Three-Dimensional Integrable Models and Associated Tangle Invariants

In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group, if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones.Comment: Number of pages: 21, Latex fil

Spherical geometry and integrable systems

We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.Comment: 15 pages, 5 figure

Numerical study of rolling process on the plastic strain distribution in wire + arc additive manufactured Ti-6Al-4V

Wire+arc additive manufacturing (WAAM) is an additive manufacturing (AM) process that employs wire as the feedstock and an arc as energy source, to construct near net-shape components at high build rates. Ti-6Al-4V deposits typically form large columnar prior β grains that can grow through the entire component height, leading to anisotropy and lower mechanical properties, compared to the equivalent wrought alloy. Cold-working techniques such as rolling can be used to promote grain refinement in Ti-6Al-4V WAAM parts, thus increasing strength and eliminating anisotropy concomitantly. Additionally, rolling can be beneficial in terms of reduction of residual stress and distortion. The aim of this study is to illustrate the effect of rolling process parameters on the plastic deformation characteristics in Ti-6Al-4V WAAM structures. To produce a certain refinement of the microstructure, a certain amount of strain is typically required; thus suitable design guidelines for practical applications are needed. The effect of different rolling process parameters, in particular, rolling load and roller profile radius on the plastic strain distribution is investigated based on the finite element method. From a numerical point of view, the effect of the stiffness of the roller is investigated, e.g. deformable vs. rigid roller. Results indicate that for an identical rolling load, the deformable roller produces lower equivalent plastic strains due to its own elastic deformation. Additionally, a lower friction coefficient produces higher equivalent plastic strains near the top surface but, it has an insignificant effect on the plastic deformation further away from the top surface. However, numerically the computation time significantly increased for a higher friction coefficient. Larger roller profile radii lead to lower plastic strain near the top surface, but simultaneously had nearly no noticeable effect on plastic strains at deeper depth. In addition, the effect of interspace between rollers on the uniformity of the plastic strain during multi-pass rolling was investigated for a selected example. The results show that a higher uniform plastic strain distribution is obtained when the interspace between two rollers is equal to the residual width of the groove produced by a single rolling pas

disk laser welding of ti 6al 4v titanium alloy plates in t joint configuration

Abstract Titanium alloys are employed in a wide range of applications, ranging from aerospace to medicine. In particular, Ti-6Al-4V is the most common, thanks to an excellent combination of low density, high specific strength and corrosion resistance. Laser welding has been increasingly considered as an alternative to traditional techniques to join titanium alloys. An increase in penetration depth and a reduction of possible welding defects is indeed achieved; moreover a smaller grain size in the fused zone is benefited in comparison to either TIG and plasma arc welding, thus providing an increase in the tensile strength of the welded structures. The aim of this work is to study disk-laser welding of 3.2mm thick Ti-6Al-4V plates in T-joint configuration without using a filler wire, defining the influence of different process parameters. The issue concerning the clamping of the plates is discussed and a proper device is developed to carry out welds. A structured plan has to be carried out in order to characterize the process thus discussing the response variables. Power and welding speed are considered as crucial input variables since they determine the thermal input to the work-piece; furthermore, given the particular configuration analyzed, tilt angle is considered as a further variable, whereas focus position is fixed below the upper surface to obtain a full penetration. Welding beads have been first examined with a coordinate measuring machine to study distortions, and then from a morphological point of view. Eventually, Vickers microhardness testing has been conducted to discuss structural changes in fusion and heat affected zone due to welding thermal cycles

Operator approach to analytical evaluation of Feynman diagrams

The operator approach to analytical evaluation of multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration by parts method and the method of "uniqueness" (which is based on the star-triangle relation), can be drastically simplified by using this operator approach. To demonstrate the advantages of the operator method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless $\phi^3$ theory (analytical results for these diagrams are expressed in terms of multiple polylogarithms). It is shown how operator formalism can be applied to calculation of certain massive Feynman diagrams and investigation of Lipatov integrable chain model.Comment: 16 pages. To appear in "Physics of Atomic Nuclei" (Proceedings of SYMPHYS-XII, Yerevan, Armenia, July 03-08, 2006

Solutions of the sDiff(2)Toda equation with SU(2) Symmetry

We present the general solution to the Plebanski equation for an H-space that admits Killing vectors for an entire SU(2) of symmetries, which is therefore also the general solution of the sDiff(2)Toda equation that allows these symmetries. Desiring these solutions as a bridge toward the future for yet more general solutions of the sDiff(2)Toda equation, we generalize the earlier work of Olivier, on the Atiyah-Hitchin metric, and re-formulate work of Babich and Korotkin, and Tod, on the Bianchi IX approach to a metric with an SU(2) of symmetries. We also give careful delineations of the conformal transformations required to ensure that a metric of Bianchi IX type has zero Ricci tensor, so that it is a self-dual, vacuum solution of the complex-valued version of Einstein's equations, as appropriate for the original Plebanski equation.Comment: 27 page

Three-Dimensional Vertex Model in Statistical Mechanics, from Baxter-Bazhanov Model

