115 research outputs found
Comparison of pure and combined search strategies for single and multiple targets
We address the generic problem of random search for a point-like target on a
line. Using the measures of search reliability and efficiency to quantify the
random search quality, we compare Brownian search with L\'evy search based on
long-tailed jump length distributions. We then compare these results with a
search process combined of two different long-tailed jump length distributions.
Moreover, we study the case of multiple targets located by a L\'evy searcher.Comment: 16 pages, 12 figure
Gradient dynamics in reinforcement learning
Despite the success achieved by the analysis of supervised learning
algorithms in the framework of statistical mechanics, reinforcement learning
has remained largely untouched. Here we move towards closing the gap by
analyzing the dynamics of the policy gradient algorithm. For a convex problem,
we show that it obeys a drift-diffusion motion with coeffcients tuned by
learning rate. Furthermore, we propose a mapping between a non-convex
reinforcement learning problem and a disordered system. This mapping enables us
to show how the learning rate acts as an effective temperature and thus is
capable of smoothing rough landscapes, corroborating what is displayed by the
drift-diffusive description and paving the way for physics-inspired algorithmic
optimization based on annealing procedures in disordered systems.Comment: 15 pages, 6 figures. Submitted to Physical Review
Conformations and dynamics of active star polymers
We study conformations and dynamics of active star polymers. The analysis
shows that active star polymers stretching behaviour is quite different from
that of active linear chains. The visual inspection of conformations and
bond-bond correlations reveal a better coordination for the alignment and
coordination of bonds for the star polymers than for the linear counterparts.
The architecture substantially affects the chain extension transition at high
values of active force. The scaling laws for the shape factor and the arm
asphericity ratio established for the passive star polymers coincide with the
passive case for active force values below the transition. For the values above
the transition range the scaling of these quantities switches to different
values.Comment: 14 pages, 17 figure
Interpretation of the vibrational spectra of glassy polymers using coarse-grained simulations
The structure and vibrational density of states (VDOS) of polymer glasses are
investigated using numerical simulations based on the classical Kremer-Grest
bead-spring model. We focus on the roles of chain length and bending stiffness,
the latter being set by imposing three-body angular potentials along chain
backbones. Upon increasing the chain length and bending stiffness, structural
reorganisation leads to volumetric expansion of the material and build-up of
internal stresses. The VDOS has two dominant bands: a low frequency one
corresponding to inter- and intra-chain non-bonding interactions and a high
frequency one corresponding principally to vibrations of bonded beads that
constitute skeletal chain backbones. Upon increasing the steepness of the
angular potential, vibrational modes associated with chain bending gradually
move from the low-frequency to the high-frequency band. This redistribution of
modes is reflected in a reduction of the so-called Boson peak upon increasing
chain stiffness. Remarkably, the finer structure and the peaks of the
high-frequency band, and their variations with stiffness, can, for short
chains, be explained using an analytical solution derived for a model triatomic
molecule. For longer chains, the qualitative evolution of the VDOS with chain
stiffness is similar, although the distinct peaks observed for short chains
become increasingly smoothed-out. Our findings can be used to guide a
systematic approach to interpretation of Brillouin and Raman scattering spectra
of glassy polymers in future work, with applications in polymer processing
diagnostics.Comment: To appear in Macromolecule
Negative diffusion of excitons in quasi-two-dimensional systems
We show how two different mobile-immobile type models explain the observation
of negative diffusion of excitons reported in experimental studies in
quasi-two-dimensional semiconductor systems. The main reason for the effect is
the initial trapping and a delayed release of free excitons in the area close
to the original excitation spot. The density of trapped excitons is not
registered experimentally. Hence, the signal from the free excitons alone
includes the delayed release of not diffusing trapped particles. This is seen
as the narrowing of the exciton density profile or decrease of mean-squared
displacement which is then interpreted as a negative diffusion. The effect is
enhanced with the increase of recombination intensity as well as the rate of
the exciton-exciton binary interactions.Comment: 14 pages, 8 figure
Parameter-free predictions of the viscoelastic response of glassy polymers from non-affine lattice dynamics
We study the viscoelastic response of amorphous polymers using theory and
simulations. By accounting for internal stresses and considering instantaneous
normal modes (INMs) within athermal non-affine theory, we make parameter-free
predictions of the dynamic viscoelastic moduli obtained in coarse-grained
simulations of polymer glasses at non-zero temperatures. The theoretical
results show very good correspondence with rheology data collected from
molecular dynamics simulations over five orders of magnitude in frequency, with
some instabilities that accumulate in the low-frequency part on approach to the
glass transition. These results provide evidence that the mechanical glass
transition itself is continuous and thus represents a crossover rather than a
true phase transition. The relatively sharp drop of the low-frequency storage
modulus across the glass transition temperature can be explained
mechanistically within the proposed theory: the proliferation of
low-eigenfrequency vibrational excitations (boson peak and nearly-zero energy
excitations) is directly responsible for the rapid growth of a negative
non-affine contribution to the storage modulus.Comment: 10 pages, 7 figure
Scaling up the lattice dynamics of amorphous materials by orders of magnitude
We generalise the non-affine theory of viscoelasticity for use with large,
well-sampled systems of arbitrary chemical complexity. Having in mind
predictions of mechanical and vibrational properties of amorphous systems with
atomistic resolution, we propose an extension of the Kernel Polynomial Method
(KPM) for the computation of the vibrational density of states (VDOS) and the
eigenmodes, including the -correlator of the affine force-field, which
is a key ingredient of lattice-dynamic calculations of viscoelasticity. We show
that the results converge well to the solution obtained by direct
diagonalization (DD) of the Hessian (dynamical) matrix. As is well known, the
DD approach has prohibitively high computational requirements for systems with
atoms or larger. Instead, the KPM approach developed here allows one
to scale up lattice dynamic calculations of real materials up to atoms,
with a hugely more favorable (linear) scaling of computation time and memory
consumption with
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