78 results about "Laplace's equation" patented technology

Method and systems of traversing through a domain is provided. One method comprises getting a set of widely spaced waypoints, assigning the next waypoint to be the goal, then using a Laplacian path planner to construct a desired finely detailed path towards the goal, through the domain that avoids boundaries and objects in the domain. Assigning a potential value of v(r)=0 for r on boundaries and obstacles. Assigning a potential value of v(r)=−1 for r on a goal region, wherein the goal is a point on a planned path. Obtaining a numerical solution to the desired path with a Laplace's equation by gridding up the domain with a multi-sized cell grid, wherein the cells near an object are denser then the cells away from the objects. Iteratively setting a potential at each interior point equal to the average of its nearest neighbors and following the numerical solution provided by the Laplace's equation to the goal region.

Reconstructing electrograms, whose experimental registration requires an invasive access, by computational way on unipolar ECGs recorded at 80 and more points of the chest surface. On the set of surface electrocardiograms for each discrete moment of the cardiocycle, values of the heart electric field potential at points of ECG-recording are determined, and a value of the electric field potential at each point of the chest surface is calculated by interpolation. Based on data of any visualization methodology, boundaries of chest and lungs surfaces and of the heart epicardial surface are determined. Further, a continuation of the electric field potential over the whole chest surface up to the heart epicardial surface with taking into account differences in electroconductivity of large anatomical structures of the chest is performed by computational way based on solution of the Cauchy problem for the Laplace equation in a piecewise-homogenous medium.

Provided is an analytical method based permanent magnet motor field analysis and torque calculation method. The method comprises the following steps of: step 1: establishing a magnetic vector potential mathematical model of a gap zone and a permanent magnet region; step 2: establishing a magnetic vector potential mathematical model of a slot area; step 3: calculating a cogging torque; and step 4: analyzing and comparing an analytical calculating result. The invention provides an analytical method based permanent magnet motor field analysis and torque calculation method. According to the structural features of a surface mounted radially magnetized permanent magnet motor model, the analytical model is divided into three sub-regions, namely a permanent magnet region, a gap zone and a slot area; a magnetic vector Laplace equation or a Poisson equation is established in each region; sub-region equations are connected through junction conditions, so as to obtain the analytical expression of a load air gap field and a slot field by using a direct analytical method.

The invention relates to an intra-frame prediction video coding method based on image inpainting and vector prediction operators. The method is technically characterized by comprising the following steps of: (1) calculating the rate distortion cost value RD1 of a current block based on a traditional intra-frame prediction mode in high efficiency video coding (HEVC); (2) calculating the rate distortion cost value RD2 of the current block based on an intra-frame prediction mode of a Laplace equation image inpainting method, and if the RD2 is smaller than the RD1, calculating the rate distortion cost value RD2 of the current block based on an intra-frame prediction mode of a total variation model image inpainting method; (3) calculating the rate distortion cost value RD3 of the current block based on an intra-frame prediction mode of the vector prediction operators; and (4) calculating the prediction pixel value of the current block according to the comparison result of the RD1, the RD2 and the RD3 by an encoder end, and predicting, compressing and coding the current block. The method is reasonable in design; the prediction accuracy of the conventional intra-frame prediction mode based on image inpainting is improved; and the coding rate can be reduced under the condition that the quality of the coded and decoded video is almost not changed, so that the compression efficiency of video coding is improved.

The invention relates to a sectional type Halbach array permanent magnet motor magnetic field calculation method. The sectional type Halbach array permanent magnet motor magnetic field calculation method comprises the steps of determining solution areas, respectively building Laplace's equations or Poisson's equations for the different solution areas, calculating the interval between magnetic blocks of a sectional type Halbach array, solving the radial and tangential component amplitudes under each order of harmonic waves of residual magnetization intensity of a permanent magnet, solving the built Laplace's equations or Poisson's equations, obtaining an expression of a scalar magnetic potential in the solution areas, and further obtaining radial and tangential components of flux densities of the areas. The sectional type Halbach array permanent magnet motor magnetic field calculation method can accurately solve the magnetic field of an inner and outer rotor sectional type Halbach array permanent magnet motor with any magnetic block number of each pole and any number of pole pairs.

