feat: 真蛙跳法重构（Python/C/C++/Fortran 四引擎统一）
- 新增 compute_accel_conservative / accel_conservative： 保守力加速度（弹簧+重力+原子间引力），不含阻尼，供蛙跳专用 - 重写 leapfrog_step / leapfrog_full： - 无阻尼：纯辛积分器，每步 1 次力计算（原 Velocity-Verlet 需 2 次） - 有阻尼：半隐式处理 v(t+dt/2)=[v(t-dt/2)*(1-α)+a_c*dt]/(1+α)，无条件稳定 - 主循环加初始化反向半步 v(-dt/2)=v(0)-0.5*a_c(0)*dt - 修复 C/C++ number of frames 字段写采样帧数而非总积分步数的 bug - Python 引擎：新增 display.npz 二进制格式，draw.py/plot_wave.py 优先读取 - 编译参数统一为 -O3 -march=native -ffast-math
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@@ -107,6 +107,24 @@ program dynamics_f90
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allocate(traj_x(record_steps, n), traj_y(record_steps, n), traj_z(record_steps, n))
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allocate(traj_vx(record_steps, n), traj_vy(record_steps, n), traj_vz(record_steps, n))
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! 真蛙跳初始化：v(0) 反推 v(-dt/2) = v(0) - 0.5*a_c(0)*dt
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if (trim(method) == 'leapfrog') then
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block
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double precision :: ax0(n), ay0(n), az0(n)
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integer :: ii
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call accel_conservative(n, x, y, z, masses, G, &
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n_bonds, bond_pairs, bond_stiffness, bond_rest_lengths, &
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gravity_field, gravity_interaction, &
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elastic_force, gravity_strength, ax0, ay0, az0)
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do ii = 1, n
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if (fixed(ii,1) /= 0 .and. fixed(ii,2) /= 0 .and. fixed(ii,3) /= 0) cycle
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vx(ii) = vx(ii) - 0.5d0 * ax0(ii) * DT
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vy(ii) = vy(ii) - 0.5d0 * ay0(ii) * DT
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vz(ii) = vz(ii) - 0.5d0 * az0(ii) * DT
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end do
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end block
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end if
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! 预热
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! 初始时刻 t=0 驱动力（与 Python run_simulation 一致）
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if (driving_force /= 0 .and. n_drivers > 0) then
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@@ -524,6 +542,24 @@ pure subroutine accel(n, x, y, z, vx, vy, vz, m, G, B, &
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end if
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end subroutine accel
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! 保守力加速度（不含阻尼），供真蛙跳法专用。
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! 传入零速度、零 B 调用 accel，阻尼项 -B*v/m 自动为零。
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subroutine accel_conservative(n, x, y, z, m, G, nb, bp, bk, br, &
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gravity_field, gravity_interaction, &
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elastic_force, gravity_strength, ax, ay, az)
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integer, intent(in) :: n, nb, bp(nb, 2)
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integer, intent(in) :: gravity_field, gravity_interaction, elastic_force
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double precision, intent(in) :: x(n), y(n), z(n), m(n), G(3)
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double precision, intent(in) :: bk(nb), br(nb), gravity_strength
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double precision, intent(out) :: ax(n), ay(n), az(n)
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double precision :: v0(n), B0(3)
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v0 = 0.0d0
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B0 = 0.0d0
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call accel(n, x, y, z, v0, v0, v0, m, G, B0, nb, bp, bk, br, &
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gravity_field, gravity_interaction, &
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elastic_force, 0, gravity_strength, ax, ay, az)
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end subroutine accel_conservative
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! 边界条件：clamp 位置 + 速度反转
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subroutine limit_in_box(pos, vel, lo, hi)
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double precision, intent(inout) :: pos, vel
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@@ -652,7 +688,13 @@ subroutine midpoint_step(n, x, y, z, vx, vy, vz, m, G, B, &
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end do
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end subroutine midpoint_step
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! ── 蛙跳法（Velocity-Verlet）──
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! 真蛙跳一步：x(t), v(t-dt/2) → x(t+dt), v(t+dt/2)
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!
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! 无阻尼：纯保守蛙跳，每步 1 次力计算，辛积分器。
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! v(t+dt/2) = v(t-dt/2) + a_c(t)*dt
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!
