Anonymous ID: 2ff751 May 28, 2020, 5:58 p.m. No.9353153   🗄️.is 🔗kun

Brownian motion or pedesis (from Ancient Greek: πήδησις /pɛːdɛːsis/ "leaping") is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving molecules in the fluid. … This pattern describes a fluid at thermal equilibrium, defined by a given temperature.

Anonymous ID: 2ff751 May 28, 2020, 6 p.m. No.9353186   🗄️.is 🔗kun

The movement never ceases. c

The movement is very irregular and made up of both translations and rotations.

The apparent mean velocity varies significantly in magnitude and direction. b

The apparent velocity does not tend to a limit as the time taken for an observation decreases. b

The actual velocity cannot be measured. b

The movement is greater when the particles are smaller.

The movement is greater if the viscosity is less.

The movement is greater if the temperature is greater. Viscosity changes partially explain this.

The composition and density of the particles seem to have no effect.

The particles move independently even if they closely approach.

Anonymous ID: 2ff751 May 28, 2020, 6:07 p.m. No.9353286   🗄️.is 🔗kun   >>3298 >>3376

#include <windows.h>

#include <iostream>

#include <string>

 

//-------------—

using namespace std;

 

//-------------—

enum states { SEED, GROWING, MOVING, REST };

enum treeStates { NONE, MOVER, TREE };

const int MAX_SIDE = 480, MAX_MOVERS = 511, MAX_CELLS = 15137;

 

//-------------—

class point

{

public:

point() { x = y = 0; }

point( int a, int b ) { x = a; y = b; }

void set( int a, int b ) { x = a; y = b; }

 

int x, y;

};

//-------------—

class movers

{

public:

point pos;

bool moving;

movers() : moving( false ){}

};

//-------------—

class myBitmap

{

public:

myBitmap() : pen( NULL ) {}

~myBitmap()

{

DeleteObject( pen );

DeleteDC( hdc );

DeleteObject( bmp );

}

 

bool create( int w, int h )

{

BITMAPINFO bi;

ZeroMemory( &bi, sizeof( bi ) );

 

bi.bmiHeader.biSize = sizeof( bi.bmiHeader );

bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8;

bi.bmiHeader.biCompression = BI_RGB;

bi.bmiHeader.biPlanes = 1;

bi.bmiHeader.biWidth = w;

bi.bmiHeader.biHeight = -h;

 

HDC dc = GetDC( GetConsoleWindow() );

bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 );

if( !bmp ) return false;

 

hdc = CreateCompatibleDC( dc );

SelectObject( hdc, bmp );

ReleaseDC( GetConsoleWindow(), dc );

 

width = w; height = h;

 

return true;

}

 

void clear()

{

ZeroMemory( pBits, width * height * sizeof( DWORD ) );

}

 

void setPenColor( DWORD clr )

{

if( pen ) DeleteObject( pen );

pen = CreatePen( PS_SOLID, 1, clr );

SelectObject( hdc, pen );

}

 

void saveBitmap( string path )

{

BITMAPFILEHEADER fileheader;

BITMAPINFO infoheader;

BITMAP bitmap;

DWORD* dwpBits;

DWORD wb;

HANDLE file;

 

GetObject( bmp, sizeof( bitmap ), &bitmap );

 

dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight];

ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) );

ZeroMemory( &infoheader, sizeof( BITMAPINFO ) );

ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) );

 

infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8;

infoheader.bmiHeader.biCompression = BI_RGB;

infoheader.bmiHeader.biPlanes = 1;

infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader );

infoheader.bmiHeader.biHeight = bitmap.bmHeight;

infoheader.bmiHeader.biWidth = bitmap.bmWidth;

infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD );

 

fileheader.bfType = 0x4D42;

fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER );

fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage;

 

GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS );

 

file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL,

CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL );

WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL );

WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL );

WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL );

CloseHandle( file );

 

delete [] dwpBits;

}

 

HDC getDC() { return hdc; }

int getWidth() { return width; }

int getHeight() { return height; }

 

private:

HBITMAP bmp;

HDC hdc;

HPEN pen;

void *pBits;

int width, height;

