918 research outputs found
Dynamical Monte Carlo Study of Equilibrium Polymers (II): The Role of Rings
We investigate by means of a number of different dynamical Monte Carlo
simulation methods the self-assembly of equilibrium polymers in dilute,
semidilute and concentrated solutions under good-solvent conditions. In our
simulations, both linear chains and closed loops compete for the monomers,
expanding on earlier work in which loop formation was disallowed. Our findings
show that the conformational properties of the linear chains, as well as the
shape of their size distribution function, are not altered by the formation of
rings. Rings only seem to deplete material from the solution available to the
linear chains. In agreement with scaling theory, the rings obey an algebraic
size distribution, whereas the linear chains conform to a Schultz--Zimm type of
distribution in dilute solution, and to an exponentional distribution in
semidilute and concentrated solution. A diagram presenting different states of
aggregation, including monomer-, ring- and chain-dominated regimes, is given
Self-organisation of tip functionalised elongated colloidal particles
Weakly attractive interactions between the tips of rod-like colloidal
particles affect their liquid-crystal phase behaviour due to a subtle interplay
between enthalpy and entropy. Here, we employ molecular dynamics simulations on
semi-flexible, repulsive bead-spring chains of which one of the two end beads
attract each other. We calculate the phase diagram as a function of both the
volume fraction of the chains and the strength of the attractive potential. We
identify a large number of phases that include isotropic, nematic, smectic A,
smectic B and crystalline states. For tip attraction energies lower than the
thermal energy, our results are qualitatively consistent with experimental
findings: we find that an increase of the attraction strength shifts the
nematic to smectic A phase transition to lower volume fractions, with only
minor effect on the stability of the other phases. For sufficiently strong tip
attraction, the nematic phase disappears completely, in addition leading to the
destabilisation of the isotropic phase. In order to better understand the
underlying physics of these phenomena, we also investigate the clustering of
the particles at their attractive tips and the effective molecular field
experienced by the particles in the smectic A phase. Based on these results, we
argue that the clustering of the tips only affects the phase stability if
lamellar structures (``micelles'') are formed. We find that an increase of the
attraction strength increases the degree of order in the layered
phases.Interestingly, we also find evidence for the existence of an
anti-ferroelectric smectic A phase transition induced by the interaction
between the tips. A simple Maier-Saupe-McMillan model confirms our findings
A Class of Convex Quadratic Nonseparable Resource Allocation Problems with Generalized Bound Constraints
We study a convex quadratic nonseparable resource allocation problem that arises in the area of decentralized energy management (DEM), where unbalance in electricity networks has to be minimized. In this problem, the given resource is allocated over a set of activities that is divided into subsets, and a cost is assigned to the overall allocated amount of resources to activities within the same subset. We derive two efficient algorithms with worst-case time complexity to solve this problem. For the special case where all subsets have the same size, one of these algorithms even runs in linear time given the subset size. Both algorithms are inspired by well-studied breakpoint search methods for separable convex resource allocation problems. Numerical evaluations on both real and synthetic data confirm the theoretical efficiency of both algorithms and demonstrate their suitability for integration in DEM systems
On a reduction for a class of resource allocation problems
In the resource allocation problem (RAP), the goal is to divide a given
amount of resource over a set of activities while minimizing the cost of this
allocation and possibly satisfying constraints on allocations to subsets of the
activities. Most solution approaches for the RAP and its extensions allow each
activity to have its own cost function. However, in many applications, often
the structure of the objective function is the same for each activity and the
difference between the cost functions lies in different parameter choices such
as, e.g., the multiplicative factors. In this article, we introduce a new class
of objective functions that captures the majority of the objectives occurring
in studied applications. These objectives are characterized by a shared
structure of the cost function depending on two input parameters. We show that,
given the two input parameters, there exists a solution to the RAP that is
optimal for any choice of the shared structure. As a consequence, this problem
reduces to the quadratic RAP, making available the vast amount of solution
approaches and algorithms for the latter problem. We show the impact of our
reduction result on several applications and, in particular, we improve the
best known worst-case complexity bound of two important problems in vessel
routing and processor scheduling from to
A fast algorithm for quadratic resource allocation problems with nested constraints
We study the quadratic resource allocation problem and its variant with lower
and upper constraints on nested sums of variables. This problem occurs in many
applications, in particular battery scheduling within decentralized energy
management (DEM) for smart grids. We present an algorithm for this problem that
runs in time and, in contrast to existing algorithms for this
problem, achieves this time complexity using relatively simple and
easy-to-implement subroutines and data structures. This makes our algorithm
very attractive for real-life adaptation and implementation. Numerical
comparisons of our algorithm with a subroutine for battery scheduling within an
existing tool for DEM research indicates that our algorithm significantly
reduces the overall execution time of the DEM system, especially when the
battery is expected to be completely full or empty multiple times in the
optimal schedule. Moreover, computational experiments with synthetic data show
that our algorithm outperforms the currently most efficient algorithm by more
than one order of magnitude. In particular, our algorithm is able to solves all
considered instances with up to one million variables in less than 17 seconds
on a personal computer
Quadratic nonseparable resource allocation problems with generalized bound constraints
We study a quadratic nonseparable resource allocation problem that arises in
the area of decentralized energy management (DEM), where unbalance in
electricity networks has to be minimized. In this problem, the given resource
is allocated over a set of activities that is divided into subsets, and a cost
is assigned to the overall allocated amount of resources to activities within
the same subset. We derive two efficient algorithms with
worst-case time complexity to solve this problem. For the special case where
all subsets have the same size, one of these algorithms even runs in linear
time given the subset size. Both algorithms are inspired by well-studied
breakpoint search methods for separable convex resource allocation problems.
Numerical evaluations on both real and synthetic data confirm the theoretical
efficiency of both algorithms and demonstrate their suitability for integration
in DEM systems
Offline and online scheduling of electric vehicle charging with a minimum charging threshold
The increasing penetration of electric vehicles (EVs) requires the development of smart charging strategies that accommodate the increasing load of these EVs on the distribution grid. Many existing charging strategies assume that an EV is allowed to charge at any rate up to a given maximum rate. However, in practice, charging at low rates is inefficient and often even impossible. Therefore, this paper presents an efficient algorithm for scheduling an EV within a decentralized energy management system that allows only charging above a given threshold. We show that the resulting optimal EV schedule is characterized by an activation level and a fill-level. Moreover, based on this result, we derive an online approach that does not require predictions of uncontrollable loads as input, but merely a prediction of these two characterizing values. Simulation results show that the online algorithm is robust against prediction errors in these values and can produce near-optimal online solutions
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