The invention relates to a progressive addition ophthalmic lens and a preparation method thereof. A distant vision zone of the lens has a constant focal power in a range having an about 120-degree flare angle upwards, the deviation is smaller than 0.25 diopters, and the center width of the zone is at least 32mm. The astigmatism in a near vision zone is smaller than 0.25 diopters, and the center width of the zone is at least 10mm. The zone with the constant focal power is substantially superposed with the zone with astigmatism smaller than 0.25 diopters. According to the invention, the contour line distribution is obtained by using a numerical method to dissolve Laplace's equation, and surface rise data of the lens to be processed can be obtained by designing the focal power distributions on the contour line and the meridian line cooperatively. The lens provided by the invention can effectively improve object observing definition and comfort of wearers.

A unilateral NMR sensor comprising a ferromagnetic yoke; a permanent magnet arranged on the yoke; a pole piece on the magnet; the pole piece including an air-pole piece interface surface whose shape corresponds to an equipotential contour of magnetic scalar potential. An approach for designing single-sided magnets suitable for unilateral magnetic resonance (UMR) measurements is presented. The method uses metal pole pieces to shape the field from permanent magnets in a target region. The pole pieces are shaped according to solutions to Laplace's equation, and can be designed using a combination of analytical methods and numerical optimization. The design leads to analytical expressions for the pole piece shape and magnetic field. The method is developed in Cartesian, polar, and spherical coordinates, and the merits of each system are discussed. The effects of finite magnet size on the field quality are explored through simulation, and are found to have a substantial effect in many cases. A magnet is designed using our method to produce a static field with a constant gradient over a region 2 cm in diameter and 2 mm thick. This leads to a compact cylindrical magnet just over 11 cm in diameter, topped with a single metal pole piece. The design is validated through simulation. The simulated field is found to agree closely with that specified analytically through the design procedure.

The invention provides a light weapon live ammunition shooting automatic target-reading device and working method and belongs to the automatic displaying and reporting technical field. The light weapon live ammunition shooting automatic target-reading device comprises a target sensor and the like. The target sensor comprises an electric conducting rubber plate A and an electric conducting rubber plate B, and the electric conducting rubber plate A and the electric conducting rubber plate B are insulated and in a parallel and overlapping state. The electric conducting rubber plate A is conductive, and a target shape picture is arranged on the outer layer of the electric conducting rubber plate A and directly connected with positive electrode of power; the electric conducting rubber plate B is resistive, and three electrodes are arranged on the edge position of the electric conducting rubber plate B and respectively connected with negative electrode of the power through three ampere meters; and data output ends of the three ampere meters are respectively connected with a computer. Due to complexity of an electric field formed by applying voltage on materials with same resistivity, resistance calculation between the electrodes is complex. Due to establishing of a resistance model between the electrodes and points of fall of the materials, numerical solution is obtained by solving the equation of Laplace, distance between the electrodes and the points of fall and relationship of the electrodes and the resistance can be obtained by fitting the numerical solution, and positions of the points of fall on the target can be determined. The light weapon live ammunition shooting automatic target-reading device and the working method achieve automatic target-reading and target-reading is accurate.

The invention relates to a complicated river channel gridding method used for simulation of a river channel hydrological numerical value. Various complicated river channel regions with tributary exit conflux, tributary entrance conflux and a central bar and the like are freely segmented into simple region sets; and according to a river channel numerical value simulation demand, a region control curve grid spacing is arranged, so that a two-dimensional grid is generated; and simple region grids are merged so as to obtain an initial grid of the complicated river channel after subdivision. For a specific region of a river channel water front, the region mesh point density can be increased flexibly according to demands, so that grid encryption division in the region can be realized. According to the invention, a Laplace equation is solved and convergence precision is set; initial grid orthogonalization can be realized, so that a river channel two-dimensional orthogonal grid is finally obtained. Moreover, the conception of the method is ingenious and adaptability is good; gridding processing can be carried out on a complicated river channel containing a central bar; and designated grid encryption can be carried out in practice according to demands.

