The present application relates to the field of particle transport, and in particular, to a method and apparatus for computing a nuclear reaction cross section and a path integral in particle transport, an electronic device, and a storage medium.
Particle transport is a phenomenon that describes the passage of microscopic particles in a medium. The study of particle transport is very important for analyzing and understanding the behavior of microscopic particles and has a wide range of modern applications. With the advancement of computer computation power, high-fidelity reactor numerical computation has become possible. In high-fidelity reactor numerical computations, one computational bottleneck is the statistical problem of particle transport in inhomogeneous media. In this field, one existing method is the collision statistical method, which is unstable in numerical computations and cannot handle vacuum materials; and another existing method is the path integral statistical method, which is not yet sufficient to be applied to inhomogeneous media.
In addition, related technologies have proposed that linear combinations of basis functions can be used to compute nuclear reaction cross sections and path integrals in particle transport. However, computations relating to more complex object functions still need to be further studied.
The above content is merely background information related to the present application known to the inventor and does not constitute an admission of prior art.
With this regard, embodiments of the present application provide a method and apparatus for computing a nuclear reaction cross section and a path integral in particle transport, an electronic device, and a computer readable storage medium, for use in solving at least one technical problem.
According to the first aspect, the embodiments of the present application provide a method for computing a nuclear reaction cross section and a path integral in particle transport, including:
The additional function is a function of spatial position and energy, where the domain of the function is a set of points in space and a set of non-negative real number energy, and the range of the function is complex numbers or vectors of the complex numbers.
According to the second aspect, the embodiments of the present application provide a particle transport equation solving method, including using the method above to perform at least one of the following: Monte Carlo particle transport computation, method of characteristics-based particle transport computation, discrete ordinates method-based particle transport computation, and solving for other scientific computation problems.
According to the third aspect, the embodiments of the present application provide an apparatus for computing a nuclear reaction cross section and a path integral in particle transport, including:
The additional function is a function of spatial position and energy, where the domain of the function is a set of points in space and a set of non-negative real number energy, and the range of the function is complex numbers or vectors of the complex numbers.
According to the fourth aspect, the embodiments of the present application provide an electronic device, including: a processor and a memory having computer program instructions stored thereon, where when executing the computer program instructions, the electronic device implements the method above.
According to the fifth aspect, the embodiments of the present application provide a computer readable storage medium, having computer program instructions stored thereon, where when executed by a processor, the computer program instructions implement the method above.
The solution provided in the embodiments of the present application solves the problem of path integral computation of functions containing cross sections in inhomogeneous media by separating cross-section dependence in path integral computation, and improves the path integral statistical method so that the method can be applied to the statistical problems of particle transport in inhomogeneous media.
To describe the technical solutions in embodiments of the present application more clearly, the accompanying drawings required for describing the embodiments of the present application are briefly introduced below. Apparently, the accompanying drawings in the following description show merely some embodiments of the present application, and a person of ordinary skill in the art can still derive other accompanying drawings from these accompanying drawings without an inventive effort.
The principle and spirit of the present application will be described below with reference to several exemplary embodiments. It should be understood that the purpose of providing these embodiments is to make the principle and spirit of the present application clearer and more thorough, so that a person skilled in the art can better understand and implement the principle and spirit of the present application. The exemplary embodiments provided herein are only some embodiments of the present application, rather than all embodiments. Based on the embodiments herein, all other embodiments obtained by a person of ordinary skill in the art without involving an inventive effort shall fall within the scope of protection of the present application.
A person skilled in the art knows that the embodiments of the present application may be implemented as a method, an apparatus, an electronic device, and a storage medium. Therefore, the present disclosure may be specifically implemented in at least one of the following forms: complete hardware, complete software (including firmware, resident software, microcode, etc.), or a combination of hardware and software.
According to the embodiments of the present application, the present application sets forth a method and apparatus for computing a nuclear reaction cross section and a path integral in particle transport, an electronic device, and a storage medium.
Herein, terms such as “first” and “second” are only used to distinguish one entity (or operation) from another entity (or operation), but not used to require or imply any order or relationship between these entities (or operations). Herein, elements (such as parts, components, processes, and steps) defined by the phrase “including . . . ” do not exclude elements other than the listed elements, that is, other elements not explicitly listed may also be included. Herein, any elements and the numbers thereof in the drawings are used for illustration rather than limitation, and any names in the drawings are only used for distinction and do not have any limiting meanings.
