c++ - 用 C++ 进行正确的核裂变模拟

Question

我正在尝试用 C++ 模拟原子裂变。

裂变核素具有已知的概率产生某些原子序数和质量数作为裂变产物，这种分布称为裂变产物产率。

我知道铀 235 的批量产品和原子产品裂变产率(可用 here )。

裂变产物产量分布加起来为 2，因为核裂变产生 2 个新核素和 2 或 3 个自由中子。

虽然我可能误解了一些物理概念，但从计算机科学的角度来看，我的问题是用伪代码生成 5 个具有已知概率分布的整数:

massYield = [...]
possibleMassProducts = [...]
atomicYield = [...]
possibleAtomicProducts = [...]
firstProductMassNumber = generateRandom(massYield, possibleMassProducts)
firstProductAtomicNumber = generateRandom(atomicYield, possibleAtomicProducts)
secondProductMassNumber = generateRandom(massYield, possibleMassProducts)
secondProductAtomicNumber = generateRandom(atomicYield, possibleAtomicProducts)
freeNeutrons = generateRandom([0.5, 0.5], [2, 3])

我创建了一个名为 IntegerRandomGenerator 的类，它生成遵循特定分布的随机数:

class IntegerRandomGenerator
{
public:
    IntegerRandomGenerator(std::vector<double> distribution, std::vector<int> values)
    {
        size_t size_dist = distribution.size();
        size_t size_val  = values.size();
        if( size_dist != size_val )
        {
            throw std::invalid_argument("distribution and values vectors shall have the same length");
        }
        else
        {
            for( double p_i : distribution )
            {
                mDist.push_back(p_i);
            }
            for( int x_i : values )
            {
                mValues.push_back(x_i);
            }
        }
    }


    int generate();

private:
    std::vector<double> mDist;
    std::vector<int>   mValues;
    std::mt19937_64 mRng;
};

int IntegerRandomGenerator::generate()
{
    uint64_t timeSeed = std::chrono::high_resolution_clock::now().time_since_epoch().count();

    std::seed_seq ss{uint32_t(timeSeed & 0xffffffff), uint32_t(timeSeed>>32)};
    mRng.seed(ss);

    std::uniform_real_distribution<double> unif(0,1);
    double random = unif(mRng);

    uint32_t distSize = static_cast<uint32_t>(mDist.size());
    for(uint32_t i = 0; i < distSize; i++)
    {
        if(random < mDist.at(i))
        {
            return mValues.at(i);
        }
        else
        {
            random -= mDist.at(i);
        }
    }

    return -1;
}

因此，我生成裂变产物的策略如下:

std::vector<int> generateFissionValues(std::vector<double> aYields, std::vector<double> zYields, std::vector<int> aNumbers, std::vector<int> zNumbers)
{
    std::vector<double> massNormalized, atomicNormalized;
    std::vector<double> unif;
    std::vector<int> nNumbers;

    for(double p_i : aYields)
    {
        massNormalized.push_back(p_i/2);
    }

    for(double q_i : zYields)
    {
        atomicNormalized.push_back(q_i/2);
    }

    unif.push_back(0.5);
    unif.push_back(0.5);
    nNumbers.push_back(2);
    nNumbers.push_back(3);

    IntegerRandomGenerator massGenerator(massNormalized, aNumbers);
    IntegerRandomGenerator atomGenerator(atomicNormalized, zNumbers);
    IntegerRandomGenerator freeGenerator(unif, nNumbers);

    int a_Product1 = massGenerator.generate();
    int z_Product1 = atomGenerator.generate();

    int a_Product2 = massGenerator.generate();
    int z_Product2 = atomGenerator.generate();

    int freeNeutr = freeGenerator.generate();

    std::vector<int> fissionProducts;

    fissionProducts.push_back(a_Product1);
    fissionProducts.push_back(z_Product1);

    fissionProducts.push_back(a_Product2);
    fissionProducts.push_back(z_Product2);

    fissionProducts.push_back(freeNeutr);

    return fissionProducts;
}

我期望得到的是，重复这个例程固定次数并计算每个原子数和质量数的出现次数，是得到与理论上已知的经验分布相似的经验分布。这是我的主要内容:

#define MIN_MASS_NUMBER 66
#define MIN_ATOMIC_NUMBER 23
#define MASS_YIELD_LENGTH 107
#define ATOMIC_YIELD_LENGTH 49