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! 有阻尼：半隐式处理，仍 1 次力计算，对任意阻尼无条件稳定。
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! v(t+dt/2) = [v(t-dt/2)*(1-α) + a_c(t)*dt] / (1+α)，α = B*dt/(2m)
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subroutine leapfrog_full(n, x, y, z, vx, vy, vz, m, G, B, &
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nb, bp, bk, br, fixed, dt, &
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gravity_field, gravity_interaction, &
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@@ -662,53 +704,36 @@ subroutine leapfrog_full(n, x, y, z, vx, vy, vz, m, G, B, &
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double precision, intent(inout) :: x(n), y(n), z(n), vx(n), vy(n), vz(n)
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double precision, intent(in) :: m(n), G(3), B(3), bk(nb), br(nb), dt, gravity_strength
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double precision :: ax(n), ay(n), az(n)
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double precision :: dmp_vx(n), dmp_vy(n), dmp_vz(n)
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double precision :: gx, gy, gz
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double precision :: alphax, alphay, alphaz
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logical :: has_damping
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integer :: i
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call accel(n, x, y, z, vx, vy, vz, m, G, B, nb, bp, bk, br, &
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gravity_field, gravity_interaction, &
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elastic_force, damping_force, gravity_strength, ax, ay, az)
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! 1 次保守力计算（不含阻尼）
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call accel_conservative(n, x, y, z, m, G, nb, bp, bk, br, &
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gravity_field, gravity_interaction, &
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elastic_force, gravity_strength, ax, ay, az)
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has_damping = (damping_force /= 0) .and. &
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(B(1) /= 0.0d0 .or. B(2) /= 0.0d0 .or. B(3) /= 0.0d0)
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! 速度半步推
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do i = 1, n
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if (fixed(i,1) /= 0 .and. fixed(i,2) /= 0 .and. fixed(i,3) /= 0) cycle
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vx(i) = vx(i) + ax(i) * dt * 0.5d0
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vy(i) = vy(i) + ay(i) * dt * 0.5d0
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vz(i) = vz(i) + az(i) * dt * 0.5d0
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end do
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! 全推位置（不含边界）
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do i = 1, n
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if (fixed(i,1) /= 0 .and. fixed(i,2) /= 0 .and. fixed(i,3) /= 0) cycle
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if (has_damping) then
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alphax = B(1) * dt / (2.0d0 * m(i))
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alphay = B(2) * dt / (2.0d0 * m(i))
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alphaz = B(3) * dt / (2.0d0 * m(i))
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vx(i) = (vx(i) * (1.0d0 - alphax) + ax(i) * dt) / (1.0d0 + alphax)
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vy(i) = (vy(i) * (1.0d0 - alphay) + ay(i) * dt) / (1.0d0 + alphay)
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vz(i) = (vz(i) * (1.0d0 - alphaz) + az(i) * dt) / (1.0d0 + alphaz)
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else
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vx(i) = vx(i) + ax(i) * dt
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vy(i) = vy(i) + ay(i) * dt
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vz(i) = vz(i) + az(i) * dt
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end if
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x(i) = x(i) + vx(i) * dt
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y(i) = y(i) + vy(i) * dt
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z(i) = z(i) + vz(i) * dt
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end do
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! 隐式阻尼处理（用临时数组 dmp_v，不覆盖 vx/vy/vz）
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do i = 1, n
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if (fixed(i,1) /= 0 .and. fixed(i,2) /= 0 .and. fixed(i,3) /= 0) then
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dmp_vx(i) = 0; dmp_vy(i) = 0; dmp_vz(i) = 0; cycle
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end if
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gx = B(1) / m(i); gy = B(2) / m(i); gz = B(3) / m(i)
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dmp_vx(i) = (vx(i) + 0.5d0 * G(1) * dt) / (1.0d0 + 0.5d0 * gx * dt)
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dmp_vy(i) = (vy(i) + 0.5d0 * G(2) * dt) / (1.0d0 + 0.5d0 * gy * dt)
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dmp_vz(i) = (vz(i) + 0.5d0 * G(3) * dt) / (1.0d0 + 0.5d0 * gz * dt)
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end do
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! 用新位置 + 阻尼速度重算加速度
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call accel(n, x, y, z, dmp_vx, dmp_vy, dmp_vz, m, G, B, nb, bp, bk, br, &
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gravity_field, gravity_interaction, &
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elastic_force, damping_force, gravity_strength, ax, ay, az)
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! 速度后半步：v = v_half + 0.5*a_next*dt（vx 仍为 v_half）
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do i = 1, n
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if (fixed(i,1) /= 0 .and. fixed(i,2) /= 0 .and. fixed(i,3) /= 0) cycle
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vx(i) = vx(i) + ax(i) * dt * 0.5d0
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vy(i) = vy(i) + ay(i) * dt * 0.5d0
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vz(i) = vz(i) + az(i) * dt * 0.5d0
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end do
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end subroutine leapfrog_full
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! ── 分发器 + 边界条件 + 自由度约束 ──
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