scholarly journals Topological acoustic triple point

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sungjoon Park ◽  
Yoonseok Hwang ◽  
Hong Chul Choi ◽  
Bohm-Jung Yang
Keyword(s):  
Triple Point ◽  
Euler Number ◽  
Longitudinal Mode ◽  
High Symmetry ◽  
Time Inversion ◽  
Goldstone Theorem ◽  
Nodal Structure ◽  
Transverse Modes ◽  
Degeneracy Point ◽  
Triple Points

AbstractAcoustic phonon is a classic example of triple degeneracy point in band structure. This triple point always appears in phonon spectrum because of the Nambu–Goldstone theorem. Here, we show that this triple point can carry a topological charge $${\mathfrak{q}}$$ q that is a property of three-band systems with space-time-inversion symmetry. The charge $${\mathfrak{q}}$$ q can equivalently be characterized by the skyrmion number of the longitudinal mode, or by the Euler number of the transverse modes. We call triple points with nontrivial $${\mathfrak{q}}$$ q the topological acoustic triple point (TATP). TATP can also appear at high-symmetry momenta in phonon and spinless electron spectrums when Oh or Th groups protect it. The charge $${\mathfrak{q}}$$ q constrains the nodal structure and wavefunction texture around TATP, and can induce anomalous thermal transport of phonons and orbital Hall effect of electrons. Gapless points protected by the Nambu–Goldstone theorem form a new platform to study the topology of band degeneracies.

Triple points of unknotting discs and the Arf invariant of knots

1994 ◽  
Vol 116 (1) ◽  
pp. 119-129 ◽  
Author(s):  
Thomas Fiedler
Keyword(s):  
Triple Point ◽  
Critical Points ◽  
Normal Bundle ◽  
Morse Function ◽  
Euler Number ◽  
Double Points ◽  
Arf Invariant ◽  
Triple Points ◽  
Coordinate Functions

AbstractAn unknotting disc is the ‘trace’ in ℝ4 of a homotopy of a diagram of a knot in ℝ3, which shrinks the diagram to a point. In this paper we study unknotting discs which have as singularities only ordinary triple points. It turns out that the Arf invariant of the knot is determined by the number of triple points in which all three branches of the disc intersect pairwise with the same index. We call such a triple point coherent. This interpretation of the Arf invariant has a surprising consequence:Let S ⊂ ℝ4 be a taut immersed sphere which has as singularities only ordinary triple points. Then the number of coherent triple points in S is even. For example, it is easy to show that there is a taut immersed sphere S with Euler number six of the normal bundle and which has exactly three ordinary double points and no other singularities. So, our result implies that the three double points of S can not be pushed together to create an ordinary triple point without the appearance of new singularities.Here ‘taut’ means that the restriction of one of the coordinate functions on S has exactly two (non-degenerate) critical points, i.e. is a perfect Morse function.

scholarly journals Supernova constraints on an axion-photon-dark photon interaction

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Anson Hook ◽  
Gustavo Marques-Tavares ◽  
Clayton Ristow
Keyword(s):  
Longitudinal Mode ◽  
Transverse Mode ◽  
The Other ◽  
Unusual Feature ◽  
Dark Sector ◽  
Longitudinal Modes ◽  
Dark Photon ◽  
Transverse Modes ◽  
Weakly Coupled ◽  
Photon Coupling

Abstract We present the supernova constraints on an axion-photon-dark photon coupling, which can be the leading coupling to dark sector models and can also lead to dramatic changes to axion cosmology. We show that the supernova bound on this coupling has two unusual features. One occurs because the scattering that leads to the trapping regime converts axions and dark photons into each other. Thus, if one of the two new particles is sufficiently massive, both production and scattering become suppressed and the bounds from bulk emission and trapped (area) emission both weaken exponentially and do not intersection The other unusual feature occurs because for light dark photons, longitudinal modes couple more weakly than transverse modes do. Since the longitudinal mode is more weakly coupled, it can still cause excessive cooling even if the transverse mode is trapped. Thus, the supernova constraints for massive dark photons look like two independent supernova bounds super-imposed on top of each other.

