5,046 research outputs found
Deposition of model chains on surfaces: anomalous relation between flux and stability
Model chains are studied via Monte Carlo simulations which are deposited with
a fixed flux on a substrate. They may represent, e.g., stiff lipophilic chains
with an head group and tail groups mimicking the alkyl chain. After some
subsequent fixed simulation time we determine the final energy as a function of
flux and temperature. Surprisingly, in some range of temperature and flux the
final energy increases with decreasing flux. The physical origin of this
counterintuitive observation is elucidated. In contrast, when performing
equivalent cooling experiments no such anomaly is observed. Furthermore, it is
elaborated whether flux experiments give rise to configurations with lower
energies as compared to cooling experiments. These results are related to
recent experiments by the Ediger group where very stable configurations of
glass-forming systems have been generated via flux experiments
Relating local structures, energies, and occurrence probabilities in a two-dimensional silica network
Recently, it became possible to experimentally generate and characterize a
very thin silica system on a substrate which can be basically described as a 2D
random network. The key structural properties, in particular related to the
ring statistics, could be numerically reproduced by performing molecular
dynamics simulations with an appropriately chosen 2D force field. Using a
maximum entropy formulation it is shown that the probability distribution of
the individual rings and triplets can be related to the ring and triplet
energies, respectively, obtained from the simulations. Using additional
Lagrange parameters, the correct average properties of random networks are
guaranteed. In agreement with previous work, based on distributions of
complementary rings and triplets, respectively, one finds a Boltzmann-type
relation albeit with an effective temperature which largely deviates from the
bath temperature. Furthermore, it is shown that the ring and triplet energies
can be estimated based on the properties of their average inner angles. This
calculation supports, on a quantitative level, the previously suggested angle
mismatch theory. It suggests that correlations among adjacent rings originate
from the net mismatch in the inner ring angles in a triplet of rings. By taking
into account an average effect from the surrounding rings of a triplet, an even
better estimate of the correlations can be provided. That approach is also
applied to estimate of the Aboav-Wearie parameter.Comment: 22 pages, 13 figure
Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
We present a framework for studying bosonic non-Gaussian channels of
continuous-variable systems. Our emphasis is on a class of channels that we
call photon-added Gaussian channels, which are experimentally viable with
current quantum-optical technologies. A strong motivation for considering these
channels is the fact that it is compulsory to go beyond the Gaussian domain for
numerous tasks in continuous-variable quantum information processing such as
entanglement distillation from Gaussian states and universal quantum
computation. The single-mode photon-added channels we consider are obtained by
using two-mode beam splitters and squeezing operators with photon addition
applied to the ancilla ports giving rise to families of non-Gaussian channels.
For each such channel, we derive its operator-sum representation, indispensable
in the present context. We observe that these channels are Fock preserving
(coherence nongenerating). We then report two examples of activation using our
scheme of photon addition, that of quantum-optical nonclassicality at outputs
of channels that would otherwise output only classical states and of both the
quantum and private communication capacities, hinting at far-reaching
applications for quantum-optical communication. Further, we see that noisy
Gaussian channels can be expressed as a convex mixture of these non-Gaussian
channels. We also present other physical and information-theoretic properties
of these channels.Comment: Published as Editor's Suggestion, v4: 19 pages, 17 figures, close to
published version, minor changes throughou
Ring statistics in 2D-silica: effective temperatures in equilibrium
The thermodynamic properties of subsystems in strong interaction with the
neighborhood can largely differ from the standard behavior. Here we study the
thermodynamic properties of rings and triplets in equilibrated disordered
2D-silica. Their statistics follows a Boltzmann behavior, albeit with a
strongly reduced temperature. This effective temperature strongly depends on
the length scale of the chosen subsystem. From a systematic analysis of the 1D
Ising model and an analytically solvable model we suggest that these
observations reflect the presence of strong local positive energy correlations.Comment: 10 pages, 3 figures, lette
OPE Methods for the Holomorphic Higgs Portal
We develop a systematic and general approach to study the effective Higgs
Lagrangian in a supersymmetric framework in which the Higgs fields in the
visible sector couple weakly to another sector. The extra sector may be
strongly coupled in general. It is assumed to be superconformal in the
ultraviolet, but develop a mass-gap with supersymmetry breaking in the
infrared. The main technique used in our approach is that of the operator
product expansion (OPE). By using OPE methods we are able to compute the
parameters in the Higgs Lagrangian to quadratic order and make general
statements that are applicable to many classes of models. Not only does this
approach allow us to understand the traditional problems plaguing simple models
from a different perspective, it also reveals new possibilities for solutions
of these problems. The methods and results of our work should be useful in
constructing a viable and natural model of physics beyond the Standard Model.Comment: 34 pages. v3: Fixed a typo in eq. (3.33) and a mistake in eq. (3.34
Critical Graphs for Minimum Vertex Cover
In the context of the chromatic-number problem, a critical graph is an
instance where the deletion of any element would decrease the graph's chromatic
number. Such instances have shown to be interesting objects of study for deepen
the understanding of the optimization problem.
