Parameters

Short description

$\nabla =\overrightarrow{i}\frac{\partial }{\partial x}+\overrightarrow{j}\frac{\partial }{\partial y}+\overrightarrow{k}\frac{\partial }{\partial z}$

the operator of vector differentiation

t

given time

${t^{\prime }}_i$

the time of the initial collision of the converging particle

$\overrightarrow{r}$

position of the ending point of the converging particle

${\overrightarrow{r}}^{\prime }$

position of the starting point of the converging particle

$\overrightarrow{u}\left({t^{\prime }}_i,{\overrightarrow{r}}^{\prime }\right)$

mass flow velocity in the point ${\overrightarrow{r}}^{\prime }$ at time ${t^{\prime }}_i$

$v_T\left({t^{\prime }}_i,{\overrightarrow{r}}^{\prime }\right)$

the average magnitude of the thermal velocity of converging particle in point ${\overrightarrow{r}}^{\prime }$ at time ${t^{\prime }}_i$

$Z_V\left({t^{\prime }}_i,{\overrightarrow{r}}^{\prime }\right)$

the rate of collisions per unit volume in the point of the collision ${\overrightarrow{r}}^{\prime }$ at the time ${t^{\prime }}_i$ of the initial collision

$\overrightarrow{v}\left({t^{\prime }}_i,{\overrightarrow{r}}^{\prime },t,\overrightarrow{r}\right)$

velocity vector in the ending point $\overrightarrow{r}$ at the given time t

$Q_i\left(t,{t^{\prime }}_i\right)$

the probability of free path traveling along the ballistic trajectory of the converging ballistic trajectory starting at time ${t^{\prime }}_i$ and ending at time t

${\Psi }_{in}\left({t^{\prime }}_i,{\overrightarrow{r}}^{\prime },t,\overrightarrow{r}\right)$

property content delivered by the converging ballistic particle in the ending point $\overrightarrow{r}$ at the given time t

${\phi }_i=t-{t^{\prime }}_i$

traveling time between an initial and ending consecutive collisions or the ballistic traveling time

n

particles density

m

particle mass

${\sigma }_c$

the cross-section of collisions

$P_c={\sigma }_{c}n$

the number of particles placed within a collision tube of a unit length

${\sigma }_c$

the cross-section of collisions

V

the volume of integration over space occupied by the model gas

${\overrightarrow{r}}_i^c\left({\overrightarrow{r}}^{\prime },{t^{\prime }}_i,\tilde{t}\right)$

the position of a virtual ballistic particle at a time $\tilde{t}$ , which has zero magnitude of thermal velocity in the starting point ${\overrightarrow{r}}^{\prime }$ at the time of the initial collision ${t^{\prime }}_i$

${\overrightarrow{v}}_i^c\left({\overrightarrow{r}}^{\prime },{t^{\prime }}_i,\tilde{t}\right)$

the velocity vector of the virtual ballistic particle having a zero component of the thermal velocity at a time $\tilde{t}$

${\overrightarrow{n}}_i=\frac{\overrightarrow{r}-{\overrightarrow{r}}_i^c\left({\overrightarrow{r}}^{\prime },{t^{\prime }}_i,t\right)}{\left|\overrightarrow{r}-{\overrightarrow{r}}_i^c\left({\overrightarrow{r}}^{\prime },{t^{\prime }}_i,t\right)\right|}$

instant unit vector directing thermal velocity component, so a traveling particle targets point $\overrightarrow{r}$ at time t

$\overrightarrow{\tilde{r}}=\overrightarrow{r}\left({\overrightarrow{r}}^{\prime },{t^{\prime }}_i,\tilde{t}\right)$

the position vector of a ballistic particle at time $\tilde{t}$

$\overrightarrow{\tilde{v}}=\overrightarrow{v}\left({t^{\prime }}_i,{\overrightarrow{r}}^{\prime },\tilde{t}\right)$

the velocity vector of the ballistic particle at time $\tilde{t}$

$\overrightarrow{g}$

an external force that applies to a particle of a unit mass

$v_{rel}$

the average magnitude of the velocity of the traveling particle with respect to a nearby passed particle