The following is a detailed explanation of the principle and spirit of the present application with reference to several exemplary or representative embodiments of the present application.
First, a brief description is given of the concepts, technical terms and other related contents that may be involved in the embodiments of the present application.
The number density of particles having energy E at a spatial position {right arrow over (x)} is N({right arrow over (x)},E), where the number density refers to the number of particles having energy E per unit volume at the position {right arrow over (x)}. At the same time, it is assumed that the particles have a moving speed v(E), where the speed is a scalar and is a function of the energy E. On this basis, the particle flux density is defined by the following equation, which represents a product of the speed and the particle number density.
For any material having N components, each component is called as a sub-material. The sub-material may refer to a nuclide, an element, a molecule or the like. Therefore, a macroscopic nuclear reaction cross section Σ(E,T) of a material may be expressed as the sum of the products of microscopic nuclear reaction cross sections of various sub-materials and corresponding number densities, as shown below:
where i is an index of the sub-material and i=1, 2, 3 . . . , or N, ai is defined as the number density of the ith-type sub-material, σi(E,T) is a microscopic nuclear reaction cross section of the ith-type sub-material, E is particle energy, and T is the temperature of the material.
In space V, if the material is an inhomogeneous medium, then the temperature, the microscopic nuclear reaction cross section, the sub-material number density, and the macroscopic nuclear reaction cross section are all functions of the spatial position {right arrow over (x)}, as shown in the following equation:
In this field, the microscopic nuclear reaction cross section σ(E,T) of a sub-material including the nuclide, the element, or the molecule has a complex energy dependence, and the energy dependence varies greatly in different sub-materials. Moreover, the macroscopic nuclear reaction cross section has a more complex energy dependence than a single sub-material, and the complexity of the energy dependence may impede path integral computation involving the macroscopic cross section.
At present, a commonly used statistical method in particle transport is the collision statistical method. In the method, it is assumed that particles undergo Q collision events within a unit time Δτ in space V, and the position of the qth collision event is {right arrow over (xq)}, where q=1, 2, 3 . . . , or Q. Then the integral of the product of the particle flux density and any object function u(E,{right arrow over (x)}) within a unit time Δτ in space V can be approximated using the following equation.
The equation represents a path integral collision statistical method for particle transport. Σt(E,{right arrow over (xq)}) is the macroscopic total nuclear reaction cross section of the material at position {right arrow over (xq)} for particles having energy E. It can be seen that when the macroscopic total nuclear reaction cross section is zero, the equation cannot be used for computation, and when the macroscopic total nuclear reaction cross section is small, the value is unstable.
In the Monte Carlo algorithm for particle transport, in any given space V, there are P particles traveling therein, and a particle traveling path having an index p is Cp, where the path may be a curve; the path may not run through the space V, that is, the path may end in the space V without leaving the space, or the path may start in the space V instead of entering from the outside of the space; and the path length is lp, where the index p=1, 2, 3 . . . , or P. Then, the integral of the particle flux density in space V within the unit time Δτ can be approximately expressed as the sum of the path lengths of P particles using the following equation.
If the particle flux density is multiplied by any object function u(E,{right arrow over (x)}), then the spatial integral of the product can be approximately expressed using the following equation.
The equation above represents a path integral statistical method for particle transport. Here, “statistical” refers to computing the integral of the product of particle flux density and any object function using the equation above. The physical quantities or numerical indicators that can be statistically analyzed using the integral include: particle flux, particle reaction rate, power, etc.
When the object function represents a constant 1, that is, u(E,{right arrow over (x)})=1, Equation (b) degenerates into Equation (a), which relates to computation of Δτ∫Vϕ({right arrow over (x)},E) d{right arrow over (x)}, that is, the particle flux in space V.
When the object function represents any macroscopic nuclear reaction cross section, that is, u(E,{right arrow over (x)})=Σ(E,{right arrow over (x)}), Equation (b) becomes Equation (c), which relates to computation of the reaction rate of any nuclear reaction. The nuclear reaction here can be, but is not limited to, elastic scattering, inelastic scattering, particle capture, fission, etc.