This work introduces critical graphs in context of Minimum Vertex Cover. We
demonstrate their potential for the generation of larger graphs with hidden a
priori known solutions. Firstly, we propose a parametrized graph-generation
process which preserves the knowledge of the minimum cover. Secondly, we
conduct a systematic search for small critical graphs. Thirdly, we illustrate
the applicability for benchmarking purposes by reporting on a series of
experiments using the state-of-the-art heuristic solver NuMVC
Combining Method of Alternating Projections and Augmented Lagrangian for Task Constrained Trajectory Optimization
Motion planning for manipulators under task space constraints is difficult as
it constrains the joint configurations to always lie on an implicitly defined
manifold. It is possible to view task constrained motion planning as an
optimization problem with non-linear equality constraints which can be solved
by general non-linear optimization techniques. In this paper, we present a
novel custom optimizer which exploits the underlying structure present in many
task constraints.
At the core of our approach are some simple reformulations, which when
coupled with the \emph{method of alternating projection}, leads to an efficient
convex optimization based routine for computing a feasible solution to the task
constraints. We subsequently build on this result and use the concept of
Augmented Lagrangian to guide the feasible solutions towards those which also
minimize the user defined cost function. We show that the proposed optimizer is
fully distributive and thus, can be easily parallelized. We validate our
formulation on some common robotic benchmark problems. In particular, we show
that the proposed optimizer achieves cyclic motion in the joint space
corresponding to a similar nature trajectory in the task space. Furthermore, as
a baseline, we compare the proposed optimizer with an off-the-shelf non-linear
solver provide in open source package SciPy. We show that for similar task
constraint residuals and smoothness cost, it can be upto more than three times
faster than the SciPy alternative.Comment: 8 page
Inducing Multi-Convexity in Path Constrained Trajectory Optimization for Mobile Manipulators
In this paper, we propose a novel trajectory optimization algorithm for
mobile manipulators under end-effector path, collision avoidance and various
kinematic constraints. Our key contribution lies in showing how this highly
non-linear and non-convex problem can be solved as a sequence of convex
unconstrained quadratic programs (QPs). This is achieved by reformulating the
non-linear constraints that arise out of manipulator kinematics and its
coupling with the mobile base in a multi-affine form. We then use techniques
from Alternating Direction Method of Multipliers (ADMM) to formulate and solve
the trajectory optimization problem. The proposed ADMM has two similar
non-convex steps. Importantly, a convex surrogate can be derived for each of
them. We show how large parts of our optimization can be solved in parallel
providing the possibility of exploiting multi-core CPUs/GPUs. We validate our
trajectory optimization on different benchmark examples. Specifically, we
highlight how it solves the cyclicity bottleneck and provides a holistic
approach where diverse set of trajectories can be obtained by trading-off
different aspects of manipulator and mobile base motion.Comment: 8 pages, under review at Conference on Decision and Control (CDC
2019
Relativistic superfluid hydrodynamics from field theory
It is well known that the hydrodynamics of a zero-temperature superfluid can
be formulated in field-theoretic terms, relating for example the superfluid
four-velocity to the gradient of the phase of a Bose-condensed scalar field. At
nonzero temperatures, where the phenomenology of a superfluid is usually
described within a two-fluid picture, this relationship is less obvious. For
the case of a uniform, dissipationless superfluid at small temperatures and
weak coupling we discuss this relationship within a phi^4 model. For instance,
we compute the entrainment coefficient, which describes the interaction between
the superfluid and the normal-fluid components, and the velocities of first and
second sound in the presence of a superflow. Our study is very general, but can
also be seen as a step towards understanding the superfluid properties of
various phases of dense nuclear and quark matter in the interior of compact
stars.Comment: 8 pages, 1 figure, contribution to the proceedings of "Xth Quark
Confinement and the Hadron Spectrum", October 8-12, 2012, Munich, German
Role reversal in first and second sound in a relativistic superfluid
Relativistic superfluidity at arbitrary temperature, chemical potential and
(uniform) superflow is discussed within a self-consistent field-theoretical
approach. Our starting point is a complex scalar field with a
interaction, for which we calculate the 2-particle-irreducible effective action
in the Hartree approximation. With this underlying microscopic theory, we can
obtain the two-fluid picture of a superfluid, and compute properties such as
the superfluid density and the entrainment coefficient for all temperatures
below the critical temperature for superfluidity. We compute the critical
velocity, taking into account the full self-consistent effect of the
temperature and superflow on the quasiparticle dispersion. We also discuss
first and second sound modes and how first (second) sound evolves from a
density (temperature) wave at low temperatures to a temperature (density) wave
at high temperatures. This role reversal is investigated for ultra-relativistic
and near-non-relativistic systems for zero and nonzero superflow. For nonzero
superflow, we also observe a role reversal as a function of the direction of
the sound wave.Comment: 32 pages, 9 figures, v2: expanded discussion of renormalization,
conclusions unchanged, version to appear in Phys. Rev.
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