File:DoubleWellSolitonAntisoliton.gif
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DoubleWellSolitonAntisoliton.gif (705 × 177 pixels, file size: 3.21 MB, MIME type: image/gif, looped, 800 frames, 48 s)
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[edit]DescriptionDoubleWellSolitonAntisoliton.gif |
English: Solution to in 1+1 dimensionsional spacetime.
v = 0.05, |
Source | Own work by uploader (source code below, click "show" to see) |
Author | Cyp |
C++ source code - click on "show" on the right to view |
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C++ source code - click on "show" on the right to view |
<nowiki>
#include <cstdio>
#include <stdint.h>
#include <vector>
#include <string>
#include <stdexcept>
#include <cmath>
#include <cassert>
struct Pixel
{
Pixel() { col[0] = 1; col[1] = 1; col[2] = 1; }
Pixel(double r, double g, double b)
{
col[0] = r;
col[1] = g;
col[2] = b;
}
Pixel const &operator +=(Pixel const &p)
{
col[0] += p.col[0];
col[1] += p.col[1];
col[2] += p.col[2];
return *this;
}
Pixel operator -() const
{
return Pixel(-col[0], -col[1], -col[2]);
}
Pixel operator *(float v) const
{
return Pixel(col[0]*v, col[1]*v, col[2]*v);
}
float col[3];
};
inline int quant(int v)
{
//return (v>>4)*0x11;
return v;
}
struct BytePixel
{
BytePixel() { col[0] = 0xFF; col[1] = 0xFF; col[2] = 0xFF; }
BytePixel(Pixel const &p)
{
col[0] = quant(std::max(0, std::min<int>(255, 256*p.col[0])));
col[1] = quant(std::max(0, std::min<int>(255, 256*p.col[1])));
col[2] = quant(std::max(0, std::min<int>(255, 256*p.col[2])));
}
uint8_t col[3];
};
class Image
{
public:
Image(unsigned x, unsigned y, double x1_, double y1_, double x2_, double y2_)
: sx(x), sy(y), x1(x1_), y1(y1_), x2(x2_), y2(y2_), facx(sx/(x2-x1)), facy(sy/(y2-y1)), pixx((x2-x1)/sx), pixy((y2-y1)/sy)
{
data.resize(x*y);
//#pragma omp parallel for
}
void save(std::string const &name)
{
std::vector<BytePixel> byteData(data.begin(), data.end());
std::string filename = name+".ppm";
FILE *f = fopen(filename.c_str(), "wb");
if(f == NULL)
throw std::runtime_error("Couldn't open file \""+filename+"\" for writing.");
std::fprintf(f, "P6\n%u %u\n255\n", sx, sy);
std::fwrite(&byteData[0], 3*sx*sy, 1, f);
std::fclose(f);
}
void addRect(double xa, double ya, double xb, double yb, Pixel const &p)
{
if(xa > x2 || xb < x1 || ya > y2 || yb < y1)
return;
double txa = std::max<double>(0, (xa-x1)*facx);
double tya = std::max<double>(0, (ya-y1)*facy);
double txb = std::min<double>(sx, (xb-x1)*facx);
double tyb = std::min<double>(sy, (yb-y1)*facy);
unsigned uxa = txa;
unsigned uya = tya;
unsigned uxb = std::min<unsigned>(sx-1, txb);
unsigned uyb = std::min<unsigned>(sy-1, tyb);
double xstart = txa-uxa; // Left edge missing in pixels.
double ystart = tya-uya; // Top edge missing in pixels.
double xend = uxb+1-txb; // Right edge missing in pixels.
double yend = uyb+1-tyb; // Bottom edge missing in pixels.
if(uxb < uxa || uyb < uya)
return; // Degenerate rectangle.
for(unsigned y = uya; y != uyb+1; ++y)
{
double yamount = 1;
if(y == uya)
yamount -= ystart;
if(y == uyb)
yamount -= yend;
for(unsigned x = uxa; x != uxb+1; ++x)
{
double xamount = 1;
if(x == uxa)
xamount -= xstart;
if(x == uxb)
xamount -= xend;
data[x + y*sx] += p * (xamount*yamount);
}
}
}
double getDx() const { return pixx; }
double getDy() const { return pixy; }
private:
unsigned sx, sy;
double x1, y1, x2, y2;
double facx, facy;
double pixx, pixy;
std::vector<Pixel> data;
};
void render(Image &img, std::vector<double> const &func, double xa, double xb, Pixel const &p)
{
double dx = (xb-xa)/(func.size()-1);
double lx = img.getDx()*.75; // 1/2 brush width.
double ly = img.getDy()*.75; // 1/2 brush height.
double invRectPix = 1./(1.5*1.5); // Reciprocal area of brush in pixels.
double px = 1/img.getDx();
double py = 1/img.getDy();
double pdx = dx*px; // dx in pixels.
double x = xa+dx*.5;
//printf("test %zu %lf %lf\n", func.size(), lx, ly);
for(unsigned i = 0; i != func.size()-1; ++i)
{
double dy = func[i+1]-func[i];
double pdy = dy*py; // dy in pixels.
