scholarly journals Lattice $$ \mathcal{N} $$ = 4 super Yang-Mills at strong coupling

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Simon Catterall ◽  
Joel Giedt ◽  
Goksu Can Toga
Keyword(s):  
Strong Coupling ◽  
Lattice Theory ◽  
Numerical Study ◽  
Lattice Action ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Sign Problem ◽  
Wide Range ◽  
Phase Out ◽  
Sign Problems

Abstract In this paper we present results from numerical simulations of $$ \mathcal{N} $$ N = 4 super Yang-Mills for two color gauge theory over a wide range of ’t Hooft coupling 0 < λ ≤ 30 using a supersymmetric lattice action [1]. Numerical study of this lattice theory has been stymied until recently by both sign problems and the occurrence of lattice artifact phases at strong coupling. We have recently developed a new action that appears capable of solving both problems. The resulting action possesses just SU(2) rather than U(2) gauge symmetry. By explicit computations of the fermion Pfaffian we present evidence that the theory possesses no sign problem and exists in a single phase out to arbitrarily strong coupling. Furthermore, preliminary work shows that the logarithm of the supersymmetric Wilson loop varies as the square root of the ’t Hooft coupling λ for large λ in agreement with holographic predictions.

scholarly journals Maximally supersymmetric Yang–Mills on the lattice

2017 ◽  
Vol 32 (36) ◽  
pp. 1747019 ◽  
Author(s):  
David Schaich ◽  
Simon Catterall
Keyword(s):  
Lattice Theory ◽  
Lattice Spacing ◽  
Recent Progress ◽  
Numerical Calculations ◽  
Static Potential ◽  
Lattice Action ◽  
Yang Mills ◽  
Preliminary Results ◽  
Sign Problem

We summarize recent progress in lattice studies of four-dimensional [Formula: see text] supersymmetric Yang–Mills theory and present preliminary results from ongoing investigations. Our work is based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, and we review a new procedure to regulate flat directions by modifying the moduli equations in a manner compatible with this supersymmetry. This procedure defines an improved lattice action that we have begun to use in numerical calculations. We discuss some highlights of these investigations, including the static potential and an update on the question of a possible sign problem in the lattice theory.

scholarly journals Strong coupling methods in QCD thermodynamics

2021 ◽  
Author(s):  
Owe Philipsen
Keyword(s):  
Monte Carlo ◽  
Strong Coupling ◽  
Chemical Potential ◽  
Yang Mills ◽  
Coupling Methods ◽  
Sign Problem ◽  
Monte Carlo Studies ◽  
Long Time ◽  
Scaling Region ◽  
Strong Coupling Expansions

AbstractFor a long time, strong coupling expansions have not been applied systematically in lattice QCD thermodynamics, in view of the success of numerical Monte Carlo studies. The persistent sign problem at finite baryo-chemical potential, however, has motivated investigations using these methods, either by themselves or combined with numerical evaluations, as a route to finite density physics. This article reviews the strategies, by which a number of qualitative insights have been attained, notably the emergence of the hadron resonance gas or the identification of the onset transition to baryon matter in specific regions of the QCD parameter space. For the simpler case of Yang–Mills theory, the deconfinement transition can be determined quantitatively even in the scaling region, showing possible prospects for continuum physics.

scholarly journals $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills thermodynamics to order λ2

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Qianqian Du ◽  
Michael Strickland ◽  
Ubaid Tantary
Keyword(s):  
Strong Coupling ◽  
Finite Temperature ◽  
Weak Coupling ◽  
Chemical Potential ◽  
Entropy Density ◽  
Thermal Mass ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Debye Mass ◽  
Infrared Divergences

Abstract We calculate the resummed perturbative free energy of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills in four spacetime dimensions (SYM4,4) through second order in the ’t Hooft coupling λ at finite temperature and zero chemical potential. Our final result is ultraviolet finite and all infrared divergences generated at three-loop level are canceled by summing over SYM4,4 ring diagrams. Non-analytic terms at $$ \mathcal{O} $$ O (λ3/2) and $$ \mathcal{O} $$ O (λ2 log λ) are generated by dressing the A0 and scalar propagators. The gauge-field Debye mass mD and the scalar thermal mass MD are determined from their corresponding finite-temperature self-energies. Based on this, we obtain the three-loop thermodynamic functions of SYM4,4 to $$ \mathcal{O} $$ O (λ2). We compare our final result with prior results obtained in the weak- and strong-coupling limits and construct a generalized Padé approximant that interpolates between the weak-coupling result and the large-Nc strong-coupling result. Our results suggest that the $$ \mathcal{O} $$ O (λ2) weak-coupling result for the scaled entropy density is a quantitatively reliable approximation to the scaled entropy density for 0 ≤ λ ≲ 2.

