Nontrivial Component Research Articles

Polarization-Addressable Optical Movement of Plasmonic Nanoparticles and Hotspot Spin Vortices.

Spin-orbit coupling in nanoscale optical fields leads to the emergence of a nontrivial spin angular momentum component, transverse to the orbital momentum. In this study, we initially investigate how this spin-orbit coupling effect influences the dynamics in gold monomers. We observe that localized surface plasmon resonance induces self-generated transverse spin, affecting the trajectory of the nanoparticles as a function of the incident polarization. Furthermore, we investigate the spin-orbit coupling in gold dimers. The resonant spin momentum distribution is characterized by the unique formation of vortex and anti-vortex spin angular momentum pairs on opposite surfaces of the nanoparticles, also affecting the particle motion. These findings hold promise for various fields, particularly for the precision control in the development of plasmonic thrusters and the development of metasurfaces and other helicity-controlled system aspects. They offer a method for the development of novel systems and applications in the realm of spin optics.

General primitivity in the mapping class group

For [Formula: see text], let [Formula: see text] be the mapping class group of the closed orientable surface [Formula: see text] of genus [Formula: see text]. In this paper, we obtain necessary and sufficient conditions under which a given pseudo-periodic mapping class can be a root of another up to conjugacy. Using this characterization, the canonical decomposition of (non-periodic) mapping classes, and some known algorithms, we give an algorithm for determining the conjugacy classes of roots of arbitrary mapping classes. Furthermore, we derive realizable bounds on the degrees of roots of pseudo-periodic mapping classes in [Formula: see text], the Torelli group, the level-[Formula: see text] subgroup of [Formula: see text], and the commutator subgroup of [Formula: see text]. In particular, we show that the highest possible (realizable) degree of a root of a pseudo-periodic mapping class [Formula: see text] is [Formula: see text], where [Formula: see text] is a unique positive integer associated with the conjugacy class of [Formula: see text]. Moreover, this bound is realized by a root of a power of a Dehn twist about a separating curve of genus [Formula: see text] in [Formula: see text], where [Formula: see text]. Finally, for [Formula: see text], we show that any pseudo-periodic mapping class having a nontrivial periodic component that is not the hyperelliptic involution, normally generates [Formula: see text]. Consequently, we establish that [Formula: see text] is normally generated by a root of bounding pair map or a root of a nontrivial power of a Dehn twist.

Relative magnetic helicity in multiply connected domains

Magnetic helicity is a conserved quantity of ideal magnetohydrodynamics (MHD) that is related to the topology of the magnetic field, and is widely studied in both laboratory and astrophysical plasmas. When the magnetic field has a non-trivial normal component on the boundary of the domain, the classical definition of helicity must be replaced by relative magnetic helicity. The purpose of this work is to review the various definitions of relative helicity and to show that they have a common origin—a general definition of relative helicity in multiply connected domains. We show that this general definition is both gauge-invariant and is conserved in time under ideal MHD, subject only to closed and line-tied boundary conditions. Other, more specific, formulae for relative helicity, that are used frequently in the literature, are shown to follow from the general expression by imposing extra conditions on the magnetic field or its vector potential.

On the asymptotic behavior of a size-structured model arising in population dynamics

We study the asymptotic behavior of a semilinear size-structured population model withdelay when the nonlinearity is small in some sense. The novelty in this work is that theoperator governing the linear part of the equation does not generate a compact semigroupunlike in the results present in literature. In such a case the spectrum does not consist whollyof eigenvalues but also has a non-trivial component called Browder’s essential spectrum. Toovercome the lack of compactness, we give a localization of Browder’s essential spectrum of theoperator governing the linear part and we use the Perron-Frobenius spectral analysis adaptedto semigroups of positive operators in Banach lattices to investigate the long time behavior ofthe system.Keywords: Perron-Frobenius, positive operators, structured population models, Browder’sessential spectrum, asymptotic behavior, semigroups of operatorsAMS Subject Classifications: 35B40, 35R10, 47D06.

The Simplest Unlimited-Player Game of Skill

The Least Unique Positive Integer game (LUPI) is among the simplest games that can be played by any number of players, N > 2, and has a nontrivial strategic component. In LUPI, players try to pick the smallest positive integer nobody else picks. Despite its simplicity, the game was not widely known until fairly recently. It was actually offered as a state run lottery game in Sweden in 2007, but players collaborated, and the game was quickly stopped. LUPI has also been proposed as the basis for a reverse auction system, and here it is proposed as a “party game”. The Nash equilibrium for the game has been previously worked out in the case where the numbers of players that make each choice are independent Poisson random variables, an assumption that can often be justified when N is large. Here we summarize previous work and derive a number of interesting new results on Nash equilibria when N is small, and when N is large using the Poisson assumption. We also investigate whether the Nash equilibrium strategies for LUPI games are evolutionary stable strategies. Finally, we look at cheating strategies for LUPI and devise ways to make it harder to cheat.

