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From: Sunipa Som on 12 Jul 2010 05:46
Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <197969483.13841.1278918254385.JavaMail.root(a)gallium.mathforum.org>...
> > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote
> > in message
> > <949632433.89696.1278593304386.JavaMail.root(a)gallium.m
> > athforum.org>...
> > > > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de>
> > wrote
> > > > in message
> > > >
> > <1630764328.89371.1278589087664.JavaMail.root(a)gallium.
> > > > mathforum.org>...
> > > > > > Torsten Hennig
> > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > wrote
> > > > > > in message
> > > > > >
> > > >
> > <128269470.77069.1278420640088.JavaMail.root(a)gallium.m
> > > > > > athforum.org>...
> > > > > > > > Torsten Hennig
> > > > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > > > wrote
> > > > > > > > in message
> > > > > > > >
> > > > > >
> > > >
> > <1394417502.76713.1278415717104.JavaMail.root(a)gallium.
> > > > > > > > mathforum.org>...
> > > > > > > > > > Torsten Hennig
> > > > > > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > > > > > wrote
> > > > > > > > > > in message
> > > > > > > > > >
> > > > > > > >
> > > > > >
> > > >
> > <2044145382.75601.1278398289051.JavaMail.root(a)gallium.
> > > > > > > > > > mathforum.org>...
> > > > > > > > > > >
> > > > > > > > > > > Best wishes
> > > > > > > > > > > Torsten.
> > > > > > > > > >
> > > > > > > > > > Hi,
> > > > > > > > > > I am facing a typical problem to
> > solve my
> > > > > > > > Boltzmann
> > > > > > > > > > equation.
> > > > > > > > > > My PDE
> > > > > > > > > > Nr(i,j)=((N(i,j)-N(i-1,j))/dr);
> > > > > > > > > > Nk(i,j)=((N(i,j+1)-N(i,j)));
> > > > > > > > > >
> > > > > > > >
> > > > > >
> > > >
> > Nt(i,j)=-(c1*sqrt(j).*Nr(i,j))+(c2*sqrt(j).*(i-1).*dr.
> > > > > > > > > > *Nk(i,j));
> > > > > > > > > > For my equation, when I am giving
> > > > Boundary
> > > > > > > > condition
> > > > > > > > > > Nr(1,j)=0;Nk(i,nk)=0;
> > > > > > > > >
> > > > > > > > > Do you mean N(1,j) = 0; N(i,nk) = 0
> > here ?
> > > > > > > > > Otherwise your boundary conditions do
> > not
> > > > make
> > > > > > > > sense
> > > > > > > > > since for a first-order differential
> > > > equation,
> > > > > > > > > it is not allowed to prescribe dN/dr =
> > 0 or
> > > > > > dN/dk =
> > > > > > > > 0
> > > > > > > > > at a boundary.
> > > > > > > > > Or where did you read that such a
> > boundary
> > > > > > > > condition
> > > > > > > > > can be applied ?
> > > > > > > > >
> > > > > > > > > > then curve is acting properly, but
> > total
> > > > > > number
> > > > > > > > of
> > > > > > > > > > particles decreasing with increasing
> > time
> > > > > > steps.
> > > > > > > > >
> > > > > > > > > If your discretization scheme is
> > > > conservative,
> > > > > > > > > this can only happen because more
> > particles
> > > > > > leave
> > > > > > > > > the domain than enter it over the four
> > > > > > boundaries
> > > > > > > > > (see my response above).
> > > > > > > > >
> > > > > > > > > > But when I am giving Boundary
> > condition
> > > > > > > > > > Nr(1,j)=0;Nk(i,nk)=0;
> > > > > > > > > > N(i,1)=0;
> > > > > > > > > > then from second time steps total
> > number
> > > > of
> > > > > > > > particles
> > > > > > > > > > are constant but figure is not moving
> > or
> > > > not
> > > > > > > > working
> > > > > > > > > > properly.
> > > > > > > > > > In my case particles are within
> > potential
> > > > > > trap,
> > > > > > > > so it
> > > > > > > > > > cant go out.
> > > > > > > > > > Can you give some idea why it is
> > > > happening?
> > > > > > > > > >
> > > > > > > > > > Thank you.
> > > > > > > > > > With regards,
> > > > > > > > > > Sunipa Som
> > > > > > > > >
> > > > > > > > > Best wishes
> > > > > > > > > Torsten.
