Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method

Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.

Solving chemical dynamic optimization problems with ranking-based differential evolution algorithms

Dynamic optimization problems(DOPs) described by differential equations are often encountered in chemical engineering. Deterministic techniques based on mathematic programming become invalid when the models are non-differentiable or explicit mathematical descriptions do not exist. Recently, evolutionary algorithms are gaining popularity for DOPs as they can be used as robust alternatives when the deterministic techniques are invalid. In this article, a technology named ranking-based mutation operator(RMO) is presented to enhance the previous differential evolution(DE) algorithms to solve DOPs using control vector parameterization. In the RMO, better individuals have higher probabilities to produce offspring, which is helpful for the performance enhancement of DE algorithms. Three DE-RMO algorithms are designed by incorporating the RMO. The three DE-RMO algorithms and their three original DE algorithms are applied to solve four constrained DOPs from the literature. Our simulation results indicate that DE-RMO algorithms exhibit better performance than previous non-ranking DE algorithms and other four evolutionary algorithms.

Pancreatic carcinoma coexisting with chronic pancreatitis versus tumor-forming pancreatitis:Diagnostic utility of the time-signal intensity curve from dynamic contrast-enhanced MR imaging

AIM: To evaluate the ability of the time-signal intensity curve (TIC) of the pancreas obtained from dynamic contrast-enhanced magnetic resonance imaging (MRI) for differentiation of focal pancreatic masses, especially pancreatic carcinoma coexisting with chronic pancreatitis and tumor-forming pancreatitis. METHODS: Forty-eight consecutive patients who underwent surgery for a focal pancreatic mass, including pancreatic ductal carcinoma (n = 33), tumor-forming pancreatitis (n = 8), and islet cell tumor (n = 7), were reviewed. Five pancreatic carcinomas coexisted with longstanding chronic pancreatitis. The pancreatic TICs were obtained from the pancreatic mass and the pancreatic parenchyma both proximal and distal to the mass lesion in each patient, prior to surgery, and were classified into 4 types according to the time to a peak: 25 s and 1, 2, and 3 min after the bolus injection of contrast material, namely, type-Ⅰ, Ⅱ, Ⅲ, and Ⅳ, respectively, and were then compared to the corresponding histological pancreatic conditions. RESULTS: Pancreatic carcinomas demonstrated type-Ⅲ (n = 13) or Ⅳ (n = 20) TIC. Tumor-forming pancreatitis showed type-Ⅱ (n = 5) or Ⅲ (n = 3) TIC. All islet cell tumors revealed type-Ⅰ. The type-Ⅳ TIC was only recognized in pancreatic carcinoma, and the TIC of carcinoma always depicted the slowest rise to a peak among the 3 pancreatic TICs measured in each patient, even in patients with chronic pancreatitis.CONCLUSION: Pancreatic TIC from dynamic MRI provides reliable information for distinguishing pancreatic carcinoma from other pancreatic masses, and may enable us to avoid unnecessary pancreatic surgery and delays in making a correct diagnosis of pancreatic carcinoma, especially, in patients with longstanding chronic pancreatitis.

A New Three-Level Hierarchical Control Algorithm for Large-Scale Systems

This paper presents a new three-level hierarchical control parallel algorithm for large-scale systems by spatial and time decomposition. The parallel variable metric (PVM)method is found to be promising third-level algorithm. In the subproblems of second-level, the constraints of the smaller subproblem requires that the initial state of a subproblem equals the terminal state of the preceding subproblem. The coordinating variables are updated using the modified Newton method. the low-level smaller subproblems are solved in parallel using extended differential dynamic programmeing (DDP). Numerical result shows that comparing with one level DDP. the PVM /DDP algorithm obtains significant speed-ups.

ANALYSIS OF REGIONAL ECONOMY GROWTH WITH THE THEORY OF DIFFERENTIAL SYSTEM DYNAMICS

In order to describe the interrelation forces among different regions during the economic growth, this paper introduces and analyzes the dynamical system model with the theory of differential systems dynamics. A practical example based on a simplified model is given to analyze the dynamical process of Sichuan economy growth.

Differential equation dynamical system based assessment model in GNSS interoperability

With the development of Global Navigation Satellite System (GNSS),the idea of GNSS interoperability is born and has become the focus of study in the field of satellite navigation.The popularity for GNSS to augment the interoperability with the existing ones necessitates the study of the assessment algorithm of this idea.In this paper,an assessment algorithm for interoperability comprehensive benefits based on the differential equation dynamical system is discussed.There are two important aspects in GNSS that interoperability will affect:one is the performance advancement;the other one is the cost of adopting interoperability.While researching the complex relationship between the performance and cost,we found this relationship is similar as what between prey and predator in biomathematics,so the Lotka-Volterra model used to depict the prey-predator relationship is a felicitous tool.After building a differential dynamical model,we analyze the existence and stability of the positive equilibrium in the model.Then a Cost-Effective Function of GNSS is constructed based on the positive equilibrium,which is employed to assess the interoperability,qualitatively and quantitatively.Finally,the paper demonstrates the significance of the model and its application by citing a numerical example.

Precise control of a magnetically suspended double-gimbal control moment gyroscope using differential geometry decoupling method

Precise control of a magnetically suspended double-gimbal control moment gyroscope （MSDGCMG） is of vital importance and challenge to the attitude positioning of spacecraft owing to its multivariable, nonlinear and strong coupled properties. This paper proposes a novel linearization and decoupling method based on differential geometry theory and combines it with the internal model controller （IMC） to guarantee the system robustness to the external disturbance and parameter uncertainty. Furthermore, by introducing the dynamic compensation for the inner-gimbal rate-servo system and the magnetically suspended rotor （MSR） system only, we can eliminate the influence of the unmodeled dynamics to the decoupling control accuracy as well as save costs and inhibit noises effectively. The simulation results verify the nice decoupling and robustness performance of the system using the proposed method.

Pareto Efficiency of Finite Horizon Switched Linear Quadratic Differential Games

A switched linear quadratic（LQ） differential game over finite-horizon is investigated in this paper. The switching signal is regarded as a non-conventional player, afterwards the definition of Pareto efficiency is extended to dynamics switching situations to characterize the solutions of this multi-objective problem. Furthermore, the switched differential game is equivalently transformed into a family of parameterized single-objective optimal problems by introducing preference information and auxiliary variables. This transformation reduces the computing complexity such that the Pareto frontier of the switched LQ differential game can be constructed by dynamic programming. Finally, a numerical example is provided to illustrate the effectiveness.

Stochastic Differential Games with Reflection and Related Obstacle Problems for Isaacs Equations

In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations （RBSDEs）. We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bettman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of E1 Karoui, Kapoudjian, Pardoux, Peng and Quenez （1997）, which turns out to be very useful because it allows us to estimate the LP-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle.