我正在尝试用 C++ 模拟原子裂变。
裂变核素具有产生某些原子序数和质量数作为裂变产物的已知概率，这种分布称为裂变产物产率。
我知道铀 235 的大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，它按照特定的分布生成随机数:
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，重复这个程序固定的次数并计算每个原子数和质量数的出现次数，是得到一个与理论已知的相似的经验分布。
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
}
这是我在 10000 次重复实验中的结果。
对于质量数:
对于原子数:
这很奇怪，因为使用相同的策略，原子数似乎被正确模拟，而质量数绝对不是。我对质量数做错了什么？
最佳答案
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
由于打字错误，您正在将原子序数结果中的数据添加到质量数计数中。
关于c++ - 在 C++ 中正确的核裂变模拟，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/59869321/