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This paper studies the conductance on the universal homology covering space Z of 2D orbifolds in a strong magnetic field, thereby removing the rationality constraint on the magnetic field in earlier works (Avron et al 1994 Phys. Rev. Lett. 73 3255–3257; Mathai and Wilkin 2019 Lett. Math. Phys. 109 2473–2484; Prieto 2006 Commun. Math. Phys. 265 373–396) in the literature. We consider a natural Landau Hamiltonian on Z and study its spectrum which we prove consists of a finite number of low-lying isolated points and calculate the von Neumann degree of the associated holomorphic spectral orbibundles when the magnetic field B is large, and obtain fractional quantum numbers as the conductance. [ABSTRACT FROM AUTHOR]

In Bergweiler and Eremenko (2016 Proc. Am. Math. Soc. 144 2911–22), Bergweiler and Eremenko computed the number of critical points of the Green’s function on a torus by investigating the dynamics of a certain family of antiholomorphic meromorphic functions on tori. They also observed that hyperbolic maps are dense in this family of meromorphic functions in a rather trivial way. In this paper, we study the parameter space of this family of meromorphic functions, which can be written as antiholomorphic perturbations of Weierstrass Zeta functions. On the one hand, we give a complete topological description of the hyperbolic components and their boundaries, and on the other hand, we show that these sets admit natural parametrizations by associated dynamical invariants. This settles a conjecture, made in Lin and Wang (2010 Ann. Math. 172 911–54), on the topology of the regions in the upper half plane where the number of critical points of the Green’s function remains constant. [ABSTRACT FROM AUTHOR]

Inertial microfluidics systems carry a great importance for particle focusing and separation due to their simple configurations, robust structures, and precise high-throughput cell manipulation ability. In this paper, a novel microchannel geometry, called Sunflower, which is developed by superimposing two microchannel geometries, is presented. An empirical formula for normalized focus quality, which enables the quantitative comparison of particle focusing abilities of different microchannel geometries via fluorescent images, is introduced. In particle focusing experiments, focus quality enhancements ranging from 14% at 0.9 ml min−1 to 487% at 0.3 ml min−1 is observed. Besides, 99.57% of the 9.9 µm polystyrene particles are collected at a flow rate of 2.5 ml min−1 from a 60 µm wide outlet section, whose location within the microchannel width is specifically tailored. A clear, stable and narrow particle focus line is observed not only at an optimum flow rate, but also in a great range of flow rates between 0.3 ml min−1 and 2.5 ml min−1, offering great levels of flexibility and robustness against disturbances. Moreover, the novel microchannel geometry is tested with HL-60 cancer cell lines, and similar results are obtained in a great flow rate range without an observed effect on the cell’s viability. [ABSTRACT FROM AUTHOR]

This paper is the first part of a series which provides a systematic treatment of the space-filling curves of self-similar sets. In the present paper, we introduce a notion of linear graph-directed IFS (linear GIFS in short). We show that to construct a space-filling curve of a self-similar set, it amounts to exploring its linear GIFS structures. Compared to the previous methods, such as the L-system or recurrent set method, the linear GIFS approach is simpler, more rigorous and leads to further studies on this topic. We also propose a new algorithm for the beautiful visualization of space-filling curves. In a series of papers Dai et al (2015 arXiv:1511.05411 [math.GN]), Rao and Zhang (2015) and Rao and Zhang (2015), we investigate for a given self-similar set how to get ‘substitution rules’ for constructing space-filling curves, which was obscure in the literature. We solve the problem for self-similar sets of finite type, which covers most of the known results on constructions of space-filling curves. [ABSTRACT FROM AUTHOR]

The performance analysis of the generalized Carlson iterating process, which can realize the rational approximation of fractional operator with arbitrary order, is presented in this paper. The reasons why the generalized Carlson iterating function possesses more excellent properties such as self-similarity and exponential symmetry are also explained. K-index, P-index, O-index, and complexity index are introduced to contribute to performance analysis. Considering nine different operational orders and choosing an appropriate rational initial impedance for a certain operational order, these rational approximation impedance functions calculated by the iterating function meet computational rationality, positive reality, and operational validity. Then they are capable of having the operational performance of fractional operators and being physical realization. The approximation performance of the impedance function to the ideal fractional operator and the circuit network complexity are also exhibited. [ABSTRACT FROM AUTHOR]