In particular, when the object function represents a macroscopic fission reaction cross section, that is, u(E,{right arrow over (x)})=Σf(E,{right arrow over (x)}), Equation (b) becomes Equation (d), which relates to computation of a fission reaction rate, where the value is proportional to power in space V, that is, energy generated in space V.
In the above description concerning the power in space V, for the sake of convenience, it is assumed that the energies released when incident particles undergo the fission reaction with different sub-materials at different energies is the same. If the energies are different, the definition of the power will be slightly different from Equation (d), and the different fission energies of each type of different sub-material at different incident particle energies need to be considered separately.
Of course, the object function can also be a more complex function, for example, the object function represents the product of the macroscopic nuclear reaction cross section and an additional function r(E,{right arrow over (x)}), that is, u(E,{right arrow over (x)})=r(E,{right arrow over (x)})Σ(E,{right arrow over (x)}), in which case Equation (b) becomes Equation (e). As shown below, equation (e) is very important for computing the spatial distribution of the nuclear reaction rate.
From the above, it can be seen that when it is assumed that r(E,{right arrow over (x)}(s))=1, Equation (c) can be obtained through Equation (e); and
It should be noted that the integrand function in the path Cp intergral in Equation (e) contains the macroscopic nuclear reaction cross section, and then when the material on the path is variable, that is, the particles are transported in an inhomogeneous medium, the macroscopic nuclear reaction cross section also varies along the path.
In particular, by setting the object function to be a component function in a function expansion counting method or a product of the component function and the macroscopic nuclear reaction cross section, the spatial distribution of physical quantities or numerical indicators can be computed.
Firstly, function expansion is defined. Any function h({right arrow over (x)}) defined in space V can be expanded in the space by using a set of component functions and the integral can be approximated by using the sum. As shown in Equation (f), a set of T given component functions Ft({right arrow over (x)}) is used, where t=1, 2, 3 . . . , or T and ht is the coefficient of the tth component function. If necessary, the space V can be expanded to the domain {tilde over (V)} required by the component functions.
When the component functions Ft({right arrow over (x)}) form a set of orthogonal conditions that satisfy Equation (g), the coefficients of the component functions can be expressed using Equation (h). In Equation (g), if t1=t2, the value of the function δt
Secondly, when the spatial distribution of the particle flux density needs to be obtained, the particle flux density ϕ({right arrow over (x)},E), as shown by Equation (f), can be expanded into Equation (i), and it is assumed that the component function Ft({right arrow over (x)}) is also a function of the energy E, namely Ft(E,{right arrow over (x)}). t=1, 2, 3 . . . , or T. ϕt(E) is the coefficient of the tth component function, and can be expressed as Equation (j) according to Equation (h). Further, according to Equation (c), and by setting the object function u(E,{right arrow over (x)})=Ft(E,{right arrow over (x)}), the component function coefficient ϕt(E) can be approximated through the path integral as shown in Equation (k).
Thirdly, when the spatial distribution of the nuclear reaction rate needs to be obtained, the nuclear reaction rate, that is, the product of the macroscopic nuclear reaction cross section Σ(E,{right arrow over (x)}) and the particle flux density ϕ({right arrow over (x)},E) R({right arrow over (x)},E)=Σ(E,{right arrow over (x)})ϕ({right arrow over (x)},E), as shown by Equation (f), can be expanded into Equation (l), where the component function Ft(E,{right arrow over (x)}) can also be a function of energy.
t=1, 2, 3 . . . , or T. Rt(E) is the coefficient of the tth component function.
According to Equation (h), Equation (l) can be expressed as Equation (m).
Further, according to Equation (c), and by setting the object function u(E,{right arrow over (x)})=Ft(E,{right arrow over (x)})Σ(E,{right arrow over (x)}), the component function coefficient Rt(E) can be approximated through the path integral as shown in Equation (n).
When it is assumed that r(E,{right arrow over (x)}(s))=Ft(E,{right arrow over (x)}(s)), Equation (n) can be obtained through Equation (e).
From the examples above, the importance of the path integral C
However, the integrand function in the path Cp integral in Equation (e) contains the macroscopic nuclear reaction cross section, and then when the material on the path is variable, that is, the particles are transported in an inhomogeneous medium, the macroscopic nuclear reaction cross section also varies along the path. Since the complex cross section energy dependence makes integral computation difficult, in existing technologies, it can only be assumed that the macroscopic nuclear reaction cross sections are constants under given energies on given paths, and the existing technologies cannot deal with the problem of particle transport in inhomogeneous media.