double MASS_YIELD[]=
{
        7.2405671e-10,  3.6155178e-09,  8.3798843e-09,  1.4793428e-08,  3.7126096e-08,  8.4074658e-08,  2.6566021e-07,
        1.0675927e-06,  3.3943611e-06,  1.0705677e-05,  3.0947722e-05,  7.5980282e-05,  2.0984921e-04,  4.4786922e-04,
        1.2829461e-03,  1.9049358e-03,  3.2662529e-03,  5.3619387e-03,  8.9643421e-03,  1.2891416e-02,  1.4066064e-02,
        2.5282028e-02,  3.4205412e-02,  4.7612426e-02,  5.8969791e-02,  5.8718196e-02,  5.9912701e-02,  6.2513918e-02,
        6.5931230e-02,  6.5585160e-02,  6.3729133e-02,  6.1194661e-02,  5.7681295e-02,  6.1623490e-02,  6.5885448e-02,
        5.1864512e-02,  4.2059644e-02,  3.0389326e-02,  1.8792336e-02,  9.7353401e-03,  4.0277579e-03,  1.4658471e-03,
        5.4222280e-04,  3.1255579e-04,  2.5608411e-04,  1.7477930e-04,  1.3934770e-04,  1.3765549e-04,  1.1957731e-04,
        1.3077006e-04,  1.3324824e-04,  1.1755897e-04,  1.1374826e-04,  1.2290949e-04,  1.2642393e-04,  1.3080367e-04,
        1.5523846e-04,  1.1021012e-04,  2.6858588e-04,  2.9061019e-04,  5.8370361e-04,  1.5268885e-03,  3.4896815e-03,
        5.3614445e-03,  1.8159164e-02,  2.8895004e-02,  4.3250233e-02,  6.7141993e-02,  7.8703816e-02,  6.5640320e-02,
        6.1137911e-02,  6.3605380e-02,  6.7934012e-02,  6.4934315e-02,  6.2395971e-02,  5.8687079e-02,  5.8447475e-02,
        5.9831620e-02,  5.5176036e-02,  3.9532454e-02,  3.0059773e-02,  2.2527624e-02,  1.6771722e-02,  1.0853545e-02,
        6.5508342e-03,  4.1317995e-03,  2.6763110e-03,  1.5870986e-03,  7.4634286e-04,  3.2221285e-04,  1.4892861e-04,
        6.1673994e-05,  3.2940204e-05,  1.0121245e-05,  3.1986347e-06,  8.5523451e-07,  1.5949051e-07,  6.1183839e-08,
        1.8867389e-08,  9.5405554e-09,  3.6338899e-09,  2.4780248e-09,  5.7277553e-10,  2.3914282e-10,  5.0200588e-11,
        2.3540988e-11,  7.7074464e-12
};

double ATOMIC_YIELD[]=
{
        2.0558300e-19,  2.8862345e-14,  1.3368750e-11,  1.6193162e-09,  1.3709663e-08,  3.0150265e-07,  3.6301782e-06,  
        1.1200954e-04,  7.0351909e-04,  4.4498299e-03,  9.1719425e-03,  3.6528367e-02,  5.2682609e-02,  1.5625724e-01,  
        1.2071735e-01,  1.9331319e-01,  1.2675553e-01,  1.8037105e-01,  6.8939851e-02,  4.3268378e-02,  3.4683702e-03,  
        4.1462569e-04,  2.2779437e-04,  3.4012286e-04,  2.7543142e-04,  1.6063619e-03,  1.7210332e-03,  3.6208508e-02,  
        7.7033688e-02,  1.7331044e-01,  1.1582092e-01,  2.0090419e-01,  1.1037331e-01,  1.6401242e-01,  6.0615264e-02,  
        4.1834320e-02,  1.3435892e-02,  4.5405310e-03,  4.6638638e-04,  1.0987593e-04,  5.1296865e-06,  3.9564637e-07,  
        1.1679425e-08,  1.9805406e-09,  7.0990343e-11,  4.8416648e-12,  2.4283831e-14,  2.4747259e-17,  0.0000000e+00
};

int main()
{
    const int nSim = 10000;

    std::vector<double> distMass(std::begin(MASS_YIELD), std::end(MASS_YIELD));
    std::vector<double> distAtom(std::begin(ATOMIC_YIELD), std::end(ATOMIC_YIELD));
    std::vector<int>   massNumbers;
    std::vector<int>   atomNumbers;

    for(int i = 0; i < MASS_YIELD_LENGTH; i++)
    {
        massNumbers.push_back(i + MIN_MASS_NUMBER);
    }
    for(int i = 0; i < ATOMIC_YIELD_LENGTH; i++)
    {
        atomNumbers.push_back(i + MIN_ATOMIC_NUMBER);
    }

    int countsPerZ[ATOMIC_YIELD_LENGTH];
    std::vector<double> relCountsPerZ;

    int countsPerA[MASS_YIELD_LENGTH];
    std::vector<double> relCountsPerA;

    memset(countsPerZ, 0x00, ATOMIC_YIELD_LENGTH * sizeof(int));
    memset(countsPerA, 0x00, MASS_YIELD_LENGTH * sizeof(int));

    std::cout << "Start " << nSim << " atomic fission simulations . . ." << std::endl;
    for(int i = 0; i < nSim;)
    {
        std::vector<int> fissionProducts = generateFissionValues(distMass, distAtom, massNumbers, atomNumbers);

        int a1 = fissionProducts.at(0);
        countsPerA[a1 - MIN_MASS_NUMBER] += 1;

        int z1 = fissionProducts.at(1);
        countsPerZ[z1 - MIN_ATOMIC_NUMBER] += 1;

        int a2 = fissionProducts.at(2);
        countsPerA[a2 - MIN_MASS_NUMBER] += 1;

        int z2 = fissionProducts.at(3);
        countsPerA[z2 - MIN_ATOMIC_NUMBER] += 1;

        i++;

        double percentage = (100.0 * i)/nSim;
        printf("Progress: %d %%\r", static_cast<int>(percentage));
        fflush(stdout);
    }

    //here I pass countsPerA and countsPerZ to another function which plots results
}

这是我重复 10000 次实验后的结果。

对于质量数: 对于原子序数:

这很奇怪，因为使用相同的策略，原子序数似乎可以正确模拟，而质量数绝对不能。我对大量数字做错了什么？

Answer 1

当您填充 countsPerA 和 countsPerZ 数组时:

    int a1 = fissionProducts.at(0);
    countsPerA[a1 - MIN_MASS_NUMBER] += 1;

    int z1 = fissionProducts.at(1);
    countsPerZ[z1 - MIN_ATOMIC_NUMBER] += 1;

    int a2 = fissionProducts.at(2);
    countsPerA[a2 - MIN_MASS_NUMBER] += 1;

    int z2 = fissionProducts.at(3);
    countsPerA[z2 - MIN_ATOMIC_NUMBER] += 1; //typo here

由于拼写错误，您正在将原子序数结果中的数据添加到质量数计数中。