We solve the Killing spinor equations for all near-horizon IIB geometries which preserve at least one supersymmetry. We show that generic horizon sections are eight-dimensional almost Hermitian spinc manifolds. Special cases include horizon sections with a Spin(7) structure and those for which the Killing spinor is pure. We also explain how the common sector horizons and the horizons with only 5-form flux are included in our general analysis. We investigate several special cases mainly focusing on the horizons with constant scalars admitting a pure Killing spinor and find that some of these exhibit a generalization of the 2-SCYT condition that arises in the horizons with 5-form fluxes only. We use this to construct new examples of near-horizon geometries with both 3-form and 5-form fluxes. [ABSTRACT FROM AUTHOR]

We use a broadband microbolometer array to measure the full three-dimensional (3D) terahertz (THz) intensity profile emitted from a twocolor femtosecond plasma and subsequently focused in a geometry useful for nonlinear spectroscopic investigations. Away from the immediate focal region we observe a sharp, conical intensity profile resembling a donut, and in the focal region the beam collapses to a central, Lorentz-shaped profile. The Lorentzian intensity profile in the focal region can be explained by considering the frequency-dependent spot size derived from measurements of the Gouy phase shift in the focal region, and the transition from the donut profile to a central peak is consistent with propagation of a Bessel-Gauss beam, as shown by simulations based on a recent transient photocurrent model (You et al 2012 Phys. Rev. Lett. 109 183902). We combine our measurements to the first full 3D visualization of the conical THz emission from the two-color plasma. [ABSTRACT FROM AUTHOR]

This paper reports a method to fabricate microlens arrays with a low processing temperature and a low pressure. The method is based on embossing a softened polymeric substrate over a mold with micro-hole arrays. Due to the effect of capillary and surface tension, microlens arrays can be formed. The embossing medium is CO2 gas, which supplies a uniform pressing pressure so that large-area microlens arrays can be fabricated. CO2 gas also acts as a solvent to plasticize the polymer substrates. With the special dissolving ability and isotropic pressing capacity of CO2 gas, microlens arrays can be fabricated at a low temperature (lower than Tg) and free of thermal-induced residual stress. Such a combined mechanism of dissolving and embossing with CO2 gas makes the fabrication of microlens arrays direct with complex processes, and is more compatible for optical usage. In the study, it is also found that the sag height of microlens changes when different CO2 dissolving pressure and time are used. This makes it easy to fabricate microlens arrays of different geometries without using different molds. The quality, uniformity and optical property of the fabricated microlens arrays have been verified with measurements of the dimensions, surface smoothness, focal length, transmittance and light intensity through the fabricated microlens arrays. [ABSTRACT FROM AUTHOR]

We study quasiconformal deformations and mixing properties of hyperbolic sets in the family of holomorphic correspondences zr  +  c, where r  >  1 is rational. Julia sets in this family are projections of Julia sets of holomorphic maps on which are skew-products when r is integer, and solenoids when r is non-integer and c is close to zero. Every hyperbolic Julia set in moves holomorphically. The projection determines a branched holomorphic motion with local (and sometimes global) parameterizations of the plane Julia set by quasiconformal curves. [ABSTRACT FROM AUTHOR]

We dimensionally reduce the bosonic sector of 10D Euclidean type IIA supergravity over a Calabi-Yau three-fold. The resulting theory describes the bosonic sector of 4D, Euclidean supergravity coupled to vector- and hyper-multiplets. We show that the scalar target manifold of the vector-multiplets is projective special para-Kähler, and is therefore of split signature, whereas the target manifold of the hyper-multiplets is (positive-definite) quaternionic Kähler. [ABSTRACT FROM AUTHOR]