The invention provides a face-based defected image inpainting method and system. The method comprises the following steps of acquiring pixels of a whole face from a defected face image; retrieving a plurality of face images, similar to the defected face image, from a face image database through sparse representation according to the pixels of the defected face image; extracting the best-matched defected portion from the face images according to a defect area; and intercepting the best-matched defected area from the best-matched face image, and fusing the defected portion by using a Laplace equation so as to obtain a repaired image. According to the method provided by the embodiments of the invention, the complexity of data calculation during image retrieval is reduced by using sparse representation, so that the efficiency is increased; and meanwhile, the image of the defect area is subjected to inpainting by using spectrogram information of the image.

The invention relates to the technical field of tunnel hydraulics, in particular to a method of calculating hydraulic pressure of a high-pressure karst tunnel lining; the method comprises: A, determining geological conditions of an excavation section of a tunnel, wherein the geological conditions include one of the tunnel excavation section being in a homogeneous formation, and the tunnel excavation section longitudinally crossing a formation; B, determining the outer diameter of each formation to the center of the tunnel, and corresponding head and osmotic coefficient of each formation; determining outer diameter of a grouting reinforcement ring, outer diameter of a primary support, outer diameter of a secondary lining, and inner diameter of the secondary lining, as well as corresponding head and osmotic coefficient; C, transforming Laplace's equation; D, calculating water inrush of the tunnel per linear meter, back head of the secondary lining, and back head of the primary support, and calculating back pore hydraulic water of the secondary lining and back pore hydraulic pressure of the primary support. The invention is intended to provide the method of calculating hydraulic pressure of a high-pressure karst tunnel lining in order to decrease the leakage risk of a tunnel.

The invention discloses a method for designing a circular pile freezing wall. The method comprises the following steps of: 1, separately taking a plurality of points on the inner and outer sides of a freezing pipe at an interval of several meters and drilling a monitoring hole at each point; 2, separately measuring the temperature of each hole by using a thermometer; 3, taking the temperatures of any two holes according to the temperatures measured in step 2 and taking a plurality of groups; and working out the temperature field analytic expression of a rectangular foundation bit by applying the method of separating variables based on the data of each group and the Laplace's equation. In the method, the temperature field of the freezing wall is analyzed in a high-precision, fast and convenient and effective way, so that the method provides a new service for the freezing method construction and ensures the construction security.

The invention relates to a design method of a progressive addition ophthalmic lens. According to the invention, a contour line is designed by using a numerical method to dissolve Laplace's equation, so as to design a method of the progressive addition ophthalmic lens. The boundary of the Laplace's equation is set to a square boundary; the boundaries of four edges of the square are linear form or a curve form; and the curve form may be a polynomial function, a trigonometric polynomial function, an exponential polynomial function, etc. A contour line cluster is obtained by dissolving the Laplace's equation with the numerical method; and the curvature radius distribution of the progressive addition ophthalmic lens can be obtained in combination with the focal power distribution on the meridian line so as to determine the surface shape of the progressive addition ophthalmic lens. The design method provided by the invention can be used for conveniently and flexibly designing multi-purpose progressive addition ophthalmic lenses to meet the requirement of different wearers.

