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Unstable dimension variability is an extreme form of non-hyperbolic behavior that causes a severe shadowing breakdown of chaotic trajectories. This phenomenon can occur in coupled chaotic systems possessing symmetries, leading to an invariant attractor with riddled basins of attraction. We consider the coupling of two Lorenz-like systems, which exhibits chaotic synchronized and anti-synchronized states, with their respective basins of attraction. We demonstrate that these basins are riddled, in the sense that they verify both the mathematical conditions for their existence, as well as the characteristic scaling laws indicating power-law dependence of parameters. Our simulations have shown that a biased random-walk model for the log-distances to the synchronized manifold can accurately predict the scaling exponents near blowout bifurcations in this high-dimensional coupled system. The behavior of the finite-time Lyapunov exponents in directions transversal to the invariant subspace has been used as numerical evidence of unstable dimension variability. [ABSTRACT FROM AUTHOR]

Placing bluff bodies in a mixing channel is an important technique to enhance mixing. This paper numerically investigates the effects of transversal spacing and axial spacing of two bluff bodies on the outlet mixing efficiency (Mout), the pressure loss (ΔP), and the combined performance parameter η (the ratio of Mout to dimensionless ΔP) of fluid flow within mixing channels with dual bluff bodies having three cross-sectional shapes of circle, square, and sector with Reynolds numbers based on bluff body dimension Red = 20, 60, and 100. The study reveals that, at Red = 20, altering the spacing between the two bluff bodies in the mixing channel does not improve mixing but instead increases ΔP, leading to a decrease in η. At Red = 60 and 100, changing the transversal spacing and axial spacing in a certain range can effectively enhance mixing and improve the combined performance. There exists an optimal transversal spacing to maximize Mout and η. Furthermore, the mixing channel with sector-shaped dual bluff bodies exhibits the highest Mout and η among the three kinds of cross-sectional shapes. When Red = 60 and 100, η of the mixing channel with sector-shaped dual bluff bodies increases by 212% and 270% by the transversal offsetting compared to the case with zero transversal spacing and increases by 489% and 331% by the axial offsetting compared to the case with an axial spacing of 2 times the bluff body dimension. The present findings hold significant implications for the design optimization and performance improvement of mixers. [ABSTRACT FROM AUTHOR]

We provide a systematic treatment of boundaries based on subgroups K ⊆ G for the Kitaev quantum double D(G) model in the bulk. The boundary sites are representations of a * -subalgebra Ξ ⊆ D(G) and we explicate its structure as a quasi-Hopf * -algebra dependent on a choice of transversal R. We provide decomposition formulae for irreducible representations of D(G) pulled back to Ξ. As an application of our treatment, we study patches with boundaries based on K = G horizontally and K = {e} vertically and show how these could be used in a quantum computer using the technique of lattice surgery. More abstractly, we also provide explicitly the monoidal equivalence of the category of Ξ-modules and the category of G-graded K-bimodules and use this to prove that different choices of R are related by Drinfeld cochain twists. Examples include Sn−1 ⊂ Sn and an example related to the octonions where Ξ is also a Hopf quasigroup. [ABSTRACT FROM AUTHOR]

We study five-body central configurations. The three-body equilateral triangle Lagrange's central configuration and four-body equilateral tetrahedron Lehmann-Filhès's central configuration were generalized to an equilateral five-body central configuration in four dimensions. Our working tool is a coordinate system that had many useful properties in considering central configurations of three, four, and five bodies. From this equilateral solution, projecting to three dimensions, we compute concave and convex five-body central configurations of five different positive masses. We discover the possibility of geometric symmetry of these solutions when two of the masses are equal. Then we study the plane symmetric central configurations with a kite figure. This figure has three masses on the symmetry axis of the kite and two equal masses symmetrically placed on a transversal orthogonal line to the axis. Our parameters are now the masses and the distances along the axis of symmetry. The distances are measured with respect to the crossing point of the diagonals. In this paper, we find and solve a linear equation for these three masses in terms of the distances. We will draw an example of typical elliptic trajectories obeying the Newton equations of motion in such a kite central configuration. [ABSTRACT FROM AUTHOR]

We observe the presence of infinitely fine-scaled alternations within the performance landscape of reservoir computers aimed for chaotic data forecasting. We investigate the emergence of the observed structures by means of variations of the transversal stability of the synchronization manifold relating the observational and internal dynamical states. Finally, we deduce a simple calibration method in order to attenuate the thus evidenced performance uncertainty. [ABSTRACT FROM AUTHOR]