> > > > > > > > Hi,
> > > > > > > > Nr(1,j)=0;Nk(i,nk)=0; means dN/dr(1,j)=0
> > and
> > > > > > > > dN/dk(i,nk)=0 which I put as boundary
> > > > condition
> > > > > > and
> > > > > > > > curve is working fine.
> > > > > > > > But particles numbers are
> > > > > > > > decreasing. In my case particles are
> > within
> > > > > > potential
> > > > > > > > trap, so it can not go out, so how can it
> > > > > > decrease?
> > > > > > > > and how can i resolve it? Because in my
> > case
> > > > > > total
> > > > > > > > number of particles should be constant.
> > > > > > > >
> > > > > > > > Thank you.
> > > > > > > > With regards,
> > > > > > > > Sunipa Som
> > > > > > >
> > > > > > > What is c1*sqrt(j)*N(i,j) for i=nr ,
> > > > > > > -c1*sqrt(j)*N(i,j) for i=1,
> > > > > > > -c2*sqrt(j)*(i-1)*dr*N(i,j) for j=1 and
> > > > > > > c2*sqrt(j)*(i-1)*dr*N(i,j) for j=nk ?
> > > > > > > If the expressions are greater than zero,
> > the
> > > > > > > number of particles in the volume will
> > decrease
> > > >
> > > > > > > in time.
> > > > > > >
> > > > > > > Best wishes
> > > > > > > Torsten.
> > > > > >
> > > > > > Hi,
> > > > > > In my case particle should be constant. So I
> > want
> > > > > > ant to make a reflecting wall or reflecting
> > > > sphere
> > > > > > which will reflect this particles(which
> > moving
> > > > out)
> > > > > > inside. Do you know how can I do it?
> > > > > >
> > > > > > Thank you.
> > > > > >
> > > > > > With Regards,
> > > > > > S Som
> > > > >
> > > > > Do you use a finite-difference or finite volume
> >
> > > > > scheme to discretize your equations ?
> > > > >
> > > > > Best wishes
> > > > > Torsten.
> > > >
> > > > I am using finite difference.
> > > > My PDE
> > > > Nr(i,j)=((N(i,j)-N(i-1,j))/dr);
> > > > Nk(i,j)=((N(i,j+1)-N(i,j))/dk);
> > > >
> > Nt(i,j)=-(c1*sqrt(j).*Nr(i,j))+(c2*sqrt(j).*(i-1).*dr.
> > > > *Nk(i,j));
> > > > Boundary condition
> > > > Nr(1,j)=0;Nk(i,nk)=0;
> > > >
> > > >
> > > > With Regards,
> > > > S Som
> > >
> > > And at the other two boundaries you want to
> > implement a
> > > reflecting boundary condition for N ?
> > >
> > > Best wishes
> > > Torsten.
> >
> > Yes, if it is possible by putting boundary condition,
> > I can do that. But what will be these conditions? So,
> > particles can not move out from the boundary rather
> > they will reflect back to the rgion.
> >
> > With Regards,
> > Sunipa Som
>
> You could set the velocities normal to the boundary
> to zero: c1 = 0 for i=1 and i=nr ; c2 = 0 for j=1
> and j=nr.
>
> Best wishes
> Torsten.

Hi,
After putting those conditions, the curve is not coming towards zero with increasing time rather it is going towards higher values of r. But curve should come towards zero with increasing time.

With regards,
Sunipa som
From: Torsten Hennig on 12 Jul 2010 03:10
> Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote
> in message
> <197969483.13841.1278918254385.JavaMail.root(a)gallium.m
> athforum.org>...
> > > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de>
> wrote
> > > in message
> > >
> <949632433.89696.1278593304386.JavaMail.root(a)gallium.m
> > > athforum.org>...
> > > > > Torsten Hennig
> <Torsten.Hennig(a)umsicht.fhg.de>
> > > wrote
> > > > > in message
> > > > >
> > >
> <1630764328.89371.1278589087664.JavaMail.root(a)gallium.
> > > > > mathforum.org>...
> > > > > > > Torsten Hennig
> > > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > > wrote
> > > > > > > in message
> > > > > > >
> > > > >
> > >
> <128269470.77069.1278420640088.JavaMail.root(a)gallium.m
> > > > > > > athforum.org>...