}

Anonymous ID: 2ff751 May 28, 2020, 6:22 p.m. No.9353538   🗄️.is 🔗kun

>>9353510

Designing attributes of a material’s building blocks in order to assemble them into a target structure is a major goal in materials science. In this thesis, I present three works exploring the role of geometry for self-assembly of anisotropic Brownian particles. The first work represents a systematic study of the assembly behavior of corner-truncated tetrahedra, leading to the discovery of new crystalline phases. This work also hinted to the possibility that face-to-face contacts between neighboring particles – as a consequence of what we then defined directional entropic forces – could lead to a general mechanism explaining entropy-driven assembly of convex hard polyhedra. The study of densest packings of those shapes, also performed in that work, revealed a complex landscape that opened doors for subsequent explorations of the relationship between shape and packing. The second work demonstrates how directional entropic forces can be used to predictively assemble a plethora of hard convex polyhedra into crystalline, quasicrystalline, liquid- and plastic-crystalline structures of unprecedented complexity. This work served not only as a roadmap for many experiments being now performed in the nanoscale but also as a framework from which new assembly strategies could be devised. Finally, the third work shows how the concepts elucidated in those previous works can be used for the assembly of a novel chiral crystalline structure with a priori choice of handedness. It also exemplifies the connection between geometry and isotropic interactions that can be used for assembly of complex crystalline and quasicrystalline structures. As a whole, this thesis explores the use of entropic forces as a tool for controllable assembly of stochastic building blocks and it demonstrates how harnessing geometry can have profound impact for the generation of new materials through target pattern design.

Anonymous ID: 2ff751 May 28, 2020, 6:24 p.m. No.9353559   🗄️.is 🔗kun   >>3624

Nature is replete with shapes. In biological systems, eukaryotic cells often adopt particular shapes, for example, polyhedral erythrocytes in blood clots (1) and dendritic neurons in the brain (2). Before the development of genetic techniques, prokaryotes were classified by shape, as bacteria of different shapes were implicated in different diseases (3). Virus capsids (4, 5) and the folded states of proteins (6) also take on well-recognized, distinct shapes. In nonliving systems, recent advances in synthesis make possible granules, colloids, and nanoparticles in nearly every imaginable shape (7⇓⇓⇓⇓–12). Even particles of nontrivial topology now are possible (13).

 

The systematic study of families of idealized colloidal and nanoscale systems by computer simulation has produced overwhelming evidence that shape is implicated in the self-assembly* of model systems of particles (14⇓⇓–17). In these model systems, the only intrinsic forces between particles are steric, and the entropic effects of shape (which we term “shape entropy”†) can be isolated. Those works show that shape entropy begins to be important when systems are at moderate density (21).

 

In laboratory systems, however, it is not possible to isolate shape entropy effects with as much control, and so the role of shape entropy in experiment is less clear. However, intuition suggests that shape entropy becomes important when packing starts to dominate intrinsic interactions and therefore should be manifest in crowded systems in the laboratory.

 

Unlike other interactions, shape entropy is an emergent‡ quantity that is expected to become important as systems become crowded. Although entropy-driven phase behavior, from the crystallization of hard spheres (22⇓⇓⇓⇓–27) to the nematic transition in hard rods (28) to colloid–polymer depletion interactions (29), has been studied for decades, linking microscopic mechanisms with macroscopic emergent behavior is difficult in principle (30). Hence, even for idealized systems, despite the overwhelming evidence that shape entropy is implicated in phase behavior, understanding how shape entropy is implicated is only now starting to be distilled (14⇓⇓–17, 31⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓⇓–59). For example, the phase behavior of binary hard sphere mixtures (60⇓⇓⇓–64) or polygons (40, 43, 65) can be deduced from global packing arguments, but for many other shapes (17), including “simple” platonic solids such as the tetrahedron (36) and its modifications (15), this is not the case.

 

One suggestion of how shape entropy is implicated in the phase behavior of systems of anisotropic particles is through the idea of directional entropic forces (DEFs). Damasceno et al. (15) inferred the existence of these forces by observing that in many idealized systems of convex polyhedral shapes, one tends to observe a high degree of face-to-face alignment between particles in crystals. However, the origin and strength of these forces are unclear.

 

Here we use computer simulations to address how these forces arise and construct a rigorous theoretical framework that enables this investigation. Our key results are as follows: (i) We quantify pairwise DEFs in arbitrary systems, compute them directly in several example systems, and show they are on the order of a few times the thermal energy (kBT

) just before the onset of crystallization. (ii) We show that the microscopic mechanism underlying the emergence of DEFs is the need for particles to optimize their local packing in order for the system to maximize shape entropy. (iii) By computing quantities for DEFs that can be compared with intrinsic forces between particles, we determine when shape entropy is important in laboratory systems and suggest how to measure DEFs in the laboratory. (iv) We explain two notable features of the hard particle literature: the observed frequent discordance between self-assembled and densest packing structures (15, 17, 39, 41, 44, 53) and the high degree of correlation between particle coordination in dense fluids and crystals (17). (v) As we illustrate in Fig. 1, we show that the same local dense packing mechanism that was known to drive the phase behavior of colloid–depletant systems also drives the behavior of monodisperse hard particle systems, thereby allowing us to view—within a single framework—the entropic ordering considered here and in previous works