scholarly journals Yang-Baxter and the Boost: splitting the difference

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Marius de Leeuw ◽  
Chiara Paletta ◽  
Anton Pribytok ◽  
Ana L. Retore ◽  
Paul Ryan
Keyword(s):  
Hilbert Space ◽  
Sigma Model ◽  
Spin Chains ◽  
Baxter Equation ◽  
Regular Solutions ◽  
One Dimensional ◽  
Difference Form ◽  
The Difference ◽  
The One

In this paper we continue our classification of regular solutions of the Yang-Baxter equation using the method based on the spin chain boost operator developed in [1]. We provide details on how to find all non-difference form solutions and apply our method to spin chains with local Hilbert space of dimensions two, three and four. We classify all 16\times1616×16 solutions which exhibit \mathfrak{su}(2)\oplus \mathfrak{su}(2)𝔰𝔲(2)⊕𝔰𝔲(2) symmetry, which include the one-dimensional Hubbard model and the SS-matrix of the {AdS}_5 \times {S}^5AdS5×S5 superstring sigma model. In all cases we find interesting novel solutions of the Yang-Baxter equation.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

Limit theorems and absorption problems for quantum radom walks in one dimension

2002 ◽  
Vol 2 (Special) ◽  
pp. 578-595
Author(s):  
N. Konno
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
The Other ◽  
One Dimension ◽  
Unitary Matrices ◽  
Quantum Random Walks ◽  
One Dimensional ◽  
The Difference ◽  
The One

In this paper we consider limit theorems, symmetry of distribution, and absorption problems for two types of one-dimensional quantum random walks determined by $2 \times 2$ unitary matrices using our PQRS method. The one type was introduced by Gudder in 1988, and the other type was studied intensively by Ambainis et al. in 2001. The difference between both types of quantum random walks is also clarified.

Classification of shallow-water acoustic signals via alpha-Stable modeling of the one-dimensional wavelet coefficients

2006 ◽  
Vol 119 (3) ◽  
pp. 1396-1405 ◽  
Author(s):  
Michael I. Taroudakis ◽  
George Tzagkarakis ◽  
Panagiotis Tsakalides
Keyword(s):  
Shallow Water ◽  
Acoustic Signals ◽  
Wavelet Coefficients ◽  
One Dimensional ◽  
The One

Using the one-dimensional S-transform as a discrimination tool in classification of hyperspectral images

2007 ◽  
Vol 33 (6) ◽  
pp. 551-560 ◽  
Author(s):  
Bhaskar C Sahoo ◽  
Thomas Oommen ◽  
Debasmita Misra ◽  
Gregory Newby
Keyword(s):  
Hyperspectral Images ◽  
One Dimensional ◽  
S Transform ◽  
The One

scholarly journals Exact Solutions and Degenerate Properties of Spin Chains with Reducible Hamiltonians

2018 ◽  
Vol 3 (4) ◽  
pp. 32
Author(s):  
Shiung Fan
Keyword(s):  
Ground State ◽  
Spin Chains ◽  
Xy Model ◽  
One Dimensional ◽  
Wigner Transformation ◽  
Lattice Fermions ◽  
Large Systems ◽  
The One ◽  
Periodic Chain ◽  
Non Locality

The Jordan–Wigner transformation plays an important role in spin models. However, the non-locality of the transformation implies that a periodic chain of N spins is not mapped to a periodic or an anti-periodic chain of lattice fermions. Since only the N − 1 bond is different, the effect is negligible for large systems, while it is significant for small systems. In this paper, it is interesting to find that a class of periodic spin chains can be exactly mapped to a periodic chain and an anti-periodic chain of lattice fermions without redundancy when the Jordan–Wigner transformation is implemented. For these systems, possible high degeneracy is found to appear in not only the ground state, but also the excitation states. Further, we take the one-dimensional compass model and a new XY-XY model ( σ x σ y − σ x σ y ) as examples to demonstrate our proposition. Except for the well-known one-dimensional compass model, we will see that in the XY-XY model, the degeneracy also grows exponentially with the number of sites.

scholarly journals Lipschitz Retractions in Hadamard Spaces via Gradient Flow Semigroups

2016 ◽  
Vol 59 (4) ◽  
pp. 673-681 ◽  
Author(s):  
Miroslav Bačák ◽  
Leonid V. Kovalev
Keyword(s):  
Hilbert Space ◽  
Finite Subset ◽  
Metric Space ◽  
Hausdorff Metric ◽  
Gradient Flow ◽  
The Other ◽  
Dimensional Sphere ◽  
Hadamard Space ◽  
One Dimensional ◽  
The One