> > > > > > > > > Torsten Hennig
> > > > > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > > > > wrote
> > > > > > > > > in message
> > > > > > > > >
> > > > > > >
> > > > >
> > >
> <1394417502.76713.1278415717104.JavaMail.root(a)gallium.
> > > > > > > > > mathforum.org>...
> > > > > > > > > > > Torsten Hennig
> > > > > > > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > > > > > > wrote
> > > > > > > > > > > in message
> > > > > > > > > > >
> > > > > > > > >
> > > > > > >
> > > > >
> > >
> <2044145382.75601.1278398289051.JavaMail.root(a)gallium.
> > > > > > > > > > > mathforum.org>...
> > > > > > > > > > > >
> > > > > > > > > > > > Best wishes
> > > > > > > > > > > > Torsten.
> > > > > > > > > > >
> > > > > > > > > > > Hi,
> > > > > > > > > > > I am facing a typical problem to
> > > solve my
> > > > > > > > > Boltzmann
> > > > > > > > > > > equation.
> > > > > > > > > > > My PDE
> > > > > > > > > > > Nr(i,j)=((N(i,j)-N(i-1,j))/dr);
> > > > > > > > > > > Nk(i,j)=((N(i,j+1)-N(i,j)));
> > > > > > > > > > >
> > > > > > > > >
> > > > > > >
> > > > >
> > >
> Nt(i,j)=-(c1*sqrt(j).*Nr(i,j))+(c2*sqrt(j).*(i-1).*dr.
> > > > > > > > > > > *Nk(i,j));
> > > > > > > > > > > For my equation, when I am giving
> > > > > Boundary
> > > > > > > > > condition
> > > > > > > > > > > Nr(1,j)=0;Nk(i,nk)=0;
> > > > > > > > > >
> > > > > > > > > > Do you mean N(1,j) = 0; N(i,nk) = 0
> > > here ?
> > > > > > > > > > Otherwise your boundary conditions
> do
> > > not
> > > > > make
> > > > > > > > > sense
> > > > > > > > > > since for a first-order
> differential
> > > > > equation,
> > > > > > > > > > it is not allowed to prescribe
> dN/dr =
> > > 0 or
> > > > > > > dN/dk =
> > > > > > > > > 0
> > > > > > > > > > at a boundary.
> > > > > > > > > > Or where did you read that such a
> > > boundary
> > > > > > > > > condition
> > > > > > > > > > can be applied ?
> > > > > > > > > >
> > > > > > > > > > > then curve is acting properly,
> but
> > > total
> > > > > > > number
> > > > > > > > > of
> > > > > > > > > > > particles decreasing with
> increasing
> > > time
> > > > > > > steps.
> > > > > > > > > >
> > > > > > > > > > If your discretization scheme is
> > > > > conservative,
> > > > > > > > > > this can only happen because more
> > > particles
> > > > > > > leave
> > > > > > > > > > the domain than enter it over the
> four
> > > > > > > boundaries
> > > > > > > > > > (see my response above).
> > > > > > > > > >
> > > > > > > > > > > But when I am giving Boundary
> > > condition
> > > > > > > > > > > Nr(1,j)=0;Nk(i,nk)=0;
> > > > > > > > > > > N(i,1)=0;
> > > > > > > > > > > then from second time steps total
> > > number
> > > > > of
> > > > > > > > > particles
> > > > > > > > > > > are constant but figure is not
> moving
> > > or
> > > > > not
> > > > > > > > > working
> > > > > > > > > > > properly.
> > > > > > > > > > > In my case particles are within
> > > potential
> > > > > > > trap,
> > > > > > > > > so it
> > > > > > > > > > > cant go out.
> > > > > > > > > > > Can you give some idea why it is
> > > > > happening?
> > > > > > > > > > >
> > > > > > > > > > > Thank you.
> > > > > > > > > > > With regards,
> > > > > > > > > > > Sunipa Som
> > > > > > > > > >
> > > > > > > > > > Best wishes
> > > > > > > > > > Torsten.
> > > > > > > > > Hi,
> > > > > > > > > Nr(1,j)=0;Nk(i,nk)=0; means
> dN/dr(1,j)=0
> > > and
> > > > > > > > > dN/dk(i,nk)=0 which I put as boundary
> > > > > condition
> > > > > > > and
> > > > > > > > > curve is working fine.
