68 results about "Mathematical physics" patented technology

A power schedule calculation method utilizes an idealized geometry to predict laser power levels on an additive path during laser deposition. The method calculates beam power for any point along the path traveled to form a build having a geometry. Each point along the path has associated with it an idealized geometry comprising a melt pool, hot zone and bulk portion. The method comprises creating a geometric description representing the geometry of the build during the process, creating a path description representing the path of the beam source through space during the process, calculating the idealized geometry for the point on the path based upon the geometric description and path description, calculating an energy balance at the melt pool for the point on the path, calculating total energy needed at the point on the path and calculating optimum beam source power. In the calculations, build temperature is based upon a calculation of hot zone temperature derived from the idealized geometry.

Provided are an apparatus and method for imaging the subsurface structure of a target area by using waveform inversion. In the apparatus and method, the subsurface structure of a target area is estimated using waveform inversion of a seismic signal in the frequency domain, the Laplace domain, or the Laplace-Fourier domain, and an objective function is defined by applying a weighting function such that the objective function makes a different contribution for each frequency, each Laplace damping constant, or each Laplace-Fourier damping constant. The objective function is not limited to a particular type of objective function and a weighting function can be automatically determined when a gradient vector for each frequency, each Laplace damping constant, or each Laplace-Fourier damping constant is normalized. In addition, a gradient direction for all frequencies can be defined by applying another weighting function to the sum of respective gradient vectors for all frequencies, all Laplace damping constants, or all Laplace-Fourier damping constants, wherein the weighting function can also be automatically determined by normalization.

The invention discloses a convex optimization algorithm-based radar array sum-difference beam directional diagram optimization method. The method comprises the steps of determining that a radar circular array containing M array elements is uniformly distributed on a circumference with the radius being R, and then determining a sum beam main lobe area, a sum beam null steering area, a sum beam side lobe area, a sum beam low side lobe area, a difference beam main lobe area, a difference beam null steering area, a difference beam side lobe area and a difference beam low side lobe area; respectively obtaining a cost function for restraining the sum beam main lobe area and a cost function for restraining the difference beam main lobe area; further obtaining a sum beam directional diagram comprehensive optimization model of the radar circular array and a difference beam directional diagram comprehensive optimization model of the radar circular array, and calculating a radar circular array sum beam optimal weight vector; sequentially obtaining a slope of an angle error normalization curve of an expected target and a curve slope of an angle error curve of a radar circular array sum-difference beam directional diagram to be optimized, and calculating an optimal weight vector of a radar circular array difference beam.

The invention discloses a multi-resolution precondition method for analyzing aerial radiation and electromagnetic scattering problems in electromagnetic simulation. The method is a method for generating a multi-resolution basis function by using a geometrical mode on a laminar grid constructed in a grid aggregation mode and further generating multi-resolution preconditions, wherein the multi-resolution basis function is formed by linear combination of a classical vector triangle basis function (RWG), and can be conveniently applied to the conventional moment method electromagnetic simulation program to effectively improve the behavior of a matrix formed in the moment method electromagnetic simulation process so as to realize acceleration of the iterative solution process of a matrix equation and fulfill the purpose of accelerating the moment method electromagnetic simulation process. Meanwhile, the multi-resolution pre-processing technology can also be conveniently combined with a quick algorithm such as a quick multi-pole algorithm. The method has the advantages of short calculation time and capability of ensuring high precision of the program and low demand of a computing memory, and can effectively improve the computing efficiency of the conventional electromagnetic simulation.

The invention discloses a gradient coil design method in a nuclear magnetic resonance system. The method comprises the following steps of: establishing a mathematical relation between a field expansion harmonic component and a cylindrical surface current distribution harmonic component under a spherical coordinate system based on a current distribution harmonic component coefficient capable of generating a specific target field through solving; combining the traditional harmonic method with a target field method; and introducing a simulated annealing algorithm to optimize and obtain the global optimum current distribution. The gradient coil design method can be used for designing a self-shielding gradient coil with cylindrical surface current distribution and optionally restraining the coil length, and ensures excellent linearity while the higher coil efficiency is achieved through comprehensively considering a plurality of design indexes. Since the gradient coil design method is optimized by utilizing a global search algorithm-simulated annealing algorithm, a global optimum design result is ensured. Meanwhile the position information of the actual distribution of a current lead is directly output by the design result, therefore, the engineering processing and manufacturing are facilitated.

