The document discusses modeling physical systems using modern object-oriented Perl, focusing on challenges in simulating dynamics via differential equations. It highlights the limitations of existing solutions and proposes a flexible interface for complex models, particularly in the context of ultrafast electron microscopy. Additionally, it presents a Perl-based solution demonstrating how to manage object states and simulate physical interactions using object-oriented programming paradigms.

1. Modeling Physical Systems
with Modern Object Oriented Perl
YAPC::NA 2012
Joel Berger
University of Illinois at Chicago
June 15, 2012
Joel Berger (UIC) OO Physical Modeling June 15, 2012 1 / 15

2. The Problems
Physical Simulations
Differential Equations
A set of rules that define how variables change with some parameter
dx
x(t2 ) = x(t1 ) + dt ∗
dt
Example: Exponential Growth
dM
= rM =⇒ M (t) = P exp(rt)
dt
Joel Berger (UIC) OO Physical Modeling June 15, 2012 2 / 15

3. The Problems
Physical Simulations
Differential Equations
A set of rules that define how variables change with some parameter
dx
x(t2 ) = x(t1 ) + dt ∗ (x, f (t1, t2))
dt
Example: Exponential Growth
dM
= rM =⇒ M (t) = P exp(rt)
dt
Joel Berger (UIC) OO Physical Modeling June 15, 2012 2 / 15

4. The Problems
Physical Simulations
Differential Equations
A set of rules that define how variables change with some parameter
dx
x(t2 ) = x(t1 ) + dt ∗ (x, f (t1, t2))
dt
Example: Exponential Growth
dM
= rM =⇒ M (t) = P exp(rt)
dt
Joel Berger (UIC) OO Physical Modeling June 15, 2012 2 / 15

5. The Problems
My Research: Ultrafast Electron Microscopy
Joel Berger (UIC) OO Physical Modeling June 15, 2012 3 / 15

6. The Problems
My Research: Ultrafast Electron Microscopy
Photocathode Magnetic Lenses Detector
Joel Berger (UIC) OO Physical Modeling June 15, 2012 3 / 15

7. The Problems
My Research: Ultrafast Electron Microscopy
Laser
Photocathode Magnetic Lenses Detector
Joel Berger (UIC) OO Physical Modeling June 15, 2012 3 / 15

8. The Problems
My Research: Ultrafast Electron Microscopy
Electron Beam
Laser
Photocathode Magnetic Lenses Detector
Joel Berger (UIC) OO Physical Modeling June 15, 2012 3 / 15

9. The Problems
My Research: Ultrafast Electron Microscopy
RF Cavity
Electron Beam
Laser
Photocathode Magnetic Lenses Detector
Joel Berger (UIC) OO Physical Modeling June 15, 2012 3 / 15

10. The Problems
The Challenge: A Flexible Interface to a Complex Model
Magnetic Lens Magnetic Lens
Electron Pulse
v = vˆ
z
w
l RF Cavity
“z lens”
Need: Compute dynamics of electron pulse (w(t), l(t))
Note: Generation and optical elements add terms to DE
Want: Representitive OO user-level interface
Joel Berger (UIC) OO Physical Modeling June 15, 2012 4 / 15

11. The Problems
The Challenge: A Flexible Interface to a Complex Model
Magnetic Lens Magnetic Lens
Electron Pulse
v = vˆ
z
w
l RF Cavity
“z lens”
Need: Compute dynamics of electron pulse (w(t), l(t))
Note: Generation and optical elements add terms to DE
Want: Representitive OO user-level interface
Joel Berger (UIC) OO Physical Modeling June 15, 2012 4 / 15

12. The Problems
The Challenge: A Flexible Interface to a Complex Model
Magnetic Lens Magnetic Lens
Electron Pulse
v = vˆ
z
w
l RF Cavity
“z lens”
Need: Compute dynamics of electron pulse (w(t), l(t))
Note: Generation and optical elements add terms to DE
Want: Representitive OO user-level interface
Joel Berger (UIC) OO Physical Modeling June 15, 2012 4 / 15

13. The Problems
The Challenge: A Flexible Interface to a Complex Model
Magnetic Lens Magnetic Lens
Electron Pulse
v = vˆ
z
w
l RF Cavity
“z lens”
Need: Compute dynamics of electron pulse (w(t), l(t))
Note: Generation and optical elements add terms to DE
Want: Representitive OO user-level interface
Joel Berger (UIC) OO Physical Modeling June 15, 2012 4 / 15