For a function containing a cross section, such as a product of a macroscopic cross section and an additional function r(E,{right arrow over (x)}(s))Σ(E,{right arrow over (x)}(s)), the present invention proposes a method for computing the path integral by separating the cross section energy dependence when the function is not a constant. The method can deal with the statistical problem of particle transport in inhomogeneous media, which is of practical significance.
The method for computing a nuclear reaction cross section and a path integral in particle transport provided in the present invention can be used to replace the collision statistical method in inhomogeneous medium transport, making computation possible in a situation where the total reaction cross section is very small or zero, and avoiding unstable numerical computation.
In some embodiments, optionally, the obtaining a product of a macroscopic nuclear reaction cross section of a material and an additional function by using a linear combination of basis functions includes:
In some embodiments, optionally, Equation (2) is integrated on a path C, and the path integral of the product of the macroscopic nuclear reaction cross section of the material and the additional function is obtained by using the linear combination of basis functions:
where the energy is E, the temperature is T({right arrow over (x)}) and the temperature is a function of a point position {right arrow over (x)} in space, a variable s is taken as a parameter of the path C, the path C is curved or straight, and {right arrow over (x)}(s) is a point position at the parameter s on the path.
In some embodiments, optionally, when a multi-group cross section is used, the energy E in Equation (3) is replaced by an energy group g, and then Equation (3) is transformed into Equation (4):
where a macroscopic nuclear reaction cross section of the energy group g is Σg({right arrow over (x)}(s)), the basis function corresponding to the energy group g is σi,j,g, and the additional function corresponding to the energy group g is rg({right arrow over (x)}(s)).
In some embodiments, optionally, the method for computing a nuclear reaction cross section and a path integral in particle transport further includes expressing the nuclear reaction cross section and the path integral obtained by polynomial expansion as the linear combination of basis functions.
The polynomial expansion is to express the function as a polynomial.
In some embodiments, optionally, the expressing the nuclear reaction cross section and the path integral obtained by polynomial expansion as the linear combination of basis functions includes:
In some embodiments, optionally, the obtaining the product of the macroscopic nuclear reaction cross section of the material and the additional function through cross section temperature polynomial expansion includes:
In some embodiments, optionally, the expressing the macroscopic nuclear reaction cross section obtained by cross section temperature polynomial expansion as the linear combination of basis functions includes:
In some embodiments, optionally, the expressing the product of the macroscopic nuclear reaction cross section and the additional function obtained by cross section temperature polynomial expansion as the linear combination of basis functions includes:
In some embodiments, optionally, the expressing the path integral of the product of the macroscopic nuclear reaction cross section and the additional function obtained by cross section temperature polynomial expansion as the linear combination of basis functions includes:
According to the method for computing a nuclear reaction cross section and a path integral in particle transport provided in the present invention, in terms on the right sides of the Approximately-Equal signs in expressions using the linear combination of basis functions including Equation (16)and Equation (15), the integral
Cr(E,{right arrow over (x)}(s))ai({right arrow over (x)}(s))ci,j(T({right arrow over (x)}(s)))ds or
cr(E,{right arrow over (x)}(s))ai({right arrow over (x)}(s))Tβ
To facilitate understanding, several specific examples are provided below.
A microscopic cross section has the form of temperature polynomial expansion as shown in the following equation, where the power of the polynomial is an integer multiple of ½ and can be a positive value, zero or a negative value. In the example implementation as shown in the following equation, I=6, and bi(E) is the coefficient of the ith polynomial and is a function of energy E, where i=−1, −(1−1), −(1−2) . . . , 0, 1, 2, . . . , or I.
It is assumed that the space V can be contained in a cuboid space B, where the coordinates (x,y,z) of a point {right arrow over (x)} in the cuboid space are within the range of the following equation.
Next, the following three equations are used to define x′, y′, and z′.
Then x′, y′, and z′ each have the range −1≤x′, y′, z′≤1. The component function Ft({right arrow over (x)}) in Equation (f) can be defined as the following equation. In addition, if it is assumed that 0≤m≤M−1, 0≤n≤N−1, and 0≤k≤K−1, then the index t is defined as t=mNK+nK+k+1 and the value range of t is 1≤t≤T=MNK.
