62,482 research outputs found
Unique Information via Dependency Constraints
The partial information decomposition (PID) is perhaps the leading proposal
for resolving information shared between a set of sources and a target into
redundant, synergistic, and unique constituents. Unfortunately, the PID
framework has been hindered by a lack of a generally agreed-upon, multivariate
method of quantifying the constituents. Here, we take a step toward rectifying
this by developing a decomposition based on a new method that quantifies unique
information. We first develop a broadly applicable method---the dependency
decomposition---that delineates how statistical dependencies influence the
structure of a joint distribution. The dependency decomposition then allows us
to define a measure of the information about a target that can be uniquely
attributed to a particular source as the least amount which the source-target
statistical dependency can influence the information shared between the sources
and the target. The result is the first measure that satisfies the core axioms
of the PID framework while not satisfying the Blackwell relation, which depends
on a particular interpretation of how the variables are related. This makes a
key step forward to a practical PID.Comment: 15 pages, 7 figures, 2 tables, 3 appendices;
http://csc.ucdavis.edu/~cmg/compmech/pubs/idep.ht
Quantum Corner-Transfer Matrix DMRG
We propose a new method for the calculation of thermodynamic properties of
one-dimensional quantum systems by combining the TMRG approach with the corner
transfer-matrix method. The corner transfer-matrix DMRG method brings
reasonable advantage over TMRG for classical systems. We have modified the
concept for the calculation of thermal properties of one-dimensional quantum
systems. The novel QCTMRG algorithm is implemented and used to study two simple
test cases, the classical Ising chain and the isotropic Heisenberg model. In a
discussion, the advantages and challenges are illuminated.Comment: 17 pages, 15 figures, to appear in Int.J.Mod.Phys.
The Renormalization Group Method and Quantum Groups: the postman always rings twice
We review some of our recent results concerning the relationship between the
Real-Space Renormalization Group method and Quantum Groups. We show this
relation by applying real-space RG methods to study two quantum group invariant
Hamiltonians, that of the XXZ model and the Ising model in a transverse field
(ITF) defined in an open chain with appropriate boundary terms. The quantum
group symmetry is preserved under the RG transformation except for the
appearence of a quantum group anomalous term which vanishes in the classical
case. This is called {\em the quantum group anomaly}. We derive the new qRG
equations for the XXZ model and show that the RG-flow diagram obtained in this
fashion exhibits the correct line of critical points that the exact model has.
In the ITF model the qRG-flow equations coincide with the tensor product
decomposition of cyclic irreps of with .Comment: LATEX file, 21 pages, no figures. To appear in "From Field Theory to
Quantum Groups", World Scientific. Proceedings to honor J.Lukierski in his
60th birthda
QPACE 2 and Domain Decomposition on the Intel Xeon Phi
We give an overview of QPACE 2, which is a custom-designed supercomputer
based on Intel Xeon Phi processors, developed in a collaboration of Regensburg
University and Eurotech. We give some general recommendations for how to write
high-performance code for the Xeon Phi and then discuss our implementation of a
domain-decomposition-based solver and present a number of benchmarks.Comment: plenary talk at Lattice 2014, to appear in the conference proceedings
PoS(LATTICE2014), 15 pages, 9 figure
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Design for Additive Manufacturing: A Method to Explore Unexplored Regions of the Design Space
Additive Manufacturing (AM) technologies enable the fabrication of parts and devices that
are geometrically complex, have graded material compositions, and can be customized. To take
advantage of these capabilities, it is important to assist designers in exploring unexplored regions
of design spaces. We present a Design for Additive Manufacturing (DFAM) method that
encompasses conceptual design, process selection, later design stages, and design for
manufacturing. The method is based on the process-structure-property-behavior model that is
common in the materials design literature. A prototype CAD system is presented that embodies
the method. Manufacturable ELements (MELs) are proposed as an intermediate representation
for supporting the manufacturing related aspects of the method. Examples of cellular materials
are used to illustrate the DFAM method.Mechanical Engineerin
Vibronic interaction in crystals with the Jahn-Teller centers in the elementary energy bands concept
The order-disorder type phase transition caused by the vibronic interaction
(collective Jahn-Teller effect) in a monoclinic CuInPS crystal is
analyzed. For this purpose, a trigonal protostructure model of CuInPS
is created, through a slight change in the crystal lattice parameters of the
CuInPS paraelectric phase. In parallel to the group-theoretical
analysis, the DFT-based {\it ab initio} band structure calculations of the
CuInPS protostructure, para-, and ferriphases are performed. Using the
elementary energy bands concept, a part of the band structure from the vicinity
of the forbidden energy gap, which is created by the -electron states of
copper, has been related with a certain Wyckoff position where the
Jahn-Teller's centers are localized. A construction procedure of the vibronic
potential energy matrix is generalized for the case of crystal using the
elementary energy bands concept and the group theoretical method of invariants.
The procedure is illustrated by the creation of the adiabatic potentials of the
- vibronic coupling for the protostructure and paraphase of
the CuInPS crystal. A structure of the obtained adiabatic potentials is
analyzed, followed by conclusions on their transformation under a phase
transition and the discussion on the possibility for the spontaneous
polarization to arise in this crystal.Comment: 17 pages, 7 figure
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