scholarly journals Exact 1/N expansion of Wilson loop correlators in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Wolfgang Mück
Keyword(s):  
Matrix Model ◽  
Wilson Loop ◽  
Model Solution ◽  
Wilson Loops ◽  
Combinatorial Formula ◽  
Expectation Value ◽  
Yang Mills ◽  
Hooft Coupling ◽  
The Matrix ◽  
Super Yang Mills Theory

Abstract Supersymmetric circular Wilson loops in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended to the more general case of two different loop contours, which is needed to discuss coincident loops with opposite orientations. A combinatorial formula representing the connected correlators of multiply wound Wilson loops in terms of the matrix model solution is derived. Two new results are obtained on the expectation value of the circular Wilson loop, the expansion of which into a series in 1/N and to all orders in the ’t Hooft coupling λ was derived by Drukker and Gross about twenty years ago. The connected correlators of two multiply wound Wilson loops with arbitrary winding numbers are calculated as a series in 1/N. The coefficient functions are derived not only as power series in λ, but also to all orders in λ by expressing them in terms of the coefficients of the Drukker and Gross series. This provides an efficient way to calculate the 1/N series, which can probably be generalized to higher-point correlators.

scholarly journals Strain Sensor via Wood Anomalies in 2D Dielectric Array

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 1022
Author(s):  
Rashid G. Bikbaev ◽  
Ivan V. Timofeev ◽  
Vasiliy F. Shabanov
Keyword(s):  
Higher Plants ◽  
Numerical Study ◽  
Reciprocal Lattice ◽  
Strain Sensing ◽  
Photonic Materials ◽  
Sensing Applications ◽  
Wide Range ◽  
Sensor Structure ◽  
Optical Behavior ◽  
Chlorophyll Absorption

Optical sensing is one of many promising applications for all-dielectric photonic materials. Herein, we present an analytical and numerical study on the strain-responsive spectral properties of a bioinspired sensor. The sensor structure contains a two-dimensional periodic array of dielectric nanodisks to mimic the optical behavior of grana lamellae inside chloroplasts. To accumulate a noticeable response, we exploit the collective optical mode in grana ensemble. In higher plants, such a mode appears as Wood’s anomaly near the chlorophyll absorption line to control the photosynthesis rate. The resonance is shown persistent against moderate biological disorder and deformation. Under the stretching or compression of a symmetric structure, the mode splits into a couple of polarized modes. The frequency difference is accurately detected. It depends on the stretch coefficient almost linearly providing easy calibration of the strain-sensing device. The sensitivity of the considered structure remains at 5 nm/% in a wide range of strain. The influence of the stretching coefficient on the length of the reciprocal lattice vectors, as well as on the angle between them, is taken into account. This adaptive phenomenon is suggested for sensing applications in biomimetic optical nanomaterials.

Numerical study of geometric morphing wings of the 1303 UCAV

2021 ◽  
pp. 1-17
Author(s):  
B. Nugroho ◽  
J. Brett ◽  
B.T. Bleckly ◽  
R.C. Chin
Keyword(s):  
Flight Control ◽  
Numerical Study ◽  
Aerodynamic Characteristics ◽  
Morphing Wing ◽  
Rolling Moment ◽  
Wide Range ◽  
Morphing Wings ◽  
Wing Geometry ◽  
Lift And Drag ◽  
Wing Morphing