14. The Problems
The “State of the Art”
Old codes are
lacking full 6D dynamics
optimized for performance vs usablilty
hard to customize
near impossible to comprehend
http://laacg.lanl.gov/laacg/services/download_sf.phtml
Getting Started with Poisson Superfish
. . . We do not recommend trying to build an input file “from scratch.”
Instead, find an example file that is similar to the problem you are trying
to solve. Make a copy of the file and then make any necessary
modifications to the geometry and options.
Joel Berger (UIC) OO Physical Modeling June 15, 2012 5 / 15

15. The Problems
The “State of the Art”
Old codes are
lacking full 6D dynamics
optimized for performance vs usablilty
hard to customize
near impossible to comprehend
http://laacg.lanl.gov/laacg/services/download_sf.phtml
Getting Started with Poisson Superfish
. . . We do not recommend trying to build an input file “from scratch.”
Instead, find an example file that is similar to the problem you are trying
to solve. Make a copy of the file and then make any necessary
modifications to the geometry and options.
Joel Berger (UIC) OO Physical Modeling June 15, 2012 5 / 15

16. The Problems
Other Attempts
Modelica:
Pros:
Mathematica:
Open-source, but behind
Pros:
close-source variants
Can solve dynamics
Unique OO language for
Pretty-printing of math for physical simulation
readability
Classes have DEs as properties
Cons:
Cons:
Closed-source and expensive!
Lacks “has-a” relationship
No OO and no key-value
Composing DEs not trivial
datatypes
User-facing object instantiation
Still rather slow ∼2mins/sim
not trivial
Some numerical problems (?)
Joel Berger (UIC) OO Physical Modeling June 15, 2012 6 / 15

17. The Problems
Other Attempts
Modelica:
Pros:
Mathematica:
Open-source, but behind
Pros:
close-source variants
Can solve dynamics
Unique OO language for
Pretty-printing of math for physical simulation
readability
Classes have DEs as properties
Cons:
Cons:
Closed-source and expensive!
Lacks “has-a” relationship
No OO and no key-value
Composing DEs not trivial
datatypes
User-facing object instantiation
Still rather slow ∼2mins/sim
not trivial
Some numerical problems (?)
Joel Berger (UIC) OO Physical Modeling June 15, 2012 6 / 15

18. The Problems
Other Attempts
Modelica:
Pros:
Mathematica:
Open-source, but behind
Pros:
close-source variants
Can solve dynamics
Unique OO language for
Pretty-printing of math for physical simulation
readability
Classes have DEs as properties
Cons:
Cons:
Closed-source and expensive!
Lacks “has-a” relationship
No OO and no key-value
Composing DEs not trivial
datatypes
User-facing object instantiation
Still rather slow ∼2mins/sim
not trivial
Some numerical problems (?)
Joel Berger (UIC) OO Physical Modeling June 15, 2012 6 / 15

19. The Problems
Other Attempts
Modelica:
Pros:
Mathematica:
Open-source, but behind
Pros:
close-source variants
Can solve dynamics
Unique OO language for
Pretty-printing of math for physical simulation
readability
Classes have DEs as properties
Cons:
Cons:
Closed-source and expensive!
Lacks “has-a” relationship
No OO and no key-value
Composing DEs not trivial
datatypes
User-facing object instantiation
Still rather slow ∼2mins/sim
not trivial
Some numerical problems (?)
Joel Berger (UIC) OO Physical Modeling June 15, 2012 6 / 15

20. The Problems
Other Attempts
Modelica:
Pros:
Mathematica:
Open-source, but behind
Pros:
close-source variants
Can solve dynamics
Unique OO language for
Pretty-printing of math for physical simulation
readability
Classes have DEs as properties
Cons:
Cons:
Closed-source and expensive!
Lacks “has-a” relationship
No OO and no key-value
Composing DEs not trivial
datatypes
User-facing object instantiation
Still rather slow ∼2mins/sim
not trivial
Some numerical problems (?)
Joel Berger (UIC) OO Physical Modeling June 15, 2012 6 / 15