AbstractLet X(n), for n ∊ ℕ, be the set of all subsets of a metric space (X, d) of cardinality at most n. The set X(n) equipped with the Hausdorff metric is called a finite subset space. In this paper we are concerned with the existence of Lipschitz retractions r: X(n)→ X(n − 1) for n ≥ 2. It is known that such retractions do not exist if X is the one-dimensional sphere. On the other hand, Kovalev has recently established their existence if X is a Hilbert space, and he also posed a question as to whether or not such Lipschitz retractions exist when X is a Hadamard space. In this paper we answer the question in the positive.

Mesoscopic free energy as a framework for modeling shape memory alloys

2019 ◽  
Vol 30 (13) ◽  
pp. 1969-2012
Author(s):  
Wesley Ballew ◽  
Stefan Seelecke
Keyword(s):  
Free Energy ◽  
Shape Memory ◽  
Latent Heat ◽  
Compressive Behavior ◽  
Temperature Dependent ◽  
One Dimensional ◽  
Dimensional Shape ◽  
The Difference ◽  
The One

This article presents a reinterpretation of the one-dimensional shape memory alloy model by Müller, Achenbach, and Seelecke (M-A-S) that offers extended capabilities and a simpler formulation. The cornerstone of this model is a continuous, multi-well free energy that governs phase change at a mesoscopic material scale. The free energy has been reformulated to allow asymmetric tensile and compressive behavior as well as temperature-dependent hysteresis while maintaining the necessary smoothness conditions. The free energy is then used to derive expressions for latent heat coefficients that include the influence of stress, the difference in stiffness between the phases, and irreversibility. Special attention is devoted to the role of irreversibility and latent heat predictions, which are compared to experimental measurements. The new model also includes an updated set of kinetics equations that operate on the convexity of the energy wells instead of the height of the energy barriers. This modification eliminates several sets of equations from the overall formulation without any compromises in performance and also bypasses limitations of the barrier-based equations.

scholarly journals Predicting heave on the expansive soil

2018 ◽  
Vol 195 ◽  
pp. 03008
Author(s):  
Willis Diana ◽  
Anita Widianti ◽  
Edi Hartono ◽  
Agus Setyo Muntohar
Keyword(s):  
Research Study ◽  
Expansive Soil ◽  
Foundation Design ◽  
One Dimensional ◽  
Design Life ◽  
Fundamental Part ◽  
Experimental Laboratory ◽  
Soil Information ◽  
The Difference ◽  
The One

The heave of expansive soil information is a fundamental part of the preparation of a foundation design to accommodate the anticipated volume change and consequences associated with the foundation movement over the design life of the structure. The one-dimensional oedometer is the most widely accepted method to identify and evaluate the amount of swell that may occur. Although the oedometer is used extensively for evaluating the amount of heave, the procedures used are quite varied, and few of the methods have been validated experimentally. An objective of this research study is to briefly explain common practices and existing heave prediction by oedometer methods and then, to validate by experimental laboratory heave tests using soil sample from Ngawi. The two prediction methods provided results that represent low and upper bound predictions of the actual soil heave movement in the laboratory. The difference between the prediction with heave measurement is about 29,50% and 45,02%, respectively.

The One-Dimensional Optimum Hydrodynamic Gas Slider Bearing

1968 ◽  
Vol 90 (1) ◽  
pp. 281-284 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Film Thickness ◽  
Load Capacity ◽  
Maximum Load ◽  
Slider Bearing ◽  
Compression Process ◽  
One Dimensional ◽  
One Step ◽  
The Difference ◽  
The One ◽  
Bearing Number

Bounded variable methods of the calculus of variations are used to determine the optimum or maximum load capacity hydrodynamic one-dimensional gas slider bearing. A lower bound is placed on the minimum film thickness in order to keep the load finite, and also to satisfy the boundary conditions. Using the Weierstrass-Erdmann corner conditions and the Weierstrass E-function it is found that the optimum gas slider bearing is stepped with a convergent leading section and a uniform thickness trailing section. The step location and the leading section film thickness depend upon the bearing number and compression process considered. It is also shown that the bearing contains one and only one step. The difference in the load capacity and maximum film pressure between the isothermal and adiabatic cases increases with increasing bearing number.

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