> > > > > > > > > But particles numbers are
> > > > > > > > > decreasing. In my case particles are
> > > within
> > > > > > > potential
> > > > > > > > > trap, so it can not go out, so how
> can it
> > > > > > > decrease?
> > > > > > > > > and how can i resolve it? Because in
> my
> > > case
> > > > > > > total
> > > > > > > > > number of particles should be
> constant.
> > > > > > > > >
> > > > > > > > > Thank you.
> > > > > > > > > With regards,
> > > > > > > > > Sunipa Som
> > > > > > > >
> > > > > > > > What is c1*sqrt(j)*N(i,j) for i=nr ,
> > > > > > > > -c1*sqrt(j)*N(i,j) for i=1,
> > > > > > > > -c2*sqrt(j)*(i-1)*dr*N(i,j) for j=1 and
>
> > > > > > > > c2*sqrt(j)*(i-1)*dr*N(i,j) for j=nk ?
> > > > > > > > If the expressions are greater than
> zero,
> > > the
> > > > > > > > number of particles in the volume will
> > > decrease
> > > > >
> > > > > > > > in time.
> > > > > > > >
> > > > > > > > Best wishes
> > > > > > > > Torsten.
> > > > > > >
> > > > > > > Hi,
> > > > > > > In my case particle should be constant.
> So I
> > > want
> > > > > > > ant to make a reflecting wall or
> reflecting
> > > > > sphere
> > > > > > > which will reflect this particles(which
> > > moving
> > > > > out)
> > > > > > > inside. Do you know how can I do it?
> > > > > > >
> > > > > > > Thank you.
> > > > > > >
> > > > > > > With Regards,
> > > > > > > S Som
> > > > > >
> > > > > > Do you use a finite-difference or finite
> volume
> > >
> > > > > > scheme to discretize your equations ?
> > > > > >
> > > > > > Best wishes
> > > > > > Torsten.
> > > > >
> > > > > I am using finite difference.
> > > > > My PDE
> > > > > Nr(i,j)=((N(i,j)-N(i-1,j))/dr);
> > > > > Nk(i,j)=((N(i,j+1)-N(i,j))/dk);
> > > > >
> > >
> Nt(i,j)=-(c1*sqrt(j).*Nr(i,j))+(c2*sqrt(j).*(i-1).*dr.
> > > > > *Nk(i,j));
> > > > > Boundary condition
> > > > > Nr(1,j)=0;Nk(i,nk)=0;
> > > > >
> > > > >
> > > > > With Regards,
> > > > > S Som
> > > >
> > > > And at the other two boundaries you want to
> > > implement a
> > > > reflecting boundary condition for N ?
> > > >
> > > > Best wishes
> > > > Torsten.
> > >
> > > Yes, if it is possible by putting boundary
> condition,
> > > I can do that. But what will be these conditions?
> So,
> > > particles can not move out from the boundary
> rather
> > > they will reflect back to the rgion.
> > >
> > > With Regards,
> > > Sunipa Som
> >
> > You could set the velocities normal to the boundary
>
> > to zero: c1 = 0 for i=1 and i=nr ; c2 = 0 for j=1
> > and j=nr.
> >
> > Best wishes
> > Torsten.
>
> Hi,
> After putting those conditions, the curve is not
> coming towards zero with increasing time rather it is
> going towards higher values of r. But curve should
> come towards zero with increasing time.
>
> With regards,
> Sunipa som

But
int_2d N(r,k) dr dk
now remains constant in time ?

Best wishes
Torsten.
From: Sunipa Som on 12 Jul 2010 07:45
Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote in message <1167946477.14656.1278933080708.JavaMail.root(a)gallium.mathforum.org>...
> > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de> wrote
> > in message
> > <197969483.13841.1278918254385.JavaMail.root(a)gallium.m
> > athforum.org>...
> > > > Torsten Hennig <Torsten.Hennig(a)umsicht.fhg.de>
> > wrote
> > > > in message
> > > >
> > <949632433.89696.1278593304386.JavaMail.root(a)gallium.m
> > > > athforum.org>...
> > > > > > Torsten Hennig
> > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > wrote
> > > > > > in message
> > > > > >
> > > >
> > <1630764328.89371.1278589087664.JavaMail.root(a)gallium.
> > > > > > mathforum.org>...
