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- /*
- * resizing_lattice.cpp
- *
- * Demonstrates the usage of resizing of the state type during integration.
- * Examplary system is a strongly nonlinear, disordered Hamiltonian lattice
- * where the spreading of energy is investigated
- *
- * Copyright 2011-2012 Mario Mulansky
- * Copyright 2012-2013 Karsten Ahnert
- * Distributed under the Boost Software License, Version 1.0. (See
- * accompanying file LICENSE_1_0.txt or copy at
- * http://www.boost.org/LICENSE_1_0.txt)
- *
- */
- #include <iostream>
- #include <utility>
- #include <boost/numeric/odeint.hpp>
- #include <boost/ref.hpp>
- #include <boost/random.hpp>
- using namespace std;
- using namespace boost::numeric::odeint;
- //[ resizing_lattice_system_class
- typedef vector< double > coord_type;
- typedef pair< coord_type , coord_type > state_type;
- struct compacton_lattice
- {
- const int m_max_N;
- const double m_beta;
- int m_pot_start_index;
- vector< double > m_pot;
- compacton_lattice( int max_N , double beta , int pot_start_index )
- : m_max_N( max_N ) , m_beta( beta ) , m_pot_start_index( pot_start_index ) , m_pot( max_N )
- {
- srand( time( NULL ) );
- // fill random potential with iid values from [0,1]
- boost::mt19937 rng;
- boost::uniform_real<> unif( 0.0 , 1.0 );
- boost::variate_generator< boost::mt19937&, boost::uniform_real<> > gen( rng , unif );
- generate( m_pot.begin() , m_pot.end() , gen );
- }
- void operator()( const coord_type &q , coord_type &dpdt )
- {
- // calculate dpdt = -dH/dq of this hamiltonian system
- // dp_i/dt = - V_i * q_i^3 - beta*(q_i - q_{i-1})^3 + beta*(q_{i+1} - q_i)^3
- const int N = q.size();
- double diff = q[0] - q[N-1];
- for( int i=0 ; i<N ; ++i )
- {
- dpdt[i] = - m_pot[m_pot_start_index+i] * q[i]*q[i]*q[i] -
- m_beta * diff*diff*diff;
- diff = q[(i+1) % N] - q[i];
- dpdt[i] += m_beta * diff*diff*diff;
- }
- }
- void energy_distribution( const coord_type &q , const coord_type &p , coord_type &energies )
- {
- // computes the energy per lattice site normalized by total energy
- const size_t N = q.size();
- double en = 0.0;
- for( size_t i=0 ; i<N ; i++ )
- {
- const double diff = q[(i+1) % N] - q[i];
- energies[i] = p[i]*p[i]/2.0
- + m_pot[m_pot_start_index+i]*q[i]*q[i]*q[i]*q[i]/4.0
- + m_beta/4.0 * diff*diff*diff*diff;
- en += energies[i];
- }
- en = 1.0/en;
- for( size_t i=0 ; i<N ; i++ )
- {
- energies[i] *= en;
- }
- }
- double energy( const coord_type &q , const coord_type &p )
- {
- // calculates the total energy of the excitation
- const size_t N = q.size();
- double en = 0.0;
- for( size_t i=0 ; i<N ; i++ )
- {
- const double diff = q[(i+1) % N] - q[i];
- en += p[i]*p[i]/2.0
- + m_pot[m_pot_start_index+i]*q[i]*q[i]*q[i]*q[i] / 4.0
- + m_beta/4.0 * diff*diff*diff*diff;
- }
- return en;
- }
- void change_pot_start( const int delta )
- {
- m_pot_start_index += delta;
- }
- };
- //]
- //[ resizing_lattice_resize_function
- void do_resize( coord_type &q , coord_type &p , coord_type &distr , const int N )
- {
- q.resize( N );
- p.resize( N );
- distr.resize( N );
- }
- //]
- const int max_N = 1024;
- const double beta = 1.0;
- int main()
- {
- //[ resizing_lattice_initialize
- //start with 60 sites
- const int N_start = 60;
- coord_type q( N_start , 0.0 );
- q.reserve( max_N );
- coord_type p( N_start , 0.0 );
- p.reserve( max_N );
- // start with uniform momentum distribution over 20 sites
- fill( p.begin()+20 , p.end()-20 , 1.0/sqrt(20.0) );
- coord_type distr( N_start , 0.0 );
- distr.reserve( max_N );
- // create the system
- compacton_lattice lattice( max_N , beta , (max_N-N_start)/2 );
- //create the stepper, note that we use an always_resizer because state size might change during steps
- typedef symplectic_rkn_sb3a_mclachlan< coord_type , coord_type , double , coord_type , coord_type , double ,
- range_algebra , default_operations , always_resizer > hamiltonian_stepper;
- hamiltonian_stepper stepper;
- hamiltonian_stepper::state_type state = make_pair( q , p );
- //]
- //[ resizing_lattice_steps_loop
- double t = 0.0;
- const double dt = 0.1;
- const int steps = 10000;
- for( int step = 0 ; step < steps ; ++step )
- {
- stepper.do_step( boost::ref(lattice) , state , t , dt );
- lattice.energy_distribution( state.first , state.second , distr );
- if( distr[10] > 1E-150 )
- {
- do_resize( state.first , state.second , distr , state.first.size()+20 );
- rotate( state.first.begin() , state.first.end()-20 , state.first.end() );
- rotate( state.second.begin() , state.second.end()-20 , state.second.end() );
- lattice.change_pot_start( -20 );
- cout << t << ": resized left to " << distr.size() << ", energy = " << lattice.energy( state.first , state.second ) << endl;
- }
- if( distr[distr.size()-10] > 1E-150 )
- {
- do_resize( state.first , state.second , distr , state.first.size()+20 );
- cout << t << ": resized right to " << distr.size() << ", energy = " << lattice.energy( state.first , state.second ) << endl;
- }
- t += dt;
- }
- //]
- cout << "final lattice size: " << distr.size() << ", final energy: " << lattice.energy( state.first , state.second ) << endl;
- }
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