Conventional coil designs, such as helical and flat serpentine (FS) coils, are commonly employed for heat transfer applications due to their higher heat transfer performance and compactness. In the last few decades, chaotic coil designs have attracted the attention of a few researchers due to their superior thermohydraulic performance. In this paper, we present a novel and simple chaotic coil design termed the curved serpentine (CS-θ) coil, which is a modified version of the conventional FS coil. The straight tubes of length L in the FS coil are bent as arcs of radius R1 and subtended angle θ (i.e., L = R1 × θ), which are interconnected with U-bends of radius R2. The laminar flow of water through the CS-θ coil is numerically investigated, and the peaks and valleys in the local Nusselt number and friction factor at various axial locations are explained with the help of velocity and temperature contours and secondary flow patterns. The chaotic nature of flow through these coils is explained with the help of streamlines and transverse flow vectors, transversal intersection of the trajectories, and the Lyapunov spectrum. The thermohydraulic performance (η) of this coil is found superior to conventional FS and helical coils. It is found that the CS-θ coils, in which the flow is fully developed just before entering the U-bend, can achieve the best thermohydraulic performance. We also propose generalized correlations for predicting the average Nusselt number and friction factor in the CS-θ coils with a maximum deviation of ±10% and ±7.5%, respectively. [ABSTRACT FROM AUTHOR]

Fiber-based devices with advanced functionalities are emerging as promising solutions for various applications in flexible electronics and bioengineering. Multimaterial thermal drawing, in particular, has attracted strong interest for its ability to generate fibers with complex architectures. Thus far, however, the understanding of its fluid dynamics has only been applied to single material preforms for which higher order effects, such as the radial dependency of the axial velocity, could be neglected. With complex multimaterial preforms, such effects must be taken into account, as they can affect the architecture and the functional properties of the resulting fiber device. Here, we propose a versatile model of the thermal drawing of fibers, which takes into account a radially varying axial velocity. Unlike the commonly used cross section averaged approach, our model is capable of predicting radial variations of functional properties caused by the deformation during drawing. This is demonstrated for two effects observed, namely, by unraveling the deformation of initially straight, transversal lines in the preform and the dependence on the draw ratio and radial position of the in-fiber electrical conductivity of polymer nanocomposites, an important class of materials for emerging fiber devices. This work sets a thus far missing theoretical and practical understanding of multimaterial fiber processing to better engineer advanced fibers and textiles for sensing, health care, robotics, or bioengineering applications. [ABSTRACT FROM AUTHOR]

We report on the implementation of a pulsed optically pumped atomic clock based on a paraffin-coated cell. The relaxation times are measured, with the longitudinal relaxation time, T1 = 9.7 ± 0.4 ms, and the transversal relaxation time, T2 = 0.40 ± 0.03 ms. We demonstrated that the measured frequency stability of the clock is 3.9 × 10−13τ−1/2 (1 s ≤ τ ≤ 100 s) and reaches a value of 3.1 × 10−14 for τ = 1000 s, where τ is the averaging time. This is an unprecedented result for a paraffin-coated vapor cell clock, and it makes significant contributions toward improving the performance of the wall-coated vapor cell atomic clock. [ABSTRACT FROM AUTHOR]

We consider the isotropic or anisotropic XY spin chain in the presence of a transversal random magnetic field, with parameters given by random variables. It is shown that eigenfunction correlator localization of the corresponding effective one-particle Hamiltonian implies a uniform area law bound in expectation for the bipartite entanglement entropy of all eigenstates of the XY chain, i.e., a form of many-body localization at all energies. Here, entanglement with respect to arbitrary connected subchains of the chain can be considered. Applications where the required eigenfunction correlator bounds are known include the isotropic XY chain in random field as well as the anisotropic chain in strong or strongly disordered random field. [ABSTRACT FROM AUTHOR]

It is shown that usually used theoretical model for double-layer heterostructures as a pseudospin ferromagnet does not explain the observed two-dimensional spectrum. Its existence is possible when neglecting Coulomb interaction destroying two-dimensional structures and can be realized only in a strong magnetic field. That is connected also with the plain vortex lattices forming in strong magnetic fields due to thermodynamic instability. This model gives reasonable explanations of various observed effects depending on the filling of the corresponding bands. In particular in this work we show that in double-layer heterostructures a large interlayer conductance really observed can exist. [ABSTRACT FROM AUTHOR]