Thermodynamic Analysis of Isotope Effects on Triple Points and/or Melting Temperatures

1995 ◽  
Vol 50 (4-5) ◽  
pp. 337-346
Author(s):  
W. Alexander Van Hook
Keyword(s):  
Melting Point ◽  
Physical Properties ◽  
Thermodynamic Analysis ◽  
Triple Point ◽  
Isotope Effects ◽  
Inorganic Salts ◽  
Literature Information ◽  
Melting Temperatures ◽  
Triple Points

Àbstract Available literature information on triple point or melting point isotope effects (and related physical properties) is subjected to thermodynamic analysis and consistency checks. New values for the melting point isotope effects for C6H6/CgD6 and c-C6H12/c-C6D12 are reported. 6Li/7Li melting point isotope effects reported recently by Hidaka and Lunden (Z. Naturforsch. 49 a, 475 (1994)) for various inorganic salts are questioned

scholarly journals Triple-crossing number and moves on triple-crossing link diagrams

2019 ◽  
Vol 28 (11) ◽  
pp. 1940001 ◽  
Author(s):  
Colin Adams ◽  
Jim Hoste ◽  
Martin Palmer
Keyword(s):  
Triple Point ◽  
Crossing Number ◽  
Reidemeister Moves ◽  
Link Diagrams ◽  
Triple Points ◽  
Definition Of ◽  
Hopf Link

Every link in the 3-sphere has a projection to the plane where the only singularities are pairwise transverse triple points. The associated diagram, with height information at each triple point, is a triple-crossing diagram of the link. We give a set of diagrammatic moves on triple-crossing diagrams analogous to the Reidemeister moves on ordinary diagrams. The existence of [Formula: see text]-crossing diagrams for every [Formula: see text] greater than one allows the definition of the [Formula: see text]-crossing number. We prove that for any nontrivial, nonsplit link, other than the Hopf link, its triple-crossing number is strictly greater than its quintuple-crossing number.

Elastic and photo-elastic constants of CH4 and CD4 obtained by Brillouin scattering

1982 ◽  
Vol 60 (3) ◽  
pp. 287-298 ◽  
Author(s):  
S. C. Rand ◽  
B. P. Stoicheff
Keyword(s):  
High Resolution ◽  
Single Crystals ◽  
Elastic Constants ◽  
Brillouin Scattering ◽  
Low Frequency ◽  
Mass Ratio ◽  
Translational Coupling ◽  
Brillouin Spectroscopy ◽  
Transverse Modes ◽  
Triple Points

The elastic constants and Pockels coefficients of CH4 and CD4 single crystals near their triple points have been determined using high-resolution Brillouin spectroscopy. For CH4 at 90.4 K, the elastic constants are C11 = 19.57 ± 0.30, C12 = 14.46 ± 0.20, C44 = 9.20 ± 0.15 kbar, and the ratios of the Pockels coefficients are p12/p11 = 1.031 ± 0.035 and p44/p11 = 0.069 ± 0.010. For CD4 at 89.2 K, C12 = 20.04 ± 0.30, C12 = 15.00 ± 0.25, C44 = 9.15 ± 0.15 kbar, and p12/p11 = 1.027 ± 0.020, P44/p11 = 0.138 ± 0.010. The velocities of the low-frequency transverse modes in CH4 and CD4 are anomalously slow in the [Formula: see text] direction, indicative of rotational–translational coupling of molecules. Isotopic differences are also evident: the Pockels coefficient p44 in CD4 is double that in CH4; and the velocities of both transverse modes in the principle directions [Formula: see text], [Formula: see text], and [Formula: see text] are in the ratio V(CH4)/V(CD4) = 1.130 instead of 1.118 as expected from the isotopic mass ratio.

Microstructural Evolution of Aluminum Interconnects During Post-Pattern Anneals: Correlation to Improved Em Lifetime

1994 ◽  
Vol 338 ◽  
Author(s):  
B. Miner ◽  
E.A. Atakov ◽  
A. Shepela ◽  
S. Bill
Keyword(s):  
Grain Boundary ◽  
Microstructural Evolution ◽  
Triple Point ◽  
Length Distribution ◽  
Microstructural Parameters ◽  
Statistical Measures ◽  
Before And After ◽  
Triple Points ◽  
Aluminum Interconnects ◽  
Cluster Length

ABSTRACTThe number of Al triple point junctions (Ntp) correlates inversely to electromigration lifetimes for partially bamboo interconnects that fail by grain boundary (GB) diffusion. This work emphasizes the evolution of statistical microstructural parameters, Ntp and cluster length distribution, during post-pattern anneals. In addition to statistical measures, the structure of specific clusters before and after anneal is compared from TEM images of the same area of the same sample.Each post-pattern anneal lowers Ntp and shortens the length of individual polycrystalline segments, but with diminishing returns for subsequent anneals. With a TiN capping layer, the statistical microstructural improvement is less but the longest clusters, those most probable as failure sites, lose triple points during anneal. The distribution of cluster lengths is characteristic for a process.