21. Perl Solution
. . . But First, Some Bookkeeping
If an object knows where it is, can it remember where it came from?
use MooseX::Declare;
use Method::Signatures::Modifiers;
use MooseX::RememberHistory;
class MyClass { use objects as data storage
has ’x’ => (
traits => [’RememberHistory’],
current data during
isa => ’Num’, is => ’rw’, simulation
default => 0 all data afterwards
);
} works for fixed width solvers
my $obj = MyClass->new;
adaptive solvers call functions
$obj->x( 1 ); repeatedly (i.e. PerlGSL::DiffEq)
$obj->x( 2 );
print join ’, ’, @{ $obj->x_history };
# 0, 1, 2
Joel Berger (UIC) OO Physical Modeling June 15, 2012 7 / 15

22. Perl Solution
. . . But First, Some Bookkeeping
If an object knows where it is, can it remember where it came from?
use MooseX::Declare;
use Method::Signatures::Modifiers;
use MooseX::RememberHistory;
class MyClass { use objects as data storage
has ’x’ => (
traits => [’RememberHistory’],
current data during
isa => ’Num’, is => ’rw’, simulation
default => 0 all data afterwards
);
} works for fixed width solvers
my $obj = MyClass->new;
adaptive solvers call functions
$obj->x( 1 ); repeatedly (i.e. PerlGSL::DiffEq)
$obj->x( 2 );
print join ’, ’, @{ $obj->x_history };
# 0, 1, 2
Joel Berger (UIC) OO Physical Modeling June 15, 2012 7 / 15

23. Perl Solution
. . . But First, Some Bookkeeping
If an object knows where it is, can it remember where it came from?
use MooseX::Declare;
use Method::Signatures::Modifiers;
use MooseX::RememberHistory;
class MyClass { use objects as data storage
has ’x’ => (
traits => [’RememberHistory’],
current data during
isa => ’Num’, is => ’rw’, simulation
default => 0 all data afterwards
);
} works for fixed width solvers
my $obj = MyClass->new;
adaptive solvers call functions
$obj->x( 1 ); repeatedly (i.e. PerlGSL::DiffEq)
$obj->x( 2 );
print join ’, ’, @{ $obj->x_history };
# 0, 1, 2
Joel Berger (UIC) OO Physical Modeling June 15, 2012 7 / 15

24. Perl Solution
. . . But First, Some Bookkeeping
If an object knows where it is, can it remember where it came from?
use MooseX::Declare;
use Method::Signatures::Modifiers;
use MooseX::RememberHistory;
class MyClass { use objects as data storage
has ’x’ => (
traits => [’RememberHistory’],
current data during
isa => ’Num’, is => ’rw’, simulation
default => 0 all data afterwards
);
} works for fixed width solvers
my $obj = MyClass->new;
adaptive solvers call functions
$obj->x( 1 ); repeatedly (i.e. PerlGSL::DiffEq)
$obj->x( 2 );
print join ’, ’, @{ $obj->x_history };
# 0, 1, 2
Joel Berger (UIC) OO Physical Modeling June 15, 2012 7 / 15

25. Perl Solution
. . . But First, Some Bookkeeping
If an object knows where it is, can it remember where it came from?
use MooseX::Declare;
use Method::Signatures::Modifiers;
use MooseX::RememberHistory;
class MyClass { use objects as data storage
has ’x’ => (
traits => [’RememberHistory’],
current data during
isa => ’Num’, is => ’rw’, simulation
default => 0 all data afterwards
);
} works for fixed width solvers
my $obj = MyClass->new;
adaptive solvers call functions
$obj->x( 1 ); repeatedly (i.e. PerlGSL::DiffEq)
$obj->x( 2 );
print join ’, ’, @{ $obj->x_history };
# 0, 1, 2
Joel Berger (UIC) OO Physical Modeling June 15, 2012 7 / 15

26. Perl Solution
. . . But First, Some Bookkeeping
If an object knows where it is, can it remember where it came from?
use MooseX::Declare;
use Method::Signatures::Modifiers;
use MooseX::RememberHistory;
class MyClass { use objects as data storage
has ’x’ => (
traits => [’RememberHistory’],
current data during
isa => ’Num’, is => ’rw’, simulation
default => 0 all data afterwards
);
} works for fixed width solvers
my $obj = MyClass->new;
adaptive solvers call functions
$obj->x( 1 ); repeatedly (i.e. PerlGSL::DiffEq)
$obj->x( 2 );
print join ’, ’, @{ $obj->x_history };
# 0, 1, 2
Joel Berger (UIC) OO Physical Modeling June 15, 2012 7 / 15