The invention provides a method for realizing quantum circuit design through quantum Fourier transform and belongs to the field of circuit design. A conventional quantum Fourier transform implementation technology is perfected and improved with the method due to the fact that a Bit Reverse circuit is absent in conventional quantum Fourier transform implementation circuits. Four quantum Fourier transform implementation circuits are constructed by an extended tensor product and basic quantum bit gates including quantum bit controlled gates and single quantum bit gates; on the basis of analysis for complexity of the quantum Fourier transform implementation circuits, complexity of the four quantum Fourier transform implementation circuits is theta(n<2>) in terms of a data set comprising 2<n> elements, which cannot be achieved by any other classic fast Fourier transform. The method is suitable for many application fields of actual information processing, for instance, efficient Fourier transform is required for algorithms of image compression, denoising, encryption, decryption and the like, and the method has great significance in perfection of the quantum computing theory and popularization of application.

The invention relates to a quantum computer quantum processing unit, a quantum circuit and a quantum circuit quantum algorithm, and belongs to the technical field of computers. The quantum processingunit (QPU) is composed of five modules and is controlled by a classic device. The quantum circuit defines two n quantum bit inputs |x) and |y) based on an SHOR algorithm. A control register and a target register are arranged. Gates Gc, G'c and Gt are defined for each algorithm. The quantum circuit quantum algorithm is a design scheme of a quantum processing architecture based on a Shor algorithm.The influence of feedback control on the proposed architecture is considered. The period searching during large number decomposition can be effectively ensured by utilizing feedback adjustment, so that the optimal performance of the quantum algorithm is effectively realized.

The invention relates to an super-directivity beam forming method based on modal decomposition and synthesis. The super-directivity beam forming method comprises the steps of firstly, decomposing the optimal solution on the basis of the beam forming theory, representing the optimal solution as a matrix form, then utilizing Gram-Schmidt orthogonal transformation for giving a solution formula of a related matrix, and then utilizing the matrix form of the optimal solution for decomposing the optimal beam into various-order modal beams with different directivities and robustness, wherein the factor with the maximum directivity is obtained by overlaying directivity factors of the various-order modal beams. Finally, a uniformity rectilinear figure array is used as an example, and the final robust super-directivity beam is obtained by selecting the proper modal beam to carry out synthesis. According to the super-directivity beam forming method based on modal decomposition and synthesis, the detects that in the prior art, accuracy is not enough, and the application range is limited are overcome according to the characteristics that the optimal solution of the beam forming theory is not limited by the matrix form, and the accurate recursion formula is used for the Gram-Schmidt orthogonal transformation.

The invention provides a method for realizing quantum circuit design through quantum Haar wavelet transformation, and belongs to the field of quantum information processing. According to the method, the existing quantum Fourier transform implementing technology is perfected and improved, and implementing circuits of two pieces of multi-layer quantum Haar wavelet transformation and two pieces of multi-layer quantum Haar wavelet inverse transformation are established separately by using extended tensor product and basic quantum bit gate (comprising quantum bit controlled door and single quantum bit gate). Based on analysis of the complex rates of the implementing circuits of the quantum Haar wavelet transformation and the quantum Haar wavelet inverse transformation, the complex rates of the implementing circuits of the two pieces of multi-layer quantum Haar wavelet transformation and the two pieces of multi-layer quantum Haar wavelet inverse transformation are Theta(n2) for one data set with 2n elements, and other typical and rapid Haar wavelet transformation cannot achieve the aim. The method is suitable for the fields of algorithms such as compression, denoising, encryption and decryption of images of actual information processing application, and has important significance in popularization of perfection and application of a quantum computing theory.