Pm(x′), Pn(y′), Pk(z′) are Legendre polynomials as shown in the following equations.
In addition, Cmlegendre, Cnlegendre, Cklegendre are defined as the following equations.
It is assumed that the space V can be contained in an infinitely-long cylinder with a radius of R and having the central axis passing through the point (x0, y0, 0) and perpendicular to the x-y plane. Then any point {right arrow over (x)} in V can be expressed as the following equation.
where the ranges of r and ϕ are 0≤r≤1 and 0≤ϕ<2π. The component function Ft({right arrow over (x)}) then can be defined as the following equation:
In addition, it is assumed that 0≤n≤N−1, |m|≤n, and the value of m−n is an even number. The value range of the index t is
and the value of (m, n) in Znm(r,ϕ) corresponding to the tth term Ft({right arrow over (x)}) is given by the tth term of an array in the following equation:
Znm(r,ϕ) is given by the following equation:
cm,nzernike is given by the following equation:
A set of G energy groups is given, where the energy groups here refer to energy intervals, the energy intervals are adjacent to each other, and there are a total of G+1 interval points in the energy intervals, which are represented by Eg, where g is an energy group index, that is, an energy interval index, g=0, 1, 2 . . . , or G, and the interval points Eg in the energy intervals are arranged in a descending order of energy as shown in the following equation.
Then, there are a total of G energy groups, and the energy groups g have an energy range [Eg,Eg−1), where g=1,2,3 . . . , or G.
The microscopic nuclear reaction cross section of the energy group g at the temperature T can be obtained by weighted-averaging the continuous energy microscopic nuclear reaction cross section σ(E,T) with a particle flux density ϕ(E,T) as the weight within the energy range of the energy group g as shown in the following equation.
Similarly, the macroscopic nuclear reaction cross section of the energy group g at the temperature T can be obtained by weighted-averaging the continuous energy microscopic nuclear reaction cross section Σ(E,T) with a particle flux density ϕ(E,T) as the weight within the energy range of the energy group g as shown in the following equation.
In addition, the multi-group particle flux density can be defined as the continuous energy particle flux density ϕ(E,T) integrated within the energy range of the energy group g as shown in the following equation.
As an application of the present application, the present application further provides a particle transport equation solving method, including using the method in at least one of the foregoing embodiments to perform at least one algorithm: Monte Carlo particle transport computation, method of characteristics-based particle transport computation, discrete ordinates method-based particle transport computation, and solving for other scientific computation problems.
That is to say, by using the method in the embodiments of the present application, Monte Carlo method-based particle transport computation, method of characteristics-based particle transport computation, discrete ordinates method-based particle transport computation, and solving for other scientific computation problems can be implemented. Compared with existing methods, the particle transport equation solving method in the embodiments of the present application solves the problem of path integral computation of functions containing cross sections in inhomogeneous media, and improves the path integral statistical method so that the method can be applied to the statistical problems of particle transport in inhomogeneous media.
In correspondence with the method provided in the present application, the present application further provides an apparatus for computing a nuclear reaction cross section and a path integral in particle transport.
Optionally, the first computation module 110 is configured to obtain the macroscopic nuclear reaction cross section Σ(E,{right arrow over (x)}) by using the leaner combination of basis functions according to Equation (1):
where N is the number of different types of sub-materials of the material, Mi is the number of basis functions of the ith-type sub-material, ai({right arrow over (x)}) is the number density of the ith-type sub-material, and when the material is a non-homogeneous medium, ai({right arrow over (x)}) is a function of a spatial position {right arrow over (x)}, σi,j(E) is the jth basis function of the ith-type sub-material, ci,j(T({right arrow over (x)})) is a coefficient of the jth basis function of the ith-type sub-material, i=1, 2, 3, . . . or N, and j=1, 2, 3, . . . or Mi.
The first computation module 110 is further configured to obtain the product of the macroscopic nuclear reaction cross section and the additional function by using the linear combination of basis functions according to Equation (2):
where r(E,{right arrow over (x)}) is the additional function.