Smooth generalized interval exchange transformations with wandering intervals, from explicit derived from pseudo-Anosov maps

Starting from any pseudo-Anosov map ϕ on a surface of genus , we construct explicitly a family of Derived from pseudo-Anosov maps f by adapting the construction of Smale’s derived from Anosov maps on the two-torus. This is done by perturbing ϕ at some fixed points. We first consider perturbations at every conical fixed point and then at regular fixed points. We establish the existence of a measure µ, supported by the non-trivial unique minimal component of the stable foliation of f, with respect to which f is mixing. In the process, we construct a uniquely ergodic generalized interval exchange transformation (GIET) with a wandering interval that is semi-conjugated to a self-similar interval exchange transformation. This GIET is obtained as the Poincaré map of a flow renormalized by f which parametrizes stable foliation. When f is , the flow and the GIET are .

Parameterized algorithms for generalizations of Directed Feedback Vertex Set

The Directed Feedback Vertex Set (DFVS) problem takes as input a directed graph G and seeks a smallest vertex set S that hits all cycles in G. This is one of Karp’s 21 NP-complete problems. Resolving the parameterized complexity status of DFVS was a long-standing open problem until Chen et al. (2008) showed its fixed-parameter tractability via a 4kk!nO(1)-time algorithm, where k=|S|.Here we show fixed-parameter tractability of two generalizations of DFVS: •Find a smallest vertex set S such that every strong component of G−S has size at most s: we give an algorithm solving this problem in time 4k(ks+k+s)!⋅nO(1). This generalizes an algorithm by Xiao (2017) for the undirected version of the problem.•Find a smallest vertex set S such that every non-trivial strong component of G−S is 1-out-regular: we give an algorithm solving this problem in time 2O(k3)⋅nO(1). We also solve the corresponding arc versions of these problems by fixed-parameter algorithms.

Chern currents of coherent sheaves

Given a finite locally free resolution of a coherent analytic sheaf $\mathcal F$, equipped with Hermitian metrics and connections, we construct an explicit current, obtained as the limit of certain smooth Chern forms of $\mathcal F$, that represents the Chern class of $\mathcal F$ and has support on the support of $\mathcal F$. If the connections are $(1,0)$-connections and $\mathcal F$ has pure dimension, then the first nontrivial component of this Chern current coincides with (a constant times) the fundamental cycle of $\mathcal F$. The proof of this goes through a generalized Poincar\'e-Lelong formula, previously obtained by the authors, and a result that relates the Chern current to the residue current associated with the locally free resolution.

Fractional Cocoloring of Graphs

The cochromatic number Z(G) of a graph G is the fewest number of colors needed to color the vertices of G so that each color class is a clique or an independent set. In a fractional cocoloring of G a non-negative weight is assigned to each clique and independent set so that for each vertex v, the sum of the weights of all cliques and independent sets containing v is at least one. The smallest total weight of such a fractional cocoloring of G is the fractional cochromatic number \(Z_f(G)\). In this paper we prove results for the fractional cochromatic number \(Z_f(G)\) that parallel results for Z(G) and the well studied fractional chromatic number \(\chi _f{(G)}\). For example \(Z_f(G)=\chi _f(G)\) when G is triangle-free, except when the only nontrivial component of G is a star. More generally, if G contains no k-clique, then \(Z_f(G)\le \chi _f(G)\le Z_f(G)+R(k,k)\), where R(k, k) is the minimum integer n such that every n-vertex graph has a k-clique or an independent set of size k. Moreover, every graph G with \(\chi _f(G)=m\) contains a subgraph H with \(Z_f(H)\ge (\frac{1}{4} - o(1))\frac{m}{\log _2 m}\). We also prove that the maximum value of \(Z_f(G)\) over all graphs G of order n is \(\varTheta (n/\log n)\), and the maximum over all graphs embedded on an orientable surface of genus g is \(\varTheta (\sqrt{g} / \log g)\).

Neighborhood Conditions for Super-λ′ Digraphs

Restricted arc-connectivity is a more refined network reliability index than arc-connectivity. An arc subset [Formula: see text] of a strong digraph [Formula: see text] is a restricted arc-cut of [Formula: see text] if [Formula: see text] has a non-trivial strong component [Formula: see text] such that [Formula: see text] contains an arc. The restricted arc-connectivity is the minimum cardinality over all restricted arc-cuts of [Formula: see text]. A strong digraph is super-[Formula: see text] if its restricted arc-connectivity is maximal and the number of its minimum restricted arc-cuts is minimal. In this paper, we present some neighborhood conditions for a digraph to be super-[Formula: see text].

On the low-dimensional cohomology groups of the IA-automorphism group of the free group of rank three

AbstractIn this paper, we study the structure of the rational cohomology groