A Haar Wavelet Series Solution of Heat Equation with Involution

It is well known that the wavelets have widely applied to solve mathematical problems connected with the differential and integral equations. The application of the wavelets possess several important properties, such as orthogonality, compact support, exact representation of polynomials at certain degree and the ability to represent functions on different levels of resolution. In this paper, new methods based on wavelet expansion are considered to solve problems arising in approximation of the solution of heat equation with involution. We have developed new numerical techniques to solve heat equation with involution and obtained new approximative representation for solution of heat equations.

The topological line of ABJ(M) theory

We construct the one-dimensional topological sector of $$ \mathcal{N} $$ N = 6 ABJ(M) theory and study its relation with the mass-deformed partition function on S3. Supersymmetric localization provides an exact representation of this partition function as a matrix integral, which interpolates between weak and strong coupling regimes. It has been proposed that correlation functions of dimension-one topological operators should be computed through suitable derivatives with respect to the masses, but a precise proof is still lacking. We present non-trivial evidence for this relation by computing the two-point function at two-loop, successfully matching the matrix model expansion at weak coupling and finite ranks. As a by-product we obtain the two-loop explicit expression for the central charge cT of ABJ(M) theory. Three- and four-point functions up to one-loop confirm the relation as well. Our result points towards the possibility to localize the one-dimensional topological sector of ABJ(M) and may also be useful in the bootstrap program for 3d SCFTs.

ON COMPARISON OF 3D ISOGEOMETRIC TIMOSHENKO AND BERNOULLI BEAM FORMULATIONS

Application of isogeometric analysis (IGA) for curved beams is very convenient for its ability of exact representation of curved geometries. Several beam formulation has been presented since the introduction of IGA. In this paper, two different beam formulations are presented: Bernoulli beam formulation of A. M. Bauer et al. [1], and Timoshenko beam element introduced by G. Zhang et al. [2]. Both beam elements are implemented and their performance is documented on the fully threedimensionalexample of helicoidal spring.

Space–time VMS isogeometric analysis of the Taylor–Couette flow

The Taylor–Couette flow is a classical fluid mechanics problem that exhibits, depending on the Reynolds number, a range of flow patterns, with the interesting ones having small-scale structures, and sometimes even wavy nature. Accurate representation of these flow patterns in computational flow analysis requires methods that can, with a reasonable computational cost, represent the circular geometry accurately and provide a high-fidelity flow solution. We use the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization to address these computational challenges and to evaluate how the method and discretization perform under different scenarios of computing the Taylor–Couette flow. We conduct the computational analysis with different combinations of the Reynolds numbers based on the inner and outer cylinder rotation speeds, with different choices of the reference frame, one of which leads to rotating the mesh, with the full-domain and rotational-periodicity representations of the flow field, with both the convective and conservative forms of the ST-VMS, with both the strong and weak enforcement of the prescribed velocities on the cylinder surfaces, and with different mesh refinements. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the flow. The ST isogeometric discretization enables exact representation of the circular geometry and increased accuracy in the flow solution. In computations where the mesh is rotating, the ST/NURBS Mesh Update Method, with NURBS basis functions in time, enables exact representation of the mesh rotation, in terms of both the paths of the mesh points and the velocity of the points along their paths. In computations with rotational-periodicity representation of the flow field, the periodicity is enforced with the ST Slip Interface method. With the combinations of the Reynolds numbers used in the computations, we cover the cases leading to the Taylor vortex flow and the wavy vortex flow, where the waves are in motion. Our work shows that all these ST methods, integrated together, offer a high-fidelity computational analysis platform for the Taylor–Couette flow and for other classes of flow problems with similar features.

Temperature adjusted cross section libraries used for criticality calculations

The change in the temperature of the nuclear reactor components (fuel, moderator, coolant, and structural materials) is considered to be a significant source of reactivity variation. This change must be taken in account during criticality calculations for safety analysis of the reactor. Hence, the exact representation of temperature in the calculations is very important. In this paper, two PWR assemblies are simulated, solid 16 ⨯ 16 and annular 12 ⨯ 12 fuel assemblies. The infinite multiplication factor and its temperature dependent parameters are calculated for both fuel assemblies. Adjusted temperature dependent libraries are created using makxsf code to exactly represent the different temperature values used in the calculations. It is shown that the results obtained using adjusted cross section libraries are more reliable. The two fuel assembly types follow the same behavior despite the differences in their geometrical configuration. The introduction of annular fuel has a very small effect on the investigated neutronic parameters because the moderator to fuel ratio is preserved.

On non-canonical degrees of freedom

Non-canonical degrees of freedom provide one of the most promising routes towards characterising a range of important phenomena in condensed matter physics. Potential candidates include the pseudogap regime of the cuprates, heavy-fermion behaviour, and also indeed magnetically ordered systems. Nevertheless it remains an open question whether non-canonical algebras can in fact provide legitimate quantum degrees of freedom. In this paper we survey progress made on this topic, complementing distinct approaches so as to obtain a unified description. In particular we obtain a novel exact representation for a self-energy-like object for non-canonical degrees of freedom. We further make a resummation of density correlations to obtain analogues of the RPA and GW approximations commonly employed for canonical degrees of freedom. We discuss difficulties related to generating higher-order approximations which are consistent with conservation laws, which represents an outstanding issue. We also discuss how the interplay between canonical and non-canonical degrees of freedom offers a useful paradigm for organising the phase diagram of correlated electronic behaviour.

Virtual Reality in der Montageplanung/Virtual Reality in assembly planning – Determining the target time of manual assembly processes using virtual reality

Der Prozess der Sollzeitermittlung von Montageprozessen sollte möglichst effizient gestaltet werden und eine genaue Abbildung der realen Montagezeit erlauben. Neueste Technologien werden bereits ergänzend zu klassischen Methoden genutzt. Dieser Beitrag zeigt auf, dass Virtual Reality eine Möglichkeit zur Sollzeitermittlung ist. Dazu wurde ein Montageprozess in Virtual Reality nachgebildet und die gemessenen Zeiten denen der MTM-1-Methode gegenübergestellt.   The process of determining the target time of assembly processes should be designed as efficiently as possible and enable an exact representation of the real assembly time. Advanced technologies are already being used to complement classic methods. This article shows that virtual reality is one way to determine target times. For this purpose, a manual small equipment assembly process was simulated in virtual reality and the measured times were compared with those of the MTM-1 method.

Wave propagation in micromorphic anisotropic continua with an application to tetragonal crystals

We study the coupled macroscopic and lattice wave propagation in anisotropic crystals seen as continua with affine microstructure (or micromorphic). In the general case, we obtain qualitative information on the frequencies and the dispersion relations. These results are then specialized to crystals of the tetragonal point group for various propagation directions: exact representation for the acoustic and optic frequencies and for the coupled vibrations modes are obtained for propagation directions along the tetragonal c-axis.