27. Perl Solution A Simple OO-DE Example
Physical Classes
use MooseX::RememberHistory;
use MooseX::Declare;
use Method::Signatures::Modifiers;
class MyForce {
has ’strength’ => ( isa => ’Num’, is => ’rw’, default => 0 );
has ’affect’ => ( isa => ’CodeRef’, is => ’ro’, required => 1 );
}
class MyThing {
has ’mass’ => ( isa => ’Num’, is => ’ro’, required => 1 );
has ’x’ => ( traits => [ ’RememberHistory’ ], isa => ’Num’,
is => ’rw’, default => 0 );
has ’vx’ => ( traits => [ ’RememberHistory’ ], isa => ’Num’,
is => ’rw’, default => 0 );
}
Joel Berger (UIC) OO Physical Modeling June 15, 2012 8 / 15

28. Perl Solution A Simple OO-DE Example
The Solver: Attributes
class MySim {
use List::Util ’sum’;
has ’start’ => ( isa => ’Num’, is => ’ro’, default => 0 );
has ’end’ => ( isa => ’Num’, is => ’ro’, default => 1 );
has ’steps’ => ( isa => ’Num’, is => ’ro’, default => 100 );
has ’step’ => ( isa => ’Num’, is => ’ro’, lazy => 1, builder => ’init_step’);
has ’time’ => ( traits => [ ’RememberHistory’ ], isa => ’Num’, is => ’rw’,
lazy => 1, builder => ’init_time’ );
has ’things’ => ( isa => ’ArrayRef[MyThing]’, is => ’rw’, default => sub{[]} );
has ’forces’ => ( isa => ’ArrayRef[MyForce]’, is => ’rw’, default => sub{[]} );
method init_step () {
my $step = ($self->end - $self->start) / $self->steps;
return $step;
}
method init_time () { return $self->start }
Joel Berger (UIC) OO Physical Modeling June 15, 2012 9 / 15

29. Perl Solution A Simple OO-DE Example
The Solver: Methods
method evolve ( MyThing $thing ) {
my $dt = $self->step;
my $vx = $thing->vx;
my $force = sum map { $_->affect->($_, $thing) } @{ $self->forces };
my $acc = $force / ($thing->mass);
$thing->vx( $vx + $acc * $dt );
$thing->x( $thing->x + $vx * $dt );
}
method run () {
while ($self->time < $self->end) {
$self->evolve( $_ ) for @{ $self->things };
$self->time( $self->time + $self->step );
}
}
} # end of class MySim
Joel Berger (UIC) OO Physical Modeling June 15, 2012 10 / 15

30. Perl Solution A Simple OO-DE Example
The Script
#!/usr/bin/env perl my $sim = MySim->new(
use strict; use warnings; end => 5,
use MySim; things => [ $thing ],
use PDL; forces => [ $acc, $dec ],
use PDL::Graphics::Prima::Simple; );
my $thing = MyThing->new( mass => 2 ); $sim->run;
my $acc = MyForce->new( my $time = pdl $sim->time_history;
strength => 2, my $x = pdl $thing->x_history;
affect => sub {shift->strength},
); line_plot($time, $x);
my $dec = MyForce->new(
strength => -30,
affect => sub {
my ($self, $thing) = @_;
return 0 if ($thing->x < 0.1);
return $self->strength;
},
);
Joel Berger (UIC) OO Physical Modeling June 15, 2012 11 / 15

31. Perl Solution A Simple OO-DE Example
The Script
#!/usr/bin/env perl my $sim = MySim->new(
use strict; use warnings; end => 5,
use MySim; things => [ $thing ],
use PDL; forces => [ $acc, $dec ],
use PDL::Graphics::Prima::Simple; );
my $thing = MyThing->new( mass => 2 ); $sim->run;
my $acc = MyForce->new( my $time = pdl $sim->time_history;
strength => 2, my $x = pdl $thing->x_history;
affect => sub {shift->strength},
); line_plot($time, $x);
my $dec = MyForce->new(
strength => -30,
affect => sub {
my ($self, $thing) = @_;
return 0 if ($thing->x < 0.1);
return $self->strength;
},
);
Joel Berger (UIC) OO Physical Modeling June 15, 2012 11 / 15