The invention discloses a method for obtaining high-precision positioning of a Gaussian beam based on a four-quadrant detector. The method comprises the following steps: to begin with, establishing apixel matrix module, the initial value of which is 0, according to image plane size of the four-quadrant detector; then, according to a Gaussian distribution function, establishing a light spot, the energy of which obeys the Gaussian distribution, to simulate imaging information of the Gaussian beam on the image plane of the four-quadrant detector after passing through an optical system; obtainingvalues of the Gaussian light spot in four quadrants at different positions within a certain range on the pixel matrix module respectively; calculating a theoretical light spot center coordinate basedon the four values by utilizing a conventional positioning algorithm; and finally, carrying out comparison analysis on the theoretical center coordinate and actual center coordinate, and obtaining ahigh-precision positioning algorithm through a polynomial fitting method. The obtained Gaussian beam positioning algorithm has the advantages of high precision, fast processing speed and high resolution and the like.

The invention discloses a millimeter wave hybrid analog/digital beam forming method based on improved Riemann manifold optimization. The millimeter wave hybrid analog/digital beam forming method comprises the following steps of projecting conjugate gradients to a tangent space to obtain Riemann gradients; searching a point in the tangent space along the Riemann gradient, determining a step lengthby using a Wolfe-Powell criterion, and backtracking the search point to the Riemann manifold; and when a stop condition is met, obtaining an analog beam forming matrix and a digital beam forming matrix through calculation. According to the method, while the algorithm complexity is reduced, the problem that minimum points are missed in the search process is avoided, so that the calculation time isgreatly shortened, the bit error rate is reduced, and the problems that the full-digital beam forming spectral efficiency cannot be achieved through hybrid beam forming and the algorithm complexity istoo high are solved.

The invention discloses an optimization method of a traveling-wave tube beam wave interaction distribution structure. The optimization method of the traveling-wave tube beam wave interaction distribution structure aims to improve the optimization efficiency of a traveling-wave tube beam wave interaction optimization algorithm. The optimization method combines the optimization algorithm with the internal mechanism of beam wave interaction and relates to a nest algorithm, through the beam wave interaction process sequencing computation characteristic and whether the relative phase angle phi meets the condition that phi > pi/2 or phi < -pi/2, computation is ended in advance. For an ordinary high-efficiency screw pitch distribution structure, the efficiency of the optimization method is improved by three to four times compared with an ordinary optimization method.

The invention relates to a method for calculating the inherent frequency of a Euler-Bernoulli beam through an improved differential transformation method. The method comprises the steps that the improved differential transformation method is deduced on the basis of a differential transformation method; a corresponding oscillatory differential equation is built, the improved differential transformation method is used for solving the free vibration problem of the homogeneous Euler-Bernoulli beam with two freely-supported ends, a control differential equation is converted into an algebraic equation, and boundary conditions are changed to an algebraic frequency equation convenient to calculate; corresponding algebraic operation is carried out to obtain the inherent frequency and the modal shape of any order of the differential equation. According to the method for calculating the inherent frequency of the Euler-Bernoulli beam through the improved differential transformation method, the improved differential transformation method is used for solving the free vibration problem of the homogeneous Euler-Bernoulli beam, an approximate solution of a nonlinear problem is obtained in the mode that iteration is carried out to converge the series, closed-form solutions such as the four-order inherent frequency and the modal shape are obtained, the solution of a Taylor expansion power series can be converged at a larger time interval, and the calculation process is rapider and more accurate.

The invention provides a monostatic MIMO (Multi-Input Multi-Output) radar direction finding method for quantum explosion. The method comprises the steps of (1) establishing a transceiving co-located narrowband monostatic MIMO radar system direction finding model; (2) determining all quantum fragments in a quantum explosion algorithm, and uniformly allocating the quantum fragments to two subsets; (3) calculating the adaptability of each quantum fragment, and determining the initial optimal quantum position of the first quantum fragment set, and the initial optimal solution quantum centroid and uniform solution quantum centroid of the second quantum fragment set; (4) updating the quantum position of each quantum fragment; (5) mapping the quantum position of each quantum fragment to the position of a defined interval, and calculating the adaptability value; (6) updating a global optimal quantum position; and (7) outputting the global optimal quantum position, and mapping the global optimal quantum position to the wave arrival direction to be estimated. The method can realize fast and high-precision direction finding under the complex environment of impulse noise and the like, and has excellent direction finding performance.