Optionally, the second computation module 120 is configured to integrate Equation (2) on the path C, and obtain the path integral of the product of the macroscopic nuclear reaction cross section of the material and the additional function by using the linear combination of basis functions:
where the energy is E, the temperature is T({right arrow over (x)}) and the temperature is a function of a point position {right arrow over (x)} in space, a variable s is taken as a parameter of the path C, the path C is curved or straight, and {right arrow over (x)}(s) is a point position at the parameter s on the path.
Optionally, the computation apparatus 100 further includes a processing module, configured to express the nuclear reaction cross section and the path integral obtained by polynomial expansion as the linear combination of basis functions.
The polynomial expansion is to express the function as a polynomial.
Optionally, the processing module includes:
Optionally, the sub-computation module 201 is configured to obtain a microscopic nuclear reaction cross section through temperature polynomial expansion according to Equation (5):
where σ(E,T) is the microscopic nuclear reaction cross section, L is the number of terms in the polynomial, and l is an index of the polynomial term and l=1,2,3 . . . L, wherein the lth term coefficient bl(E) is a function of particle energy E, βl is the degree of the lth term, and βl may be any value.
Optionally, the macroscopic nuclear reaction cross section of the material is obtained through temperature polynomial expansion according to Equation (6), where the macroscopic nuclear reaction cross section of the material is the sum of the products of microscopic nuclear reaction cross sections of various sub-materials and corresponding number densities, as shown in Equation (7):
Optionally, the product of the microscopic nuclear reaction cross section and the additional function r(E,{right arrow over (x)}) is obtained through temperature polynomial expansion according to Equation (9):
where Equation (9) represents the product of the macroscopic nuclear reaction cross section and the additional function.
Optionally, the sub-computation module 202 is configured to define Equation (10), Equation (11), and Equation (12); and
where σi,j(E) is the jth basis function of the ith-type sub-material.
Optionally, the sub-computation module 203 is configured to use the definitions of Equation (10), Equation (11), and Equation (12), replace the index (with the index j, and transform Equation (9) into Equation (14):
where Equation (14) represents the product of the macroscopic nuclear reaction cross section and the additional function by using the linear combination of basis functions.
Optionally, the sub-computation module 204 is configured to perform integration on the path C according to Equation (9) to obtain Equation (15):
Optionally, the definitions of Equation (10), Equation (11), and Equation (12) are used, the index l is replaced with the index j, and Equation (15) is transformed into Equation (16):
where σi,j(E) is the linear combination of basis functions, and Equation (16) represents the path integral of the product of the macroscopic nuclear reaction cross section and the additional function obtained by using the linear combination of basis functions.
The present application further provides an electronic device, including: a processor and a memory having computer program instructions stored thereon, where when executing the computer program instructions, the electronic device implements the method according to any one of the foregoing embodiments.
As shown in
Specifically, the processor 601 may include at least one of the following: a central processing unit (CPU), a graphics processing unit (GPU), a neural network chip, and a field programmable gate array (FPGA) computation chip.
The memory 602 may include a large-capacity memory for data or instructions. For the purpose of exemplification instead of limitation, the memory 602 may include a hard disk drive (HDD), a floppy disk drive, a flash memory, an optical disk, a magneto-optical disk, a magnetic tape, or a universal serial bus (USB) drive or a combination of two or more of the components. In appropriate cases, the memory 602 may include a removable or non-removable (or fixed) medium. In appropriate cases, the memory 602 may be inside or outside an integrated gateway disaster recovery device. In a specific embodiment, the memory 602 is a non-volatile solid-state memory.
The memory may include a read-only memory (ROM), a random access memory (RAM), a magnetic disk storage medium device, an optical storage medium device, a flash memory device, and electrical, optical or other physical/tangible memory storage devices. Thus, typically, the memory includes one or more tangible (non-transitory) computer-readable storage media (e.g., memory devices) encoded with software including computer-executable instructions, and when the software is executed (e.g., by one or more processors), the software is operable to perform the operations described with reference to the method according to an aspect of the present disclosure.
The processor 601 reads and executes the computer program instructions stored in the memory 602 to implement parallel computation of the nuclear reaction cross section value and the path integral in particle transport in the foregoing embodiments.
In one example, the electronic device may further include a communication interface 603 and a bus 610. As shown in
The communication interface 603 is mainly configured to implement communication between various modules, apparatuses, units and/or devices in the embodiments of the present application.