The invention relates to a progressive addition lens with fixed channel length. The progressive addition lens comprises a distant vision zone, a near vision zone and a progressive channel. The length of the progressive channel having a focal power change amount being 85% of additional focal power on different lens meridian lines with different additional focal powers is 15mm. A vision clear range (astigmatism smaller than 0.25 diopters) on the progressive channel penetrates through the distant vision zone and the near vision zone. The vision clear range of the distant vision region has a sector shape with a 90-degree to 120-degree central angle; the vision clear range of the near vision region has a bell shape facing downwards and having a 37-degree to 57-degree flare angle; and the focal power change is smaller than 0.25 diopters in the vision clear range of both the distant vision zone and the near vision zone. According to the invention, the contour line distribution is obtained by dissolving Laplace's equation by a numerical method; an arctan function serves as the meridian line of the lens; and surface rise data of the lens to be processed can be obtained by designing the focal power distributions on the contour line and the meridian line cooperatively. The lens provide by the invention can effectively improve comfort of wearers.

The invention provides an estimation method of wave force submerging an offshore bridge upper structure. A theory accrual model of the wave action of a bridge upper structure in a submerging state isbuilt based on a potential flow wave theory, a control equation of the model is a Laplace's equation, boundary conditions such as impassable and impermeable characteristics of a free surface and a seabed and zero object plane normal velocity are met, a velocity field can be solved by solving a control equation and by the aid of continuity of velocity potential and horizontal velocity, and the waveaction force can be solved by the aid of a Bernoulli's equation. By a built wave action force computing method, maximum wave action force applied to an offshore bridge structure in the submerging state can be accurately calculated, and accuracy is obviously improved as compared with a previous method.

The invention relates to a permanent magnet motor magnetic field calculation method adopting a non-uniform segmented Halbach permanent magnet array. The method comprises the following steps: determining a solution area; respectively establishing a Laplace equation or a Poisson equation for different solution regions; calculating the radial and tangential component amplitudes of the permanent magnet under each harmonic wave of the residual magnetization by considering the non-uniform segmentation of the magnetic block under each pole in the segmented Halbach permanent magnet array and the gap between the magnetic blocks; and solving the established Laplace equation and Poisson equation to obtain an expression of a scalar magnetic potential in a solving region, thereby obtaining a radial component and a tangential component of the magnetic density of each region. The method can be used for accurately calculating the magnetic field of the internal and external rotor sectional Halbach array permanent magnet motor with any number of pole pairs, any number of magnetic blocks per pole and non-uniform sections of the magnetic blocks under each pole, and can be used for researching the coupling influence of the non-uniform sections of the magnetic blocks under each pole and the gaps between the magnetic blocks on the magnetic field of the motor.

Systems and methods for conformal additive manufacturing are disclosed. In particular, systems and methods are disclosed utilizing variable offset curves and/or a manipulated solution to Laplace's equation to generate layers between an initial boundary and a desired boundary.

The invention discloses a dynamic simulation prediction method for a machining gap and an erosion removal rate in a rotary printing electrolytic machining process, and belongs to the technical field of electrolytic machining. According to the method, an actual rotary printing electrolytic machining process is simulated by establishing a dissolution model of a material on surface of a workpiece anode; an analytical solution of current density of any point on the surface of the workpiece anode is solved by utilizing a laplacian equation of complex fractional linear mapping; each circle of machining process of the workpiece anode is dispersed into a plurality of extremely small time periods by adopting a discrete method, and the erosion removal thickness of the material on the surface of theworkpiece anode is reduced along the radial direction; and the discrete and iterative simulation of Matlab are used to solve the dynamic change values of the machining gap and the erosion removal rateof the anode surface material after one circle. In the actual rotary printing electrolytic machining process, the optimal electrolytic machining process parameters can be obtained by means of the method, test time is greatly saved, and theoretical guidance is provided for selection of rotary printing electrolytic machining parameters.

