On O(1) contributions to the free energy in Bethe Ansatz systems: the exact g-function

We investigate the sub-leading contributions to the free energy of Bethe Ansatz solvable (continuum) models with different boundary conditions. We show that the Thermodynamic Bethe Ansatz approach is capable of providing the O(1) pieces if both the density of states in rapidity space and the quadratic fluctuations around the saddle point solution to the TBA are properly taken into account. In relativistic boundary QFT the O(1) contributions are directly related to the exact g-function. In this paper we provide an all-orders proof of the previous results of P. Dorey et al. on the g-function in both massive and massless models. In addition, we derive a new result for the g-function which applies to massless theories with arbitrary diagonal scattering in the bulk.Comment: 28 pages, 2 figures, v2: minor corrections, v3: minor corrections and references adde

The effect of project based learning on level of content knowledge of pre-vocational subject

Project based learning (PoBL) offers promise as an instructional method that engaged student in school grounded through their experience with authentically learning. Findings from previous research shows results of positive effects on student such as create active, interesting and meaningful learning. The PoBL can be used as a teaching method in building 21st century skills. This article reports the effect of PoBL towards students’ level of knowledge in the Integrated Living Skills subject. This subject is a pre-vocational subject and has offers to students of lower secondary school education. The quasi experimental design was employed with the pre and post group design of two groups, the control group of 30 respondents and the treatment group of 33 respondents. The intervention executed took about eight weeks while the instruments used consist of a set of pre-test and post-test for one topic called Project Designs and Production in the subject. The finding shows that there is significant difference in mean scores between the treatment and control group. As a conclusion, the PoBL method can be practiced by teachers in the field of technical and vocational education as well as be made into a pedagogical practice besides traditional teaching in improving students’ level of knowledge

Exactly solvable Wadati potentials in the PT-symmetric Gross-Pitaevskii equation

This note examines Gross-Pitaevskii equations with PT-symmetric potentials of the Wadati type: $V=-W^2+iW_x$. We formulate a recipe for the construction of Wadati potentials supporting exact localised solutions. The general procedure is exemplified by equations with attractive and repulsive cubic nonlinearity bearing a variety of bright and dark solitons.Comment: To appear in Proceedings of the 15 Conference on Pseudo-Hermitian Hamiltonians in Quantum Physics, May 18-23 2015, Palermo, Italy (Springer Proceedings in Physics, 2016

Quantum Sine(h)-Gordon Model and Classical Integrable Equations

We study a family of classical solutions of modified sinh-Gordon equation, $\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\ \re^{-2\eta}=0$with$p(z)=z^{2\alpha}-s^{2\alpha}$. We show that certain connection coefficients for solutions of the associated linear problem coincide with the$Q$-function of the quantum sine-Gordon$(\alpha>0)$or sinh-Gordon$(\alpha<-1)$ models.Comment: 35 pages, 3 figure

Form factors at strong coupling via a Y-system

We compute form factors in planar N=4 Super Yang-Mills at strong coupling. Namely we consider the overlap between an operator insertion and 2n gluons. Through the gauge/string duality these are given by minimal surfaces in AdS space. The surfaces end on an infinite periodic sequence of null segments at the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We derive set of functional equations for the cross ratios as functions of the spectral parameter. These equations are of the form of a Y-system. The integral form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of Yang-Yang functional. We consider a restricted set of operators which have small conformal dimension

Virtual reality pre-prosthetic hand training with physics simulation and robotic force interaction