The bus 610 includes hardware, software or both, and couples components of an online data traffic billing device to each other. For the purpose of exemplification instead of limitation, the bus may include an accelerated graphics port (AGP) or another graphics bus, an extended industry standard architecture (EISA) bus, a front-side bus (FSB), a hypertransport (HT) interconnect, an industry standard architecture (ISA) bus, an infinite bandwidth interconnect, a low pin count (LPC) bus, a memory bus, a micro channel architecture (MCA) bus, a peripheral component interconnect (PCI) bus, a PCI-Express (PCI-X) bus, a serial advanced technology attachment (SATA) bus, a video electronics standards association local (VLB) bus or other suitable buses or a combination of two or more of these components. In appropriate cases, the bus 610 may include one or more buses. Although the embodiments of the present application describe and show specific buses, the present application considers any suitable bus or interconnect.
In addition, the embodiments of the present application can provide a computer storage medium for implementing the method for computing a nuclear reaction cross section and a path integral in particle transport in the foregoing embodiments. The computer storage medium stores computer program instructions. When the computer program instructions are executed by a processor, the method for computing a nuclear reaction cross section and a path integral in particle transport in the foregoing embodiments is implemented.
It should be noted that the present application is not limited to the specific configurations and processing described above and shown in the figures. For the sake of conciseness, the detailed description for the known method is omitted here. In the foregoing embodiments, several specific steps are described and shown as examples. However, the method process of the present application is not limited to the specific steps described and shown, and a person skilled in the art can make various changes, modifications and additions, or change the order of the steps after understanding the spirit of the present application.
The functional blocks shown in the structural block diagrams described above can be implemented as hardware, software, firmware or a combination thereof. When implemented as hardware, the functional blocks can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented as software, the elements in the present application are programs or code segments used to execute required tasks. The programs or code segments can be stored in a machine-readable medium, or transmitted on a transmission medium or a communication link via a data signal carried in a carrier. The “machine-readable medium” may include any medium capable of storing or transmitting information. The machine-readable medium may include a non-transient computer-readable storage medium, such as an electronic circuit, a semiconductor memory device, a ROM, a flash memory, an erasable ROM (EROM), a floppy disk, a CD-ROM, an optical disk, a hard disk, and an optical fiber medium, and the machine-readable medium may also include a radio frequency (RF) link, etc. The code segments can be downloaded via a computer network such as the Internet and an intranet.
It should also be noted that although the exemplary embodiments mentioned in the present application describe some methods or systems based on a series of steps or apparatuses, the present application is not limited to the order of the steps above. That is to say, the steps can be performed in the order mentioned in the embodiments, or can be performed in an order different from that in the embodiments, or several steps can be performed simultaneously.
The aspects of the present disclosure are described above with reference to flowcharts and/or block diagrams of the method, apparatus (system), and computer program product according to the embodiments of the present disclosure. It should be understood that each block of the flowcharts and/or block diagrams, and combinations of the blocks in the flowcharts and/or block diagrams can be implemented by computer program instructions. The computer program instructions may be provided to a processor of a general-purpose computer, a special-purpose computer, or another programmable data processing apparatus to produce a machine, such that the instructions executed by the processor of the computer or another programmable data processing apparatus enable implementation of the functions/acts specified in one or more blocks of the flowcharts and/or block diagrams. The processor may be, but is not limited to, a general-purpose processor, a special-purpose processor, a special application processor, or a field programmable logic circuit. It should also be understood that each block in the block diagrams and/or flowcharts, and combinations of blocks in the block diagrams and/or flowcharts, can also be implemented by special-purpose hardware that executes specified functions or acts or implemented by combinations of special-purpose hardware and computer instructions.
Specific implementations of the present application are described above. A person skilled in the art can clearly know that for convenience and conciseness of description, reference can be made to corresponding process descriptions in the foregoing method embodiments for the working processes of the systems, modules, and units described above, and details are not described herein again. It should be understood that the scope of protection of the present application are not limited thereto. Any technician familiar with this technical field can easily conceive of various equivalent modifications or replacement within the scope of the present application, and these modifications or replacements should be included in the scope of protection of the present application.
Number | Date | Country | Kind |
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PCT/CN2022/074953 | Jan 2022 | WO | international |
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/CN2022/131119 | 11/10/2022 | WO |