A radar system is provided that includes a radar transceiver integrated circuit (IC) configurable to transmit a first frame of chirps, and another radar transceiver IC configurable to transmit a second frame of chirps at a time delay ΔT, wherein ΔT=T.sub.c/K, K≥2 and T.sub.c is an elapsed time from a start of one chirp in the first frame and the second frame and a start of a next chirp in the first frame and the second frame, wherein the radar system is configured to determine a velocity of an object in a field of view of the radar system based on first digital intermediate frequency signals generated responsive to receiving reflected chirps of the first frame and second digital IF signals generated responsive to receiving reflected chirps of the time delayed second frame, wherein the maximum measurable velocity is increased by a factor of K.

A radar system is provided that includes a radar transceiver integrated circuit (IC) configurable to transmit a first frame of chirps, and another radar transceiver IC configurable to transmit a second frame of chirps at a time delay ΔT, wherein ΔT=T.sub.c/K, K≥2 and T.sub.c is an elapsed time from a start of one chirp in the first frame and the second frame and a start of a next chirp in the first frame and the second frame, wherein the radar system is configured to determine a velocity of an object in a field of view of the radar system based on first digital intermediate frequency signals generated responsive to receiving reflected chirps of the first frame and second digital IF signals generated responsive to receiving reflected chirps of the time delayed second frame, wherein the maximum measurable velocity is increased by a factor of K.

A computer-readable non-transitory storage medium stores a multilayer fluid analysis program for analyzing a multilayer fluid as 2.5 dimensions in which each layer is divided into elements and each of the elements has information about a layer thickness in a finite element model for the multilayer fluid. The multilayer fluid analysis program allowing a computer to function as: a layer thickness calculation process for calculating the layer thickness of the elements from a simultaneous equation indicating a relationship between stress in a normal direction and a fluid viscosity in the elements without considering a fluid flow in a thickness direction of the layer thickness under a condition that stresses in the normal direction and a tangential direction are balanced at an interface of respective layers and a flow velocity at the interface is continuous; and a display process for displaying a calculation result.

A computer-readable non-transitory storage medium stores a multilayer fluid analysis program for analyzing a multilayer fluid as 2.5 dimensions in which each layer is divided into elements and each of the elements has information about a layer thickness in a finite element model for the multilayer fluid. The multilayer fluid analysis program allowing a computer to function as: a layer thickness calculation process for calculating the layer thickness of the elements from a simultaneous equation indicating a relationship between stress in a normal direction and a fluid viscosity in the elements without considering a fluid flow in a thickness direction of the layer thickness under a condition that stresses in the normal direction and a tangential direction are balanced at an interface of respective layers and a flow velocity at the interface is continuous; and a display process for displaying a calculation result.

A method includes: receiving a mathematical model of a control system, with state variables and control parameters; discretizing at least a part of a space to obtain a set of tuples; determining for each tuple at least one successor state; obtaining an initial winning set of tuples; determining an updated winning set of tuples, including comparing the at least one successor state with the initial winning set of tuples, where the comparison is distributed over available processing elements by choosing one processing element from the available processing elements for each tuple to perform the comparison and where the available processing elements are used simultaneously at least in part; repeating the determination of the updated winning set of tuples to obtain a new updated winning set of tuples if a convergence measure does not meet a criterion, and constructing a controller for the control system from the new updated winning set.

A method includes: receiving a mathematical model of a control system, with state variables and control parameters; discretizing at least a part of a space to obtain a set of tuples; determining for each tuple at least one successor state; obtaining an initial winning set of tuples; determining an updated winning set of tuples, including comparing the at least one successor state with the initial winning set of tuples, where the comparison is distributed over available processing elements by choosing one processing element from the available processing elements for each tuple to perform the comparison and where the available processing elements are used simultaneously at least in part; repeating the determination of the updated winning set of tuples to obtain a new updated winning set of tuples if a convergence measure does not meet a criterion, and constructing a controller for the control system from the new updated winning set.

Embodiments of the present application provide a method and a device for optimizing a target operation speed curve in an ATO of a train. The method includes: calculating a plurality of performance indexes of the train driving in a current section of a line, and constructing an objective function for optimizing the target operation speed curve of the train according to the plurality of performance indexes; determining constraint conditions of the objective function according to speed limit information of the line and running time of the train in the current section; and solving the objective function according to the constraint conditions based on a differential evolution algorithm to obtain the target operation speed curve of the train. The objective function for optimizing the target operation speed curve of the train are constructed using the plurality of performance indexes, which makes the optimization of the train speed curve more accurate.

Embodiments of the present application provide a method and a device for optimizing a target operation speed curve in an ATO of a train. The method includes: calculating a plurality of performance indexes of the train driving in a current section of a line, and constructing an objective function for optimizing the target operation speed curve of the train according to the plurality of performance indexes; determining constraint conditions of the objective function according to speed limit information of the line and running time of the train in the current section; and solving the objective function according to the constraint conditions based on a differential evolution algorithm to obtain the target operation speed curve of the train. The objective function for optimizing the target operation speed curve of the train are constructed using the plurality of performance indexes, which makes the optimization of the train speed curve more accurate.

Embodiments relate to a computing system for solving differential equations. The system is configured to receive problem packages corresponding to problems to be solved, each comprising at least a differential equation and a domain, and to select a solver of a plurality of solvers, based upon availability of each of the plurality of solvers. Each solver comprises a coordinator that partitions the domain of the problem into a plurality of sub-domains, and assigns each of the plurality of sub-domains to a differential equation accelerator (DEA) of a plurality of DEAs. Each DEA comprises at least two memory units, and processes the sub-domain data over a plurality of time-steps by passing the sub-domain data through a selected systolic array from one memory unit, and storing the processed sub-domain data in the other memory unit, and vice versa.

Systems, methods, and non-transitory computer-readable storage media for a fast power network simulator. A system configured per this disclosure can use identify a power network, the power network comprising generators, transmission lines, and loads, and receive a model of the power network. The model of the power network can include: models of the generators modeled as differential equations, and models of the transmission lines and the loads modeled as algebraic equations. The system can convert, via a processor, the algebraic equations of the models of the transmission lines and the loads to additional differential equations, then combine, via the processor, the differential equations and the additional differential equations, to yield combined differential equations. The system can then iteratively solve linear equations, via the processor, associated with the combined differential equations, to yield solutions, and output the solutions as part of a power simulation of the power network.