We find that the Boltzmann weight of the three-dimensional Baxter-Bazhanov model is dependent on four spin variables which are the linear combinations of the spins on the corner sites of the cube and the Wu-Kadanoff duality between the cube and vertex type tetrahedron equations is obtained explicitly for the Baxter-Bazhanov model. Then a three-dimensional vertex model is obtained by considering the symmetry property of the weight function, which is corresponding to the three-dimensional Baxter-Bazhanov model. The vertex type weight function is parametrized as the dihedral angles between the rapidity planes connected with the cube. And we write down the symmetry relations of the weight functions under the actions of the symmetry group $G$ of the cube. The six angles with a constrained condition, appeared in the tetrahedron equation, can be regarded as the six spectrums connected with the six spaces in which the vertex type tetrahedron equation is defined.Comment: 29 pages, latex, 8 pasted figures (Page:22-29

Notes on a paper of Mess

These notes are a companion to the article "Lorentz spacetimes of constant curvature" by Geoffrey Mess, which was first written in 1990 but never published. Mess' paper will appear together with these notes in a forthcoming issue of Geometriae Dedicata.Comment: 26 page

On the Quantum Invariant for the Spherical Seifert Manifold

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that those modular forms have a direct connection with the polyhedral group by showing that the invariant polynomials of modular forms satisfy the polyhedral equations associated to $\Gamma$.Comment: 36 page

СРАВНИТЕЛЬНАЯ ХАРАКТЕРИСТИКА АНЕСТЕЗИОЛОГИЧЕСКОГО ОБЕСПЕЧЕНИЯ И ВИДОВ ОПЕРАТИВНОГО ВМЕШАТЕЛЬСТВА У ПАЦИЕНТОВ С АТЕРОСКЛЕРОТИЧЕСКИМ ПОРАЖЕНИЕМ БРАХИОЦЕФАЛЬНЫХ АРТЕРИЙ

Introduction. Atherosclerotic lesions of the branches of the aortic arch in 60% of cases is the cause of the development of ischemic stroke. As a radical means of preventing neurological disorders, carotid endarterectomy is used, since there is currently no effective drug treatment.Material and methods. This article presents a comparative characteristic of anesthesiological support and types of surgical intervention in 710 patients with atherosclerotic lesions of brachiocephalic arteries in the period from January 2010 to December 2017 in Department of Vascular Surgery at the Clinic of the Bashkir State Medical University. To perform this comparative characteristic, the patients were divided into 2 groups, depending on the time interval. Group 1 — patients operated from 2010 to 2013 (291 patients). Group 2 — patients operated from 2014 to 2017 (491 patients). In Group 1, operations were predominantly performed under regional anesthesia and classical carotid endarterectomy predominated over an eversion. In Group 2, operations were performed under general anesthesia, and here the overthe-top carotid endarterectomy predominated over the classical one. Patients were comparable in age, sex and risk of anesthesia and surgical intervention according to the ASA classification. The overall incidence of ischemic postoperative complications was 4.22%.Results. According to our data, the application of the eversion method of carotid endarterectomy under general anesthesia reduces the relative risk of neurological complications by 1.648 times (as in the 2nd group the technique of eversion carotid endarterectomy under general anesthesia was used). The use of general anesthesia with carotid endarterectomy allows to provide adequate gas exchange, manageability by hemodynamic parameters, absence of emotional reactions from the patient.Conclusion. Thus, at the present moment, our experience in treating patients with atherosclerotic lesions of the brachiocephalic arteries is approaching the optimal one, allowing us to achieve good results of carotid endarterectomy. Введение. Атеросклеротическое поражение ветвей дуги аорты в 60% случаев является причиной развития ишемического инсульта. Как радикальное средство профилактики неврологических нарушений применяется операция каротидная эндартерэктомия, поскольку эффективного медикаментозного лечения в настоящее время не существует.Материалы и методы. В данной статье представлена сравнительная характеристика анестезиологического обеспечения и видов оперативного вмешательства у 710 пациентов с атеросклеротическим поражением брахиоцефальных артерий в период с января 2010 г. по декабрь 2017 г. в отделении сосудистой хирургии Клиники Башкирского государственного медицинского университета. Для проведения данной сравнительной характеристики больные были разделены на две группы в зависимости от временного интервала: 1-я группа — пациенты, прооперированные с 2010 по 2013 г. (291 пациент); 2-я группа — пациенты, прооперированные с 2014 по 2017 г. (491 пациент). Пациенты были сопоставимы по возрасту, полу и риску анестезиологического и оперативного вмешательства согласно классификации ASA. В 1-й группе операции преимущественно выполнялись под регионарной анестезией и доминировала классическая каротидная эндартерэктомия над эверсионной. Во 2-й группе операции выполнялись под общей анестезией, и здесь доминировала эверсионная каротидная эндартерэктомия над классической. Общая частота ишемических послеоперационных осложнений составила 4,22%.Результаты. По нашим данным, применение эверсионной методики каротидной эндартерэктомии под общей анестезией с применением церебральной оксиметрии снижает относительный риск неврологических осложнений в 1,648 раза (так как во 2-й группе в основном применялась методика эверсионной каротидной эндартерэктомии под общей анестезией). Применение общей анестезии при КЭАЭ позволяет обеспечить адекватный газообмен, управляемость гемодинамическими показателями, отсутствие эмоциональных реакций со стороны пациента.Заключение. Таким образом, на настоящий момент наш опыт лечения пациентов с атеросклеротическим поражением брахиоцефальных артерий приближается к оптимальному, позволяет достичь хороших результатов проведения каротидной эндартерэктомии.