Consider the following coupled Schrödinger system with Sobolev critical exponent −Δui+λiui=∑j=1dβij|uj|[Formula presented]|ui|[Formula presented]−2ui in Ω,i=1,2,.,d, where d≥2, 2⁎=[Formula presented] is the...
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We report an extensive molecular dynamics study of ab-initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surface...
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We consider backward stochastic differential equations (BSDEs) with mean-field and McKean–Vlasov interactions in their generators in a general setting, where the drivers are square–integrable martingales, with a foc...
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In today’s digital world,the most inevitable challenge is the protection of digital *** to the weak confidentiality preserving techniques,the existing world is facing several digital information *** make our digital d...
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In today’s digital world,the most inevitable challenge is the protection of digital *** to the weak confidentiality preserving techniques,the existing world is facing several digital information *** make our digital data indecipherable to the unauthorized person,a technique forfinding a crypto-graphically strong Substitution box(S-box)have *** S-box with sound cryptographic assets such as nonlinearity(NL),strict avalanche criterion(SAC),bit independence criteria(BIC),bit independence criteria of nonlinearity(BIC-NL),Bit independence criteria of Strict avalanche criteria(BIC-SAC),and Input/output XOR is considered as the robust *** Decision-Making Trial and Evaluation Laboratory(DEMATEL)approach of multi-criteria decision making(MCDM)is proposed forfinding the interrelation among cryptographic properties.A combination of two MCDM methods namely Entropy and multi-objective optimization based on ratio analysis(MOORA)is applied for the best S-box selection.A robust substitution box is selected for secure communications in cryptography by using the combination of DEMETAL selection criteria,entro-py weight assigning,and MOORA ranking *** combination of these three methods provides a fast selection procedure for the secure confusion *** offered selection method can also be utilized for the choice of the best cryptosystem with highly secure properties and resistive against all possible linear and differential attacks in the cryptanalysis.
In this paper we propose and analyze a second order accurate numericalscheme for the Cahn-Hilliard equation with logarithmic Flory Huggins energy potential. A modified Crank-Nicolson approximation is applied to the l...
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In this paper we propose and analyze a second order accurate numericalscheme for the Cahn-Hilliard equation with logarithmic Flory Huggins energy potential. A modified Crank-Nicolson approximation is applied to the logarithmic nonlinear term, while the expansive term is updated by an explicit second order AdamsBashforth extrapolation, and an alternate temporal stencil is used for the surface diffusion term. A nonlinear artificial regularization term is added in the numerical scheme,which ensures the positivity-preserving property, i.e., the numerical value of the phasevariable is always between -1 and 1 at a point-wise level. Furthermore, an unconditional energy stability of the numerical scheme is derived, leveraging the special formof the logarithmic approximation term. In addition, an optimal rate convergence estimate is provided for the proposed numerical scheme, with the help of linearizedstability analysis. A few numerical results, including both the constant-mobility andsolution-dependent mobility flows, are presented to validate the robustness of the proposed numerical scheme.
To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and be...
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To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and been widely applied;*** learning potentials(MLPs).One recently developed type of MLP is the deep potential(DP)*** this review,we provide an introduction to DP methods in computational materials *** theory underlying the DP method is presented along with a step-by-step introduction to their development and *** also review materials applications of DPs in a wide range of materials *** DP Library provides a platform for the development of DPs and a database of extant *** discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.
Recent investigations have revealed that dynamics of complex networks and systems are crucially dependent on the temporal structures. Accurate detection of the time instant at which a system changes its internal struc...
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Recent investigations have revealed that dynamics of complex networks and systems are crucially dependent on the temporal structures. Accurate detection of the time instant at which a system changes its internal structures has become a tremendously significant mission, beneficial to fully understanding the underlying mechanisms of evolving systems, and adequately modeling and predicting the dynamics of the systems as well. In real-world applications, due to a lack of prior knowledge on the explicit equations of evolving systems, an open challenge is how to develop a practical and model-free method to achieve the mission based merely on the time-series data recorded from real-world systems. Here, we develop such a model-free approach, named temporal change-point detection(TCD), and integrate both dynamical and statistical methods to address this important challenge in a novel way. The proposed TCD approach, basing on exploitation of spatial information of the observed time series of high dimensions, is able not only to detect the separate change points of the concerned systems without knowing, a priori, any information of the equations of the systems, but also to harvest all the change points emergent in a relatively high-frequency manner, which cannot be directly achieved by using the existing methods and *** effectiveness is comprehensively demonstrated using the data from the representative complex dynamics and real-world systems from biology to geology and even to social science.
We prove the low Mach number limit of non-isentropic ideal magnetohydrodynamic (MHD) equations with general initial data in the half-space whose boundary satisfies the perfectly conducting wall condition. By observing...
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We consider Lévy processes that are approximated by compound Poisson processes and, correspondingly, BSDEs driven by Lévy processes that are approximated by BSDEs driven by their compound Poisson approximati...
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In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniquen...
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