60,921 research outputs found
Intertwined Orders in Holography: Pair and Charge Density Waves
Building on [1], we examine a holographic model in which a U(1) symmetry and
translational invariance are broken spontaneously at the same time. The
symmetry breaking is realized through the St\"{u}ckelberg mechanism, and leads
to a scalar condensate and a charge density which are spatially modulated and
exhibit unidirectional stripe order. Depending on the choice of parameters, the
oscillations of the scalar condensate can average out to zero, with a frequency
which is half of that of the charge density. In this case the system realizes
some of the key features of pair density wave order. The model also admits a
phase with co-existing superconducting and charge density wave orders, in which
the scalar condensate has a uniform component. In our construction the various
orders are intertwined with each other and have a common origin. The fully
backreacted geometry is computed numerically, including for the case in which
the theory contains axions. The latter can be added to explicitly break
translational symmetry and mimic lattice-type effects.Comment: 37 pages, 17 figure
Multilevel refinable triangular PSP-splines (Tri-PSPS)
A multi-level spline technique known as partial shape preserving splines (PSPS) (Li and Tian, 2011) has recently been developed for the design of piecewise polynomial freeform geometric surfaces, where the basis functions of the PSPS can be directly built from an arbitrary set of polygons that partitions a giving parametric domain. This paper addresses a special type of PSPS, the triangular PSPS (Tri-PSPS), where all spline basis functions are constructed from a set of triangles. Compared with other triangular spline techniques, Tri-PSPS have several distinctive features. Firstly, for each given triangle, the corresponding spline basis function for any required degree of smoothness can be expressed in closed-form and directly written out in full explicitly as piecewise bivariate polynomials. Secondly, Tri-PSPS are an additive triangular spline technique, where the spline function built from a given triangle can be replaced with a set of refined spline functions built on a set of smaller triangles that partition the initial given triangle. In addition, Tri-PSPS are a multilevel spline technique, Tri-PSPS surfaces can be designed to have a continuously varying levels of detail, achieved simply by specifying a proper value for the smoothing parameter introduced in the spline functions. In terms of practical implementation, Tri-PSPS are a parallel computing friendly spline scheme, which can be easily implemented on modern programmable GPUs or on high performance computer clusters, since each of the basis functions of Tri-PSPS can be directly computed independent of each other in parallel
Thermodynamic stability of small-world oscillator networks: A case study of proteins
We study vibrational thermodynamic stability of small-world oscillator
networks, by relating the average mean-square displacement of oscillators
to the eigenvalue spectrum of the Laplacian matrix of networks. We show that
the cross-links suppress effectively and there exist two phases on the
small-world networks: 1) an unstable phase: when , ; 2) a
stable phase: when , , \emph{i.e.}, . Here, is the parameter of small-world, is the number of
oscillators, and is the number of cross-links. The results are
exemplified by various real protein structures that follow the same scaling
behavior of the stable phase. We also show that it is the
"small-world" property that plays the key role in the thermodynamic stability
and is responsible for the universal scaling , regardless
of the model details.Comment: 7 pages, 5 figures, accepted by Physical Review
- …