Optimal conditions for first passage of jump processes with resetting
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(2)
Published: Feb. 1, 2025
We
investigate
the
first
passage
time
beyond
a
barrier
located
at
b≥0
of
random
walk
with
independent
and
identically
distributed
jumps,
starting
from
x0=0.
The
is
subject
to
stochastic
resetting,
meaning
that
after
each
step
evolution
restarted
fixed
probability
r.
consider
resetting
protocol
an
intermediate
situation
between
(r=0)
uncorrelated
sequence
jumps
all
origin
(r=1)
derive
general
condition
for
determining
when
restarting
process
0<r<1
more
efficient
than
jump.
If
mean
in
absence
larger
this
sufficient
establish
existence
optimal
0<r∗<1
represents
best
strategy,
outperforming
both
r=0
r=1.
Our
findings
are
discussed
by
considering
two
important
examples
jump
processes
which
we
draw
phase
diagram
illustrating
regions
parameter
space
where
some
optimal.
Language: Английский
Hyperbolic Diffusion Functionals on a Ring with Finite Velocity
Entropy,
Journal Year:
2025,
Volume and Issue:
27(2), P. 105 - 105
Published: Jan. 22, 2025
I
study
a
lattice
with
periodic
boundary
conditions
using
non-local
master
equation
that
evolves
over
time.
investigate
different
system
regimes
classical
theories
like
Fisher
information,
Shannon
entropy,
complexity,
and
the
Cramér–Rao
bound.
To
simulate
spatial
continuity,
employ
large
number
of
sites
in
ring
compare
results
continuous
systems
Telegrapher’s
equations.
The
information
revealed
power-law
decay
t−ν,
ν=2
for
short
times
ν=1
long
times,
across
all
jump
models.
Similar
trends
were
also
observed
complexity
related
to
entropy
Furthermore,
analyze
toy
models
only
two
understand
behavior
entropy.
As
expected,
small
quickly
converges
uniform
distribution
times.
examine
Language: Английский
Generalized time-fractional kinetic-type equations with multiple parameters
Chaos An Interdisciplinary Journal of Nonlinear Science,
Journal Year:
2025,
Volume and Issue:
35(2)
Published: Feb. 1, 2025
In
this
paper,
we
study
a
new
generalization
of
the
kinetic
equation
emerging
in
run-and-tumble
models
[see,
e.g.,
Angelani
et
al.,
J.
Stat.
Phys.
191,
129
(2024)
for
time-fractional
version
equation].
We
show
that
leads
to
wide
class
generalized
fractional
(GFK)
and
telegraph-type
equations
depend
on
two
(or
three)
parameters.
provide
an
explicit
expression
solution
Laplace
domain
that,
particular
choice
parameters,
fundamental
GFK
can
be
interpreted
as
probability
density
function
stochastic
process
obtained
by
suitable
transformation
inverse
subordinator.
Then,
discuss
some
particularly
interesting
cases,
such
telegraph
models,
diffusion
involving
higher
order
time
derivatives,
integral
equations.
Language: Английский
Effects of a moving barrier on the first-passage time of a diffusing particle under stochastic resetting
Communications in Nonlinear Science and Numerical Simulation,
Journal Year:
2025,
Volume and Issue:
unknown, P. 108732 - 108732
Published: March 1, 2025
Language: Английский
First-passage times for generalized heterogeneous telegrapher's processes
Physical review. E,
Journal Year:
2025,
Volume and Issue:
111(4)
Published: April 7, 2025
We
consider
two
different
fractional
generalizations
of
the
heterogeneous
telegrapher's
process
with
and
without
stochastic
resetting.
Both
governing
equations
can
be
obtained
from
corresponding
standard
by
using
subordination
approach.
The
first-passage
time
problems
are
solved
analytically
for
both
models
finding
survival
probabilities,
densities,
mean
times.
showed
that
cases
there
optimal
resetting
rates
which
times
minimal.
present
work
carries
implications
toward
our
understanding
anomalous
diffusion
random
search
in
media.
Published
American
Physical
Society
2025
Language: Английский
A Novel and Effective Scheme for Solving the Fractional Telegraph Problem via the Spectral Element Method
Tao Liu,
No information about this author
Runqi Xue,
No information about this author
Bin Ding
No information about this author
et al.
Fractal and Fractional,
Journal Year:
2024,
Volume and Issue:
8(12), P. 711 - 711
Published: Nov. 29, 2024
The
combination
of
fractional
derivatives
(due
to
their
global
behavior)
and
the
challenges
related
hyperbolic
PDEs
pose
formidable
obstacles
in
solving
equations.
Due
importance
applications
telegraph
equation,
it
presenting
accurate
solutions
via
a
novel
effective
method
can
be
useful.
This
work
introduces
implements
based
on
spectral
element
(SEM)
that
relies
interpolating
scaling
functions
(ISFs).
Through
use
an
orthonormal
projection,
maps
equation
spaces
raised
from
multi-resolution
analysis
(MRA).
To
achieve
this,
Caputo
derivative
(CFD)
is
represented
by
ISFs
as
square
matrix.
Remarkable
efficiency,
ease
implementation,
precision
are
distinguishing
features
presented
method.
An
provided
demonstrate
convergence
scheme,
illustrative
examples
validate
our
Language: Английский