For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a gradient network dynamical system is of an undirected cell graph, and we use tools from graph theory to deduce the general form of such functions, relating it to the topological structure of the graph defining the network. The coupling of pairs of dynamical systems cells is represented by edges of the graph, and from spectral graph theory we detect the existence and nature of equilibria of the gradient system from the critical points of the coupling function. In particular, we study fully synchronous and 2-state patterns of equilibria on regular graphs. These are two special types of equilibrium configurations for gradient networks. We also investigate equilibrium configurations of -invariant admissible functions on a ring of cells. [ABSTRACT FROM AUTHOR]

The short- and long-scale behaviour of tangled wave vortices (nodal lines) in random three-dimensional (3D) wave fields is studied via computer experiment. The zero lines are tracked in numerical simulations of periodic superpositions of 3D complex plane waves. The probability distribution of local geometric quantities such as curvature and torsion are compared to previous analytical and new Monte Carlo results from the isotropic Gaussian random wave model. We further examine the scaling and self-similarity of tangled wave vortex lines individually and in the bulk, drawing comparisons with other physical systems of tangled filaments. [ABSTRACT FROM AUTHOR]

Accounting for brachytherapy applicator attenuation is part of the recommendations from the recent report of AAPM Task Group 186. To do so, model based dose calculation algorithms require accurate modelling of the applicator geometry. This can be non-trivial in the case of irregularly shaped applicators such as the Fletcher Williamson gynaecological applicator or balloon applicators with possibly irregular shapes employed in accelerated partial breast irradiation (APBI) performed using electronic brachytherapy sources (EBS). While many of these applicators can be modelled using constructive solid geometry (CSG), the latter may be difficult and time-consuming. Alternatively, these complex geometries can be modelled using tessellated geometries such as tetrahedral meshes (mesh geometries (MG)). Recent versions of Monte Carlo (MC) codes Geant4 and MCNP6 allow for the use of MG. The goal of this work was to model a series of applicators relevant to brachytherapy using MG. Applicators designed for 192Ir sources and 50 kV EBS were studied; a shielded vaginal applicator, a shielded Fletcher Williamson applicator and an APBI balloon applicator.All applicators were modelled in Geant4 and MCNP6 using MG and CSG for dose calculations. CSG derived dose distributions were considered as reference and used to validate MG models by comparing dose distribution ratios.In general agreement within 1% for the dose calculations was observed for all applicators between MG and CSG and between codes when considering volumes inside the 25% isodose surface. When compared to CSG, MG required longer computation times by a factor of at least 2 for MC simulations using the same code. MCNP6 calculation times were more than ten times shorter than Geant4 in some cases.In conclusion we presented methods allowing for high fidelity modelling with results equivalent to CSG. To the best of our knowledge MG offers the most accurate representation of an irregular APBI balloon applicator. [ABSTRACT FROM AUTHOR]

In contrast to finite dimensions where disordered systems display multifractal statistics only at criticality, the tree geometry induces multifractal statistics for disordered systems also off criticality. For the Anderson tight-binding localization model defined on a tree of branching ratio K = 2 with N generations, we consider the Miller-Derrida scattering geometry (1994 J. Stat. Phys. 75 357), where an incoming wire is attached to the root of the tree, and where KN outcoming wires are attached to the leaves of the tree. In terms of the KN transmission amplitudes tj, the total Landauer transmission is T [?] [?]j|tj|2, so that each channel j is characterized by the weight wj = |tj|2/T. We numerically measure the typical multifractal singularity spectrum f(a) of these weights as a function of the disorder strength W and we obtain the following conclusions for its left termination point a+(W). In the delocalized phase W 0 and is associated with a moment index q+(W) > 1. At criticality, it vanishes a+(Wc) = 0 and is associated with the moment index q+(Wc) = 1. In the localized phase W > Wc, a+(W) = 0 is associated with some moment index q+(W) < 1. We discuss the similarities with the exact results concerning the multifractal properties of the directed polymer on the Cayley tree. [ABSTRACT FROM AUTHOR]