double y = (func[i]+func[i+1])*-.5;
img.addRect(x-lx, y-ly, x+lx, y+ly, p*(invRectPix*sqrt(pdx*pdx + pdy*pdy)));
//if(i == func.size()/2)
// printf("%lf %lf %lf %lf %lf\n", x-lx, y-ly, x+lx, y+ly, (invRectPix*sqrt(pdx*pdx + pdy*pdy)));
x += dx;
}
}
void setTanh(std::vector<double> &func, std::vector<double> &dfuncdt, double xa, double xb)
{
double dx = (xb-xa)/(func.size()-1);
double x = xa;
for(unsigned i = 0; i != func.size(); ++i)
{
func[i] = tanh(x);
x += dx;
}
dfuncdt.assign(func.size(), 0);
}
void setDiTanh(std::vector<double> &func, std::vector<double> &dfuncdt, double xa, double xb)
{
double dx = (xb-xa)/(func.size()-1);
double x = xa;
for(unsigned i = 0; i != func.size(); ++i)
{
func[i] = tanh(x+4) - tanh(x-4) - 1;
x += dx;
}
dfuncdt.assign(func.size(), 0);
}
void setDiTanhBump(std::vector<double> &func, std::vector<double> &dfuncdt, double xa, double xb)
{
dfuncdt.assign(func.size(), 0);
double dx = (xb-xa)/(func.size()-1);
double x = xa;
for(unsigned i = 0; i != func.size(); ++i)
{
double v1 = 0.05; // Velocity of leftmost bump. (Exact velocity = sinh(v1).)
double v2 = -0.05; // Velocity of rightmost bump.
double tanh1 = tanh((x+6)*cosh(v1));
double tanh2 = tanh((x-6)*cosh(v2));
func[i] = tanh1 - tanh2 - 1;// + 0.2*exp(-((x+1)*(x+1)));
dfuncdt[i] = (1-tanh1*tanh1)*-sinh(v1) + (1-tanh2*tanh2)*sinh(v2);
x += dx;
}
}
// \mathcal{L} = \partial_\mu\phi\partial^\mu\phi - (\phi^2 - 1)^2
// d²f/dt² = d²f/dx² - 2f(f²-1)²
void stepTime(std::vector<double> &func, std::vector<double> &dfuncdt, double xa, double xb, double dt)
{
assert(func.size() == dfuncdt.size());
double dx = (xb-xa)/(func.size()-1);
double dtinvdx2 = dt/(dx*dx);
dfuncdt[0] = (func[1] - func[0]) / dt;
for(unsigned i = 1; i != func.size()-1; ++i)
dfuncdt[i] += dtinvdx2*(func[i+1] + func[i-1] - 2*func[i]) - 2*dt*func[i]*(func[i]*func[i] - 1);
dfuncdt[func.size()-1] = -(func[func.size()-1] - func[func.size()-2]) / dx;
for(unsigned i = 0; i != func.size(); ++i)
func[i] += dt*dfuncdt[i];
}
int main()
{
double fxa = -208; // Function min x.
double fxb = 208; // Function max x.
unsigned fxr = 20000; // Function resolution.
double imxa = -8; // Display min x.
double imxb = 8; // Display max x.
double imya = -2; // Display min f(x).
double imyb = 2; // Display max f(x).
Image img(801, 201, imxa, imya, imxb, imyb);
img.addRect(-1000, 0-img.getDx(), 1000, 0+img.getDx(), -Pixel(1, 1, 1));
img.addRect(-1000, 1-img.getDx(), 1000, 1+img.getDx(), -Pixel(.5, 1, 1)*.5);
img.addRect(-1000, -1-img.getDx(), 1000, -1+img.getDx(), -Pixel(.5, 1, 1)*.5);
std::vector<double> func(fxr);
std::vector<double> dfuncdt(fxr);
setTanh(func, dfuncdt, fxa, fxb);
render(img, func, fxa, fxb, -Pixel(1, 1, .75));
img.save("soliton");
setDiTanhBump(func, dfuncdt, fxa, fxb);
for(unsigned frame = 0; frame != 800; ++frame)
{
Image imgf(801, 201, imxa, imya, imxb, imyb);
imgf.addRect(-1000, 0-img.getDx(), 1000, 0+img.getDx(), -Pixel(1, 1, 1));
imgf.addRect(-1000, 1-img.getDx(), 1000, 1+img.getDx(), -Pixel(.5, 1, 1)*.5);
imgf.addRect(-1000, -1-img.getDx(), 1000, -1+img.getDx(), -Pixel(.5, 1, 1)*.5);
render(imgf, func, fxa, fxb, -Pixel(1, 1, .75));
for(unsigned i = 0; i != 1000; ++i)
stepTime(func, dfuncdt, fxa, fxb, 1./2000);
//render(imgf, func, -8, 8, -Pixel(1, .75, 1));
//render(imgf, dfuncdt, -8, 8, -Pixel(.75, 1, .75)*.25);
char str[100];
std::sprintf(str, "disoliton%03u", frame);
imgf.save(str);
}
}
</nowiki>
|
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 10:05, 30 March 2020 | 705 × 177 (3.21 MB) | Bürgerentscheid (talk | contribs) | resized to fit 100 MP limit | |
21:44, 29 September 2008 | 801 × 201 (2.54 MB) | Cyp (talk | contribs) | {{Information |Description={{en|1=Solution to <math>\mathcal{L} = \partial_\mu\phi\partial^\mu\phi - (\phi^2 - 1)^2</math> in 1+1 dimensionsional spacetime. v = 0.05,<br /> <math>\phi_0(x, t) = \tanh x</math>,<br /> <math>\phi_\pm(x, t) = \phi_0(x\cosh v |
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