The invention discloses a method for determining an initial orbit of spacecraft based on a precise orbit model. On the basis of the precise orbit model and a laplace equation, a weighted least squaresconditional equation of ground-based radar orbit measurement data, space-based optical angle measurement data, GNSS and Beidou orbit measurement data is established, and improved values of initial positions and velocity are iteratively solved by integrating different kinds of orbit measurement data by using two methods of a direct synthesis method or a federated synthesis method. According to themethod for determining the initial orbit of spacecraft based on the precise orbit model, the complete or incomplete external ballistic observation data, the position and velocity component observation data and the space-based angle measurement data can be directly combined to carry out the satellite-rocket separation initial orbit calculation, and the unique initial orbit output is produced.

The invention discloses a method and device for predicting interaction among liquid drops absorbing a surfactant. The method comprises that when two second-phase dielectric liquid drops make face-to-face elastic collision when moving towards to each other and separate from each other after collision, the radii and collision speed of the two second-phase dielectric liquid drops are determined; a separation pressure in the face-to-face elastic collision process is determined according to the radii and collision speed of the two second-phase dielectric liquid drops; according to a convection-diffusion equation, an drainage equation, a generalized Young-Laplace equation and the separation pressure, a dynamic water application force in the face-to-face elastic collision process and the interface concentration and migration speed of the surfactant in the surfaces of the liquid drops are determined; and according to the dynamic water application force and separation pressure, a total action force between the two second-phase dielectric liquid drops is determined. Thus, the action force between two liquid drops and distribution and migration of the surfactant in the two-phase interface ina disperse medium with the surfactant can be predicted accurately.

The invention discloses a method and a device for determining a corona initial voltage. The disclosed method comprises the steps of: calculating a potential distribution value of a boundary region ofa nominal electric field when a specified voltage is applied to a selected electrode model based on a charge simulation method; solving a Laplace equation based on an SOR algorithm to calculate a potential distribution value of a non-boundary region of the nominal electric field; and iteratively performing the steps of solving a charge continuity equation by using an FCT algorithm based on the potential distribution value of the nominal electric field at the first time or based on the potential distribution value obtained through calculation by calling the SOR algorithm previously when not atthe first time, calculating a potential distribution value corresponding to the called SOR algorithm at this time by adopting the SOR algorithm, and determining the potential distribution value as a corona initial voltage corresponding to a designated position when the designated position meets a corona generating condition. The disclosed method and device can determine the corona initial voltagedirectly by adopting the method different from a numerical value calculation method in the prior art without performing an experiment.

The invention discloses a method for measuring the grounding resistance of a grounding grid, which belongs to a method for measuring the grounding resistance of a grounding grid in a power plant and a substation. Geological survey soil resistivity or water conductivity to prepare model conductive medium; according to the electric field geometric simulation theory of Laplace equation, the length of the grounding grid can be enlarged in equal proportions at the beginning of the design of the repower plant or distribution station project Or shrink, provide improvement measures for the design of the grounding grid, predict the grounding resistance after the grounding grid is installed, and optimize the design when the performance of the grounding resistance is met, further reduce the project cost risk, and the measurement cost is disclosed, which realizes The technology of measuring the grounding resistance of the grounding network is economical, and the invention can be directly applied to various electric places, and has a wide range of applications.

The invention discloses an electric capacitance tomography method based on improved particle swarm optimization. The method comprises applying voltage so that the electrostatic field in the measured field satisfies the Laplace equation, carrying out taylor expansion on the capacitance value between the electrodes and the relative dielectric constant relationship, ignoring the high order phase, carrying out normalization processing to obtain a normalized capacitance vector, reconstructing the electric capacitance tomography images to optimize a target, acquiring an objective function of the Landweber algorithm according to the vector norm function definition, rebuilding an iterative formula of the electric capacitance tomography according to the steepest descent principle, improving the rebuilding quality through a particle swarm optimized fitness function, acquiring a modified particle velocity update formula through an exponential decay weight mechanism, and optimizing the data. The electric capacitance tomography method utilizes the inertia weight exponential decay particle swarm optimization algorithm to optimize the rebuilding result obtained by the Landweber algorithm, solvesthe problem in the Landweber imaging process and reduces the influence caused by a soft field on the image reconstruction.