scholarly journals ON HOMOTOPIES WITH TRIPLE POINTS OF CLASSICAL KNOTS

2012 ◽  
Vol 21 (04) ◽  
pp. 1250038
Author(s):  
THOMAS FIEDLER ◽  
ARNAUD MORTIER
Keyword(s):  
Triple Point ◽  
Simple Proof ◽  
Intersection Index ◽  
Vassiliev Invariant ◽  
Triple Points ◽  
New Formula

We consider a knot homotopy as a cylinder in 4-space. An ordinary triple point p of the cylinder is called coherent if all three branches intersect at p pairwise with the same intersection index. A triple unknotting of a classical knot K is a homotopy which connects K with the trivial knot and which has as singularities only coherent triple points. We give a new formula for the first Vassiliev invariant v2(K) by using triple unknottings. As a corollary we obtain a very simple proof of the fact that passing a coherent triple point always changes the knot type. As another corollary we show that there are triple unknottings which are not homotopic as triple unknottings even if we allow more complicated singularities to appear in the homotopy of the triple homotopy.

Some Thermodynamic Properties of Pure and Impure Nitrogen

1974 ◽  
Vol 52 (16) ◽  
pp. 1521-1531 ◽  
Author(s):  
J. Ancsin
Keyword(s):  
Thermodynamic Properties ◽  
Triple Point ◽  
Boiling Point ◽  
Normal Boiling Point ◽  
Vapor Pressures ◽  
Freezing Points ◽  
Boiling Points ◽  
Triple Points

Boiling points, freezing points, and vapor pressures (from 56 K to the normal boiling point) for pure and various doped N2 samples have been measured. The normal boiling points for N2 and N2 doped with 100 v.p.p.m. of O2, Ar, Kr, and CO impurities were found to be 77.3439 K, 77.3458 K, 77.3452 K, 77.3454 K, and 77.3444 K respectively. The triple points of the same samples are 63.14635 K, 63.1445 K, 63.14575 K, 63.1487 K, and 63.14675 K respectively. The values obtained for the heats of sublimation, vaporization, and fusion at the triple point of pure N2 were 6773.8, 6049.6, and 724.3 J/mole respectively and the above impurities changed these quantities by the amounts given in Tables 5 and 6.

OPTICAL VORTEX INTERACTION IN LASERS

1994 ◽  
Vol 04 (03) ◽  
pp. 675-691
Author(s):  
MARK JEFFERY ◽  
E.J. D’ANGELO
Keyword(s):  
Longitudinal Mode ◽  
Interaction Force ◽  
High Gain ◽  
Optical Vortices ◽  
Color Coding ◽  
Time Step ◽  
Transverse Modes ◽  
Close Range ◽  
Best Fit ◽  
Very High

The Maxwell-Bloch equations describing the transverse modes of a large aspect ratio homogeneously broadened single-longitudinal-mode laser are solved numerically. The solutions are visualized by color-coding the intensity and phase of the transverse electric field at each time step and a video showing the detailed time evolution has been made. As the gain is increased optical vortices, or defects, are observed. These vortices interact and for very high gain optical turbulence exists. The orbits of the single- and two-defect solutions are analyzed and the effective force law coupling the defects is numerically calculated. The best fit force is a modified Bessel function which is proportional to r−1/2 exp (−r/α) at large distances and ln(α/r) at close range where α is approximately 2. This interaction force law for optical defects is similar to the force law between Abrikosov vortices in a superconductor.

scholarly journals KNOTTED SURFACES AND EQUIVALENCIES OF THEIR DIAGRAMS WITHOUT TRIPLE POINTS

2012 ◽  
Vol 21 (03) ◽  
pp. 1250019 ◽  
Author(s):  
M. JABŁONOWSKI
Keyword(s):  
Triple Point ◽  
Finite Sequence ◽  
Closed Surface ◽  
Branch Points ◽  
Double Points ◽  
Generic Projection ◽  
Projection Image ◽  
Triple Points ◽  
Standard Projection ◽  
Three Space

The singularity set of a generic standard projection to the three space of a closed surface linked in four space, consists of at most three types: double points, triple points or branch points. We say that this generic projection image is p-diagram if it does not contain any triple point. Two p-diagrams of equivalent surface links are called p-equivalent if there exist a finite sequence of local moves, such that each of them is one of the four moves taken from the seven on the well known Roseman list, that connects only p-diagrams. It is natural to ask that whether any of two p-diagrams of equivalent surface links always p-equivalent? We introduce an invariant of p-equivalent diagrams and an example of linked surfaces that answers our question negatively.

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