184 research outputs found
Finite size analysis of the pseudo specific heat in SU(2) gauge theory
We investigate the pseudo specific heat of SU(2) gauge theory near the
crossover point on to lattices. Several different methods are used
to determine the specific heat. The curious finite size dependence of the peak
maximum is explained from the interplay of the crossover phenomenon with the
deconfinement transition occurring due to the finite extension of the lattice.
In this context we calculate the modulus of the lattice average of the Polyakov
loop on symmetric lattices and compare it to the prediction from a random walk
model.Comment: Talk presented at LATTICE96(finite temperature), 3 pages, 4
Postscript figure
The Pseudo Specific Heat in SU(2) Gauge Theory : Finite Size Dependence and Finite Temperature Effects
We investigate the pseudo specific heat of SU(2) gauge theory near the
crossover point on to lattices. Several different methods are used
to determine the specific heat. The curious finite size dependence of the peak
maximum is explained from the interplay of the crossover phenomenon with the
deconfinement transition occurring due to the finite extension of the lattice.
We find, that for lattices of size and larger the crossover peak is
independent of lattice size at and has a peak height of
. We conclude therefore that the crossover peak is not the
result of an ordinary phase transition. Further, the contributions to
from different plaquette correlations are calculated. We find, that at the peak
and far outside the peak the ratio of contributions from orthogonal and
parallel plaquette correlations is different. To estimate the finite
temperature influence on symmetric lattices far off the deconfinement
transition point we calculate the modulus of the lattice average of the
Polyakov loop on these lattices and compare it to predictions from a random
walk model.Comment: Latex 2e,10 pages including 5 postscript figure
Corrections to Scaling and Critical Amplitudes in SU(2) Lattice Gauge Theory
We calculate the critical amplitudes of the Polyakov loop and its
susceptibility at the deconfinement transition of SU(2) gauge theory. To this
end we carefully study the corrections to the scaling functions of the
observables coming from irrelevant exponents. As a guiding line for determining
the critical amplitudes we use envelope equations derived from the finite size
scaling formulae for the observables. The equations are then evaluated with new
high precision data obtained on N^3 x 4 lattices for N=12,18,26 and 36. We find
different correction-to-scaling behaviours above and below the transition. Our
result for the universal ratio of the susceptibility amplitudes is
C_+/C_-=4.72(11) and agrees perfectly with a recent measurement for the 3d
Ising model.Comment: LATTICE98(hightemp
Direct determination of the gauge coupling derivatives for the energy density in lattice QCD
By matching Wilson loop ratios on anisotropic lattices we measure the
coefficients \cs and \ct, which are required for the calculation of the
energy density. The results are compared to that of an indirect method of
determination. We find similar behaviour, the differences are attributed to
different discretization errors.Comment: Talk presented at LATTICE97(finite temperature), 3 pages, 5
Postscript figure
The Canonical Amoebot Model: Algorithms and Concurrency Control
The amoebot model abstracts active programmable matter as a collection of simple computational elements called amoebots that interact locally to collectively achieve tasks of coordination and movement. Since its introduction (SPAA 2014), a growing body of literature has adapted its assumptions for a variety of problems; however, without a standardized hierarchy of assumptions, precise systematic comparison of results under the amoebot model is difficult. We propose the canonical amoebot model, an updated formalization that distinguishes between core model features and families of assumption variants. A key improvement addressed by the canonical amoebot model is concurrency. Much of the existing literature implicitly assumes amoebot actions are isolated and reliable, reducing analysis to the sequential setting where at most one amoebot is active at a time. However, real programmable matter systems are concurrent. The canonical amoebot model formalizes all amoebot communication as message passing, leveraging adversarial activation models of concurrent executions. Under this granular treatment of time, we take two complementary approaches to concurrent algorithm design. Using hexagon formation as a case study, we first establish a set of sufficient conditions for algorithm correctness under any concurrent execution, embedding concurrency control directly in algorithm design. We then present a concurrency control framework that uses locks to convert amoebot algorithms that terminate in the sequential setting and satisfy certain conventions into algorithms that exhibit equivalent behavior in the concurrent setting. Together, the canonical amoebot model and these complementary approaches to concurrent algorithm design open new directions for distributed computing research on programmable matter
Local Mutual Exclusion for Dynamic, Anonymous, Bounded Memory Message Passing Systems
Mutual exclusion is a classical problem in distributed computing that provides isolation among concurrent action executions that may require access to the same shared resources. Inspired by algorithmic research on distributed systems of weakly capable entities whose connections change over time, we address the local mutual exclusion problem that tasks each node with acquiring exclusive locks for itself and the maximal subset of its "persistent" neighbors that remain connected to it over the time interval of the lock request. Using the established time-varying graphs model to capture adversarial topological changes, we propose and rigorously analyze a local mutual exclusion algorithm for nodes that are anonymous and communicate via asynchronous message passing. The algorithm satisfies mutual exclusion (non-intersecting lock sets) and lockout freedom (eventual success with probability 1) under both semi-synchronous and asynchronous concurrency. It requires ?(?) memory per node and messages of size ?(1), where ? is the maximum number of connections per node. We conclude by describing how our algorithm can implement the pairwise interactions assumed by population protocols and the concurrency control operations assumed by the canonical amoebot model, demonstrating its utility in both passively and actively dynamic distributed systems
Protocol for deposition of conductive oxides onto 3D-printed materials for electronic device applications
Additively manufactured (AM) three-dimensional (3D) mesostructures can be designed to enhance mechanical, thermal, or optical properties, driving future device applications at the micron to millimeter scale. We present a protocol for transforming AM mesostructures into 3D electronics by growing nanoscale conducting films on 3D-printed polymers. In this generalizable approach, we describe steps to utilize precision thermal atomic layer deposition (ALD) of conducting, semiconducting, and dielectric metal oxides. This can be applied to ultrasmooth, customizable photopolymer lattices printed by high-resolution microstereolithography. For complete details on the use and execution of this protocol, please refer to Huddy et al. (2022)
A Study of Finite Temperature Gauge Theory in (2+1) Dimensions
We determine the critical couplings and the critical exponents of the finite
temperature transition in SU(2) and SU(3) pure gauge theory in (2+1)
dimensions. We also measure Wilson loops at on a wide range of
values using APE smearing to improve the signal. We extract the string tension
from a fit to large distances, including a string fluctuation term.
With these two entities we calculate .Comment: Talk presented at LATTICE96(finite temperature), not espcrc2 style: 7
pages, 4 ps figures, 22 k
Convex Hull Formation for Programmable Matter
We envision programmable matter as a system of nano-scale agents (called
particles) with very limited computational capabilities that move and compute
collectively to achieve a desired goal. We use the geometric amoebot model as
our computational framework, which assumes particles move on the triangular
lattice. Motivated by the problem of sealing an object using minimal resources,
we show how a particle system can self-organize to form an object's convex
hull. We give a distributed, local algorithm for convex hull formation and
prove that it runs in asynchronous rounds, where is the
length of the object's boundary. Within the same asymptotic runtime, this
algorithm can be extended to also form the object's (weak) -hull,
which uses the same number of particles but minimizes the area enclosed by the
hull. Our algorithms are the first to compute convex hulls with distributed
entities that have strictly local sensing, constant-size memory, and no shared
sense of orientation or coordinates. Ours is also the first distributed
approach to computing restricted-orientation convex hulls. This approach
involves coordinating particles as distributed memory; thus, as a supporting
but independent result, we present and analyze an algorithm for organizing
particles with constant-size memory as distributed binary counters that
efficiently support increments, decrements, and zero-tests --- even as the
particles move
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