The present invention provides an elastic Gaussian beam migration imaging method and a system. The method includes the steps of acquiring the initial parameter information and a multi-component seismic record, and determining the half width of a Gaussian window and the coordinate position of a beam center point; within the range of the Gaussian window of each beam center point, decomposing the multi-component seismic record to obtain a multi-component locally plane wave; based on a wave-type separation matrix, converting the multi-component locally plane wave into a multi-wave type scalar local plane wave; shooting Gaussian beams in different directions, calculating an expression in the vector form, the complex travel time of Gaussian beams and the complex amplitude thereof; based on a wave-field migration imaging formula, calculating the summing superimposition of imaging points according to the scalar local plane wave, the complex travel time and the complex amplitude; modifying the beam center point and the shot gather so as to obtain the migration imaging through iterative computation. According to the technical scheme of the invention, the complete and effective 3D elastic Ti-medium multi-component Gaussian beam migration method is designed. In the vector representation form, wave-field propagation properties are described. Therefore, a reasonable migration imaging formula is provided. The method and the system are high in applicability.

The invention proposes a quick calculation method for terahertz band surface rough target electromagnetic scattering. The method is a patch grading semi-deterministic target modeling method, and in the method a full-wave theory proposed by E.Bahar for the rough surface scattering problem is used to implement electromagnetic scattering calculation of surface rough target. The patch grading based semi-deterministic target modeling method can satisfy a requirement that a shape of a target are depicted and rough features of the target surface are reflected, and meanwhile, can reduce storage space occupied by a target model. The full-wave theory based rough surface quick calculation method has good adaptability to roughness parameters in a relatively wide range, and is high in calculation efficiency, thereby implementing quick calculation of a rough target scattering.

The invention discloses a method for calculating a load coefficient of a uniform cross-section and simply-supported beam comprising near-field blast and far-field blast. The method comprises the stepsof: firstly, establishing a uniform load model of a uniform cross-section and simply-supported beam under the action of near-field blast and far-field blast, and establishing a coordinate by taking the mid-span position of the uniform cross-section and simply-supported beam as the coordinate origin, the horizontal rightward parallel beam direction as the x axis direction and the direction vertical to the x axis direction as the y axis direction; and, selecting the mid-span cross section of the uniform cross-section and simply-supported beam as an observation position, wherein constraint conditions of two end parts of the uniform cross-section and simply-supported beam are same, solving a first-order vibration mode function by adopting Taylor's third-order substitution, selecting a typicalblast impact wave overpressure peak parameter value and an explosive equivalent, and thus, determining the blast load coefficient of the uniform cross-section and simply-supported beam comprising near-field blast and far-field blast. A uniform calculation formula obtained by the method can provide relatively accurate calculation numerical value for structural design calculation; and the design risk due to ignoring of the near-field blast in the traditional method can be reduced.

The invention provides a method for realizing quantum circuit design by quantum D(4) wavelet transform, and belongs to the field of quantum information processing. The method designs single-layer quantum D(4) wavelet transform, uses two rotary matrixes to replace a general unitary matrix and is an innovation for an existing quantum D(4) wavelet transform technology on an aspect of methods. From the complexity analysis of the implementation circuit of the quantum D(4) wavelet transform and quantum D(4) wavelet inverse transform, for a dataset which contains 2n pieces of elements, the complexities of the circuits of the quantum D(4) wavelet transform and the quantum D(4) wavelet inverse transform are both [Theta](n2) which can not be achieved by other classic quick D(4) wavelet transform. The method is suitable for a plurality of practical information processing application fields, for example, algorithms, including image compression, denoising, encryption, decryption and the like, all need efficient D(4) wavelet transform, and the method has an important meaning for the perfection and the application of a quantum computing theory.

The invention relates to a method for acquiring spherical harmonic coefficient of gradient field of magnetic resonance imaging system, which comprises the following steps of : (a) constructing a water model coordinate system selecting a mark point Pc(u0, v0) closest to the image center as the original point Op, selecting the u axis direction of an MRI image as the c axis direction, selecting the v axis direction in the image as the r axis direction, and selecting the direction forming a right-handed coordinate system with the c and the r axes as the s axis direction; (b) calculating the MRI coordinates of the mark point Pi according to the water model coordinate system by following steps: (1) ignoring the rotation of the water model in the plane thereof and the translation of the original point; (2) considering the rotation by a theta angle in the plane of the water model around the center of Op and a shaft in the direction of a scan layer slice; and (3) considering the translation of the coordination original point of the water model; and (c) obtaining a linear equation group concerning spherical harmonic coefficients a and b if the magnetic field intensity parameters gamma, theta, phi and image coordinates of a certain point are known, and calculating the coefficients a and b by solving the linear equation group.