Virtual reality (VR) rehabilitation systems have been proposed to enable prosthetic hand users to perform training before receiving their prosthesis. Improving pre-prosthetic training to be more representative and better prepare the patient for prosthesis use is a crucial step forwards in rehabilitation. However, existing VR platforms lack realism and accuracy in terms of the virtual hand and the forces produced when interacting with the environment. To address these shortcomings, this work presents a VR training platform based on accurate simulation of an anthropomorphic prosthetic hand, utilising an external robot arm to render realistic forces that the user would feel at the attachment point of their prosthesis. Experimental results with non-disabled participants show that training with this platform leads to a significant improvement in Box and Block scores compared to training in VR alone and a control group with no prior training. Results performing pick-and-place tasks with a wider range of objects demonstrates that training in VR alone negatively impacts performance, whereas the proposed platform has no significant impact on performance. User perception results highlight that the platform is much closer to using a physical prosthesis in terms of physical demand and effort, however frustration is significantly higher during training

Classical conformal blocks from TBA for the elliptic Calogero-Moser system

The so-called Poghossian identities connecting the toric and spherical blocks, the AGT relation on the torus and the Nekrasov-Shatashvili formula for the elliptic Calogero-Moser Yang's (eCMY) functional are used to derive certain expressions for the classical 4-point block on the sphere. The main motivation for this line of research is the longstanding open problem of uniformization of the 4-punctured Riemann sphere, where the 4-point classical block plays a crucial role. It is found that the obtained representation for certain 4-point classical blocks implies the relation between the accessory parameter of the Fuchsian uniformization of the 4-punctured sphere and the eCMY functional. Additionally, a relation between the 4-point classical block and the $N_f=4$, ${\sf SU(2)}$ twisted superpotential is found and further used to re-derive the instanton sector of the Seiberg-Witten prepotential of the $N_f=4$, ${\sf SU(2)}$ supersymmetric gauge theory from the classical block.Comment: 25 pages, no figures, latex+JHEP3, published versio

TBA for non-perturbative moduli spaces

Recently, an exact description of instanton corrections to the moduli spaces of 4d N=2 supersymmetric gauge theories compactified on a circle and Calabi-Yau compactifications of Type II superstring theories was found. The equations determining the instanton contributions turn out to have the form of Thermodynamic Bethe Ansatz. We explore further this relation and, in particular, we identify the contact potential of quaternionic string moduli space with the free energy of the integrable system and the Kahler potential of the gauge theory moduli space with the Yang-Yang functional. We also show that the corresponding S-matrix satisfies all usual constraints of 2d integrable models, including crossing and bootstrap, and derive the associated Y-system. Surprisingly, in the simplest case the Y-system is described by the MacMahon function relevant for crystal melting and topological strings.Comment: 25 pages, 1 figur

Categorification of skew-symmetrizable cluster algebras

We propose a new framework for categorifying skew-symmetrizable cluster algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with the action of a finite group G, we construct a G-equivariant mutation on the set of maximal rigid G-invariant objects of C. Using an appropriate cluster character, we can then attach to these data an explicit skew-symmetrizable cluster algebra. As an application we prove the linear independence of the cluster monomials in this setting. Finally, we illustrate our construction with examples associated with partial flag varieties and unipotent subgroups of Kac-Moody groups, generalizing to the non simply-laced case several results of Gei\ss-Leclerc-Schr\"oer.Comment: 64 page

MECHANICAL CONDITION ASSESSMENT OF TNB IN-SERVICE DISTRIBUTION TRANSFORMERS USING SWEEP FREQUENCY RESPONSE ANALYSIS (SFRA)

Distribution transformers in TNB (Tenaga Nasional Berhad) are exposed to the thermal and electrical stresses. Those stresses are effecting to the main mechanical active parts in transformer such as core and winding. In field, lightning strikes and cable faults may cause problem due to transformer core and winding. Sweep Frequency Response Analysis (SFRA) is an off-line diagnostic tool used for finding out any possible winding displacement or mechanical deterioration inside the transformer especially core and winding. SFRA diagnosis is made based on the comparison between two SFRA responses and any significant difference in low, middle and high frequency sub-bands region would potentially indicate mechanical or electrical problem to the winding and core of transformer. The aim of this paper is to assess the condition of TNB in-service distribution transformers by using SFRA method