISBN:
(数字)9783540353751
ISBN:
(纸本)9783540353737;9783642071263
This book presents a broad survey of models for critical and catastrophic phenomena in the geosciences, with strong emphasis on earthquakes. It assumes the perspective of statistical physics, which provides the theoretical frame for dealing with complex systems in general. This volume addresses graduate students wishing to specialize in the field and researchers working or interested in the field having a background in the physics, geosciences or appliedmathematics.
In this paper, the dynamics behaviors on fo-δ parameter surface is investigated for Gledzer-Ohkitani- Yamada model We indicate the type of intermittency chaos transitions is saddle node bifurcation. We plot phase dia...
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In this paper, the dynamics behaviors on fo-δ parameter surface is investigated for Gledzer-Ohkitani- Yamada model We indicate the type of intermittency chaos transitions is saddle node bifurcation. We plot phase diagram on fo-δ parameter surface, which is divided into periodic, quasi-periodic, and intermittent chaos areas. By means of varying Taylor-microscale Reynolds number, we calculate the extended self-similarity of velocity structure function.
In this paper the nonlinear response of zero-force members is investigated in linear elastic pin-jointed trusses and it is shown that in such members the normal force is typically a quadratic function of the load para...
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In this paper the nonlinear response of zero-force members is investigated in linear elastic pin-jointed trusses and it is shown that in such members the normal force is typically a quadratic function of the load parameter, and so the sign of the normal force does not depend on the sign of the load. A simple, intuitive method is provided to determine the sign of the normal force. A 'degenerate' example is also demonstrated, containing zero-force members in which the dependence of the internal force on the load parameter is of arbitrary order.
We propose the coarse-grained spectral projection method (CGSP), a deep learning assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show that CGSP can extract spect...
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We propose the coarse-grained spectral projection method (CGSP), a deep learning assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show that CGSP can extract spectral components of many-body quantum states systematically with a sophisticated neural network quantum ansatz. CGSP fully exploits the linear unitary nature of the quantum dynamics and is potentially superior to other quantum Monte Carlo methods for ergodic dynamics. Preliminary numerical results on one-dimensional XXZ models with periodic boundary conditions are carried out to demonstrate the practicality of CGSP.
In this paper, the recent studies of laboratory astrophysics with strong magnetic fields in China have been *** the Shenguang-II laser facility of the National Laboratory on High-Power Lasers and physics, a laser-driv...
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In this paper, the recent studies of laboratory astrophysics with strong magnetic fields in China have been *** the Shenguang-II laser facility of the National Laboratory on High-Power Lasers and physics, a laser-driven strong magnetic field up to 200 T has been achieved. The experiment was performed to model the interaction of solar wind with dayside magnetosphere. Also the low beta plasma magnetic reconnection(MR) has been studied. Theoretically, the model has been developed to deal with the atomic structures and processes in strong magnetic field. Also the study of shock wave generation in the magnetized counter-streaming plasmas is introduced.
Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,...
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Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary,spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.
Atomic-scale defects generated in materials under both equilibrium and irradiation conditions can significantly impact their physical and mechanical *** the energetically most favorable ground-state configurations of ...
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Atomic-scale defects generated in materials under both equilibrium and irradiation conditions can significantly impact their physical and mechanical *** the energetically most favorable ground-state configurations of these defects is an important step towards the fundamental understanding of their influence on the performance of materials ranging from photovoltaics to advanced nuclear ***,using fluorite-structured thorium dioxide(ThO_(2))as an exemplar,we demonstrate how density functional theory and machine learning interatomic potential can be synergistically combined into a powerful tool that enables exhaustive exploration of the large configuration spaces of small point defect *** study leads to several unexpected discoveries,including defect polymorphism and ground-state structures that defy our physical *** physical origins of these unexpected findings are elucidated using a local cluster expansion model developed in this work.
In this article, we introduce Tsinghua Global Minimum （TGMin） as a new program for the global minimum searching of geometric structures of gas-phase or surface-supported atomic clusters, and the constrained basin-ho...
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In this article, we introduce Tsinghua Global Minimum （TGMin） as a new program for the global minimum searching of geometric structures of gas-phase or surface-supported atomic clusters, and the constrained basin-hopping （BH） algorithm implemented in this program. To improve the efficiency of the BH algorithm, several types of constraints are introduced to reduce the vast search space, including constraints on the random displacement step size, displacement of low-coordination atoms, and geometrical structure adjustment after displacement. The ultrafast shape-recognition （USR） algorithm and its variants are implemented to identify duplicate structures during the global minimum search. In addition to the Metropolis acceptance criterion, we also implemented a morphology-based constraint that confines the global minimum search to a specific type of morphology, such as planar or non-planar structures, which offers a strict divide-and-conquer strategy for the BH algorithm. These improvements are implemented in the TGMin program, which was developed over the past decade and has been used in a number of publications. We tested our TGMin program on global minimum structural searches for a number of metal and main-group clusters including C60, Au20 and B20 clusters. Over the past five years, the TGMin program has been used to determine the global minimum structures of a series of boron atomic clusters （such as [B26]^-, [B28]^-, [B30]^-, [B35]^-, [B36]^-, [B39]^-, [B40]^-, [MnB16]^-, [COB18]^-, [RhB18]^-, and [TaB20]^-）, metal-containing clusters Lin （n = 3-20）, Aug（CO）8^＋ and [Cr6O19]^2-. and the oxide-supported metal catalyst Au7/γ-Al2O3, as well as other isolated and surface-supported atomic clusters. In this article we present the major features of TGMin program and show that it is highly efficient at searching for global-minimum structures of atomic clusters in the gas phase and on various surface supports.
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