The invention discloses an energy interband non-local quantum tunneling simulation method with a current conservation characteristic. The method comprises the steps of generating a linear equation system which adopts a nodal value increment of a solved physical variable as a variable in a dispersing semiconductor device physical region; processing non-local quantum tunneling, determining a public energy zone for defining a first side and a second side; carrying out weight distribution on point-to-point tunneling current density and energy integral volume produced by interpolation; dividing a coefficient matrix of the linear equation system into a principal matrix caused by general differential equation dispersing and an additional coefficient matrix caused by non-local quantum tunneling with the current conservation characteristic, and storing; adopting a Gaussian origin eliminating method to solve the coefficient matrix. According to the energy interband non-local quantum tunneling simulation method with the current conservation characteristic provided by the invention, the non-local quantum tunneling current conservativeness is ensured, and the simulation error and the uncertainty brought by non-conservation are eliminated; by utilizing a method combining the principal matrix and an auxiliary incidence matrix, the coefficient linear equation system obtained through linearizing a non-linear equation system can be quickly solved, and the solving efficiency is improved.

The invention belongs to the field of aerospace complex beam structure component calculation, and provides a reduced order model-based free vibration analysis method for a beam structure. The method comprises the following steps: 1) obtaining a mass matrix and a stiffness matrix of a fine structure by using finite element software; 2) using a polynomial interpolation function to construct a reduced base vector, so as to realize order reduction of an original complex beam structure; and 3) solving a kinetic equation of the reduced order model, and obtaining the overall frequency and part of low-order frequencies of the structure. According to the method disclosed by the present invention, the polynomial interpolation function is used to construct the reduced base vector, nodes in a finite element model of the complex structure are condensed to the section centroid in the form of displacement interpolation so as to realize the order reduction of the original structure, and the calculation precision of the reduced order model can be controlled by polynomial orders. The method disclosed by the present invention has the advantages that: without depending on the experience of the user, the adverse influence of the difference of selection of the master and slave freedom degrees on the calculation precision is reduced; a large amount of matrix operation is not needed, so that the calculation efficiency of order reduction of the model is improved; and the obtained reduced order model has a wide application range.

The invention brings forward a three-dimensional geometric body surface smooth vector field calculating method under the guidance of a typical line. The method comprises the following steps: S100, calculating three-dimensional vectors at the grid summits of a three-dimensional geometric body, a set of the three-dimensional vectors constituting a harmonic vector field of the three-dimensional geometric body; S200, introducing the typical line as a boundary condition, by taking all summit tangential vectors which the typical line passes through as updating values, adding the updating values into a penalty diagonal matrix, and employing a supernode algorithm to obtain a harmonic vector field after the boundary condition is updated; and S300, utilizing a greedy algorithm to calculate a vector field by taking the current typical line as a boundary condition, and obtaining a smooth vector field under the guidance of the typical line. The method provided by the invention has the following advantages: in the prior art, only a surface smooth vector field can be calculated, and a vector field under the guidance of a typical line cannot be calculated, however, the method provided by the invention realizes rapid calculation of typical line orientation by use of a dynamically updated harmonic vector field.

The invention discloses a time-domain high-order Nystrom method for analyzing a transient electromagnetic scattering property of a conductor. The method comprises: establishing a conductor surface time-domain integral equation; performing time discretization on the conductor surface time-domain integral equation by adopting a triangular basis function, and performing spatial discretization by adopting a two-order curved surface triangular unit; forming a to-be-solved matrix equation by adopting a Galerkin test in time and point matching in space, wherein an unknown current is a transient surface current of the conductor; and solving the matrix equation to obtain a transient surface current coefficient of the conductor, and calculating a transient electromagnetic scattering parameter by the current coefficient according to a reciprocal theory. Compared to a conventional RWG basis function based time domain integral equation method, the time-domain high-order Nystrom method has the advantage of robustness of a discrete grid.