> > > > > > > > Torsten Hennig
> > > > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > > > wrote
> > > > > > > > in message
> > > > > > > >
> > > > > >
> > > >
> > <128269470.77069.1278420640088.JavaMail.root(a)gallium.m
> > > > > > > > athforum.org>...
> > > > > > > > > > Torsten Hennig
> > > > > > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > > > > > wrote
> > > > > > > > > > in message
> > > > > > > > > >
> > > > > > > >
> > > > > >
> > > >
> > <1394417502.76713.1278415717104.JavaMail.root(a)gallium.
> > > > > > > > > > mathforum.org>...
> > > > > > > > > > > > Torsten Hennig
> > > > > > > > <Torsten.Hennig(a)umsicht.fhg.de>
> > > > > > > > > > wrote
> > > > > > > > > > > > in message
> > > > > > > > > > > >
> > > > > > > > > >
> > > > > > > >
> > > > > >
> > > >
> > <2044145382.75601.1278398289051.JavaMail.root(a)gallium.
> > > > > > > > > > > > mathforum.org>...
> > > > > > > > > > > > >
> > > > > > > > > > > > > Best wishes
> > > > > > > > > > > > > Torsten.
> > > > > > > > > > > >
> > > > > > > > > > > > Hi,
> > > > > > > > > > > > I am facing a typical problem to
> > > > solve my
> > > > > > > > > > Boltzmann
> > > > > > > > > > > > equation.
> > > > > > > > > > > > My PDE
> > > > > > > > > > > > Nr(i,j)=((N(i,j)-N(i-1,j))/dr);
> > > > > > > > > > > > Nk(i,j)=((N(i,j+1)-N(i,j)));
> > > > > > > > > > > >
> > > > > > > > > >
> > > > > > > >
> > > > > >
> > > >
> > Nt(i,j)=-(c1*sqrt(j).*Nr(i,j))+(c2*sqrt(j).*(i-1).*dr.
> > > > > > > > > > > > *Nk(i,j));
> > > > > > > > > > > > For my equation, when I am giving
> > > > > > Boundary
> > > > > > > > > > condition
> > > > > > > > > > > > Nr(1,j)=0;Nk(i,nk)=0;
> > > > > > > > > > >
> > > > > > > > > > > Do you mean N(1,j) = 0; N(i,nk) = 0
> > > > here ?
> > > > > > > > > > > Otherwise your boundary conditions
> > do
> > > > not
> > > > > > make
> > > > > > > > > > sense
> > > > > > > > > > > since for a first-order
> > differential
> > > > > > equation,
> > > > > > > > > > > it is not allowed to prescribe
> > dN/dr =
> > > > 0 or
> > > > > > > > dN/dk =
> > > > > > > > > > 0
> > > > > > > > > > > at a boundary.
> > > > > > > > > > > Or where did you read that such a
> > > > boundary
> > > > > > > > > > condition
> > > > > > > > > > > can be applied ?
> > > > > > > > > > >
> > > > > > > > > > > > then curve is acting properly,
> > but
> > > > total
> > > > > > > > number
> > > > > > > > > > of
> > > > > > > > > > > > particles decreasing with
> > increasing
> > > > time
> > > > > > > > steps.
> > > > > > > > > > >
> > > > > > > > > > > If your discretization scheme is
> > > > > > conservative,
> > > > > > > > > > > this can only happen because more
> > > > particles
> > > > > > > > leave
> > > > > > > > > > > the domain than enter it over the
> > four
> > > > > > > > boundaries
> > > > > > > > > > > (see my response above).
> > > > > > > > > > >
> > > > > > > > > > > > But when I am giving Boundary
> > > > condition
> > > > > > > > > > > > Nr(1,j)=0;Nk(i,nk)=0;
> > > > > > > > > > > > N(i,1)=0;
> > > > > > > > > > > > then from second time steps total
> > > > number
> > > > > > of
> > > > > > > > > > particles
> > > > > > > > > > > > are constant but figure is not
> > moving
> > > > or
> > > > > > not
> > > > > > > > > > working
> > > > > > > > > > > > properly.
> > > > > > > > > > > > In my case particles are within
> > > > potential
> > > > > > > > trap,
> > > > > > > > > > so it
> > > > > > > > > > > > cant go out.
> > > > > > > > > > > > Can you give some idea why it is
> > > > > > happening?
> > > > > > > > > > > >
> > > > > > > > > > > > Thank you.