32. Units Handling
Unit Handling (The Implied Covenant)
Mars Surveyor ’98 Orbiter
Software used force in Newtons
Users entered force in Foot-Pounds
The Covenant:
Between programmer and user
“Use the same units!”
Unexpected and possibly undocumented action at a distance
With Perl and Moose we can do better . . .
Joel Berger (UIC) OO Physical Modeling June 15, 2012 12 / 15

33. Units Handling
Unit Handling (The Implied Covenant)
Mars Surveyor ’98 Orbiter (Sorry Larry!)
Software used force in Newtons
Users entered force in Foot-Pounds
The Covenant:
Between programmer and user
“Use the same units!”
Unexpected and possibly undocumented action at a distance
With Perl and Moose we can do better . . .
Joel Berger (UIC) OO Physical Modeling June 15, 2012 12 / 15

34. Units Handling
Unit Handling (The Implied Covenant)
Mars Surveyor ’98 Orbiter (Sorry Larry!)
Software used force in Newtons
Users entered force in Foot-Pounds
The Covenant:
Between programmer and user
“Use the same units!”
Unexpected and possibly undocumented action at a distance
With Perl and Moose we can do better . . .
Joel Berger (UIC) OO Physical Modeling June 15, 2012 12 / 15

35. Units Handling
Unit Handling (The Implied Covenant)
Mars Surveyor ’98 Orbiter (Sorry Larry!)
Software used force in Newtons
Users entered force in Foot-Pounds
The Covenant:
Between programmer and user
“Use the same units!”
Unexpected and possibly undocumented action at a distance
With Perl and Moose we can do better . . .
Joel Berger (UIC) OO Physical Modeling June 15, 2012 12 / 15

36. Units Handling
Unit Handling (The Implied Covenant)
Mars Surveyor ’98 Orbiter (Sorry Larry!)
Software used force in Newtons
Users entered force in Foot-Pounds
The Covenant:
Between programmer and user
“Use the same units!”
Unexpected and possibly undocumented action at a distance
With Perl and Moose we can do better . . .
Joel Berger (UIC) OO Physical Modeling June 15, 2012 12 / 15

37. Units Handling
Unit Handling (The Implied Covenant)
Mars Surveyor ’98 Orbiter (Sorry Larry!)
Software used force in Newtons
Users entered force in Foot-Pounds
The Covenant:
Between programmer and user
“Use the same units!”
Unexpected and possibly undocumented action at a distance
With Perl and Moose we can do better . . .
Joel Berger (UIC) OO Physical Modeling June 15, 2012 12 / 15

38. Units Handling
MooseX::Types::NumUnit
Str to Num coercions
convert unit if needed
use MooseX::Declare;
use Method::Signatures::Modifiers;
class SphericalCow {
use MooseX::Types::NumUnit qw/num_of_unit/;
has ’radius’ => ( isa => num_of_unit(’m’), is => ’rw’, default => 1 );
has ’velocity’ => ( isa => num_of_unit(’m/s’), is => ’rw’, default => 0 );
}
use strict; use warnings;
my $cow = SphericalCow->new(
radius => ’1 ft’,
);
print $cow->radius . "n"; # 0.3048
Joel Berger (UIC) OO Physical Modeling June 15, 2012 13 / 15

39. Real World Example
Example of Physics::UEMColumn
Back to Electron Column Modeling
Magnetic Lens Magnetic Lens
Electron Pulse
v = vˆ
z
w
l RF Cavity
“z lens”
As yet unreleased Physics::UEMColumn
https://github.com/jberger/Physics-UEMColumn
Uses: PerlGSL::DiffEq on CPAN
C-level solver of Perl-level DE closures
Joel Berger (UIC) OO Physical Modeling June 15, 2012 14 / 15

40. Finally
Acknowledgements
Graduate College Dean’s Fellowship (Major Student Funding)
LAS Ph.D. Travel Award (Conference Funding)
Department of Energy #DE-FG52-09NA29451
(UEM Research Grant)
https://github.com/jberger/YAPCNA2012
Joel Berger (UIC) OO Physical Modeling June 15, 2012 15 / 15