ABSTRACT Unmanned Combat Aerial Vehicles (UCAVs) are believed by many to be the future of aerial strike/reconnaissance capability. This belief led to the design of the UCAV 1303 by Boeing Phantom Works and the US Airforce Lab in the late 1990s. Because UCAV 1303 is expected to take on a wide range of mission roles that are risky for human pilots, it needs to be highly adaptable. Geometric morphing can provide such adaptability and allow the UCAV 1303 to optimise its physical feature mid-flight to increase the lift-to-drag ratio, manoeuvrability, cruise distance, flight control, etc. This capability is extremely beneficial since it will enable the UCAV to reconcile conflicting mission requirements (e.g. loiter and dash within the same mission). In this study, we conduct several modifications to the wing geometry of UCAV 1303 via Computational Fluid Dynamics (CFD) to analyse its aerodynamic characteristics produced by a range of different wing geometric morphs. Here we look into two specific geometric morphing wings: linear twists on one of the wings and linear twists at both wings (wash-in and washout). A baseline CFD of the UCAV 1303 without any wing morphing is validated against published wind tunnel data, before proceeding to simulate morphing wing configurations. The results show that geometric morphing wing influences the UCAV-1303 aerodynamic characteristics significantly, improving the coefficient of lift and drag, pitching moment and rolling moment.

scholarly journals A Computational Study on the Role of Parameters for Identification of Thyroid Nodules by Infrared Images (and Comparison with Real Data)

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4459
Author(s):  
José R. González ◽  
Charbel Damião ◽  
Maira Moran ◽  
Cristina A. Pantaleão ◽  
Rubens A. Cruz ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thyroid Nodules ◽  
Numerical Study ◽  
Computational Study ◽  
Internal Heat ◽  
Heat Transfer Process ◽  
The Body ◽  
Physical Parameters ◽  
Infrared Sensors ◽  
Wide Range

According to experts and medical literature, healthy thyroids and thyroids containing benign nodules tend to be less inflamed and less active than those with malignant nodules. It seems to be a consensus that malignant nodules have more blood veins and more blood circulation. This may be related to the maintenance of the nodule’s heat at a higher level compared with neighboring tissues. If the internal heat modifies the skin radiation, then it could be detected by infrared sensors. The goal of this work is the investigation of the factors that allow this detection, and the possible relation with any pattern referent to nodule malignancy. We aim to consider a wide range of factors, so a great number of numerical simulations of the heat transfer in the region under analysis, based on the Finite Element method, are performed to study the influence of each nodule and patient characteristics on the infrared sensor acquisition. To do so, the protocol for infrared thyroid examination used in our university’s hospital is simulated in the numerical study. This protocol presents two phases. In the first one, the body under observation is in steady state. In the second one, it is submitted to thermal stress (transient state). Both are simulated in order to verify if it is possible (by infrared sensors) to identify different behavior referent to malignant nodules. Moreover, when the simulation indicates possible important aspects, patients with and without similar characteristics are examined to confirm such influences. The results show that the tissues between skin and thyroid, as well as the nodule size, have an influence on superficial temperatures. Other thermal parameters of thyroid nodules show little influence on surface infrared emissions, for instance, those related to the vascularization of the nodule. All details of the physical parameters used in the simulations, characteristics of the real nodules and thermal examinations are publicly available, allowing these simulations to be compared with other types of heat transfer solutions and infrared examination protocols. Among the main contributions of this work, we highlight the simulation of the possible range of parameters, and definition of the simulation approach for mapping the used infrared protocol, promoting the investigation of a possible relation between the heat transfer process and the data obtained by infrared acquisitions.

scholarly journals Scrambling in Yang-Mills

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Robert de Mello Koch ◽  
Eunice Gandote ◽  
Augustine Larweh Mahu
Keyword(s):  
Relaxation Time ◽  
Weak Coupling ◽  
Degrees Of Freedom ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Dilatation Operator ◽  
Super Yang Mills Theory

Abstract Acting on operators with a bare dimension ∆ ∼ N2 the dilatation operator of U(N) $$ \mathcal{N} $$ N = 4 super Yang-Mills theory defines a 2-local Hamiltonian acting on a graph. Degrees of freedom are associated with the vertices of the graph while edges correspond to terms in the Hamiltonian. The graph has p ∼ N vertices. Using this Hamiltonian, we study scrambling and equilibration in the large N Yang-Mills theory. We characterize the typical graph and thus the typical Hamiltonian. For the typical graph, the dynamics leads to scrambling in a time consistent with the fast scrambling conjecture. Further, the system exhibits a notion of equilibration with a relaxation time, at weak coupling, given by t ∼ $$ \frac{\rho }{\lambda } $$ ρ λ with λ the ’t Hooft coupling.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

2021 ◽  
pp. 095440622110272
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Litan Kumar Saha ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Characteristics ◽  
Wide Range

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

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