> > > > > > > > > > > > With regards,
> > > > > > > > > > > > Sunipa Som
> > > > > > > > > > >
> > > > > > > > > > > Best wishes
> > > > > > > > > > > Torsten.
> > > > > > > > > > Hi,
> > > > > > > > > > Nr(1,j)=0;Nk(i,nk)=0; means
> > dN/dr(1,j)=0
> > > > and
> > > > > > > > > > dN/dk(i,nk)=0 which I put as boundary
> > > > > > condition
> > > > > > > > and
> > > > > > > > > > curve is working fine.
> > > > > > > > > > But particles numbers are
> > > > > > > > > > decreasing. In my case particles are
> > > > within
> > > > > > > > potential
> > > > > > > > > > trap, so it can not go out, so how
> > can it
> > > > > > > > decrease?
> > > > > > > > > > and how can i resolve it? Because in
> > my
> > > > case
> > > > > > > > total
> > > > > > > > > > number of particles should be
> > constant.
> > > > > > > > > >
> > > > > > > > > > Thank you.
> > > > > > > > > > With regards,
> > > > > > > > > > Sunipa Som
> > > > > > > > >
> > > > > > > > > What is c1*sqrt(j)*N(i,j) for i=nr ,
> > > > > > > > > -c1*sqrt(j)*N(i,j) for i=1,
> > > > > > > > > -c2*sqrt(j)*(i-1)*dr*N(i,j) for j=1 and
> >
> > > > > > > > > c2*sqrt(j)*(i-1)*dr*N(i,j) for j=nk ?
> > > > > > > > > If the expressions are greater than
> > zero,
> > > > the
> > > > > > > > > number of particles in the volume will
> > > > decrease
> > > > > >
> > > > > > > > > in time.
> > > > > > > > >
> > > > > > > > > Best wishes
> > > > > > > > > Torsten.
> > > > > > > >
> > > > > > > > Hi,
> > > > > > > > In my case particle should be constant.
> > So I
> > > > want
> > > > > > > > ant to make a reflecting wall or
> > reflecting
> > > > > > sphere
> > > > > > > > which will reflect this particles(which
> > > > moving
> > > > > > out)
> > > > > > > > inside. Do you know how can I do it?
> > > > > > > >
> > > > > > > > Thank you.
> > > > > > > >
> > > > > > > > With Regards,
> > > > > > > > S Som
> > > > > > >
> > > > > > > Do you use a finite-difference or finite
> > volume
> > > >
> > > > > > > scheme to discretize your equations ?
> > > > > > >
> > > > > > > Best wishes
> > > > > > > Torsten.
> > > > > >
> > > > > > I am using finite difference.
> > > > > > My PDE
> > > > > > Nr(i,j)=((N(i,j)-N(i-1,j))/dr);
> > > > > > Nk(i,j)=((N(i,j+1)-N(i,j))/dk);
> > > > > >
> > > >
> > Nt(i,j)=-(c1*sqrt(j).*Nr(i,j))+(c2*sqrt(j).*(i-1).*dr.
> > > > > > *Nk(i,j));
> > > > > > Boundary condition
> > > > > > Nr(1,j)=0;Nk(i,nk)=0;
> > > > > >
> > > > > >
> > > > > > With Regards,
> > > > > > S Som
> > > > >
> > > > > And at the other two boundaries you want to
> > > > implement a
> > > > > reflecting boundary condition for N ?
> > > > >
> > > > > Best wishes
> > > > > Torsten.
> > > >
> > > > Yes, if it is possible by putting boundary
> > condition,
> > > > I can do that. But what will be these conditions?
> > So,
> > > > particles can not move out from the boundary
> > rather
> > > > they will reflect back to the rgion.
> > > >
> > > > With Regards,
> > > > Sunipa Som
> > >
> > > You could set the velocities normal to the boundary
> >
> > > to zero: c1 = 0 for i=1 and i=nr ; c2 = 0 for j=1
> > > and j=nr.
> > >
> > > Best wishes
> > > Torsten.
> >
> > Hi,
> > After putting those conditions, the curve is not
> > coming towards zero with increasing time rather it is
> > going towards higher values of r. But curve should
> > come towards zero with increasing time.
> >
> > With regards,
> > Sunipa som
>
> But
> int_2d N(r,k) dr dk
> now remains constant in time ?
>
> Best wishes
> Torsten.

It is still decreasing but not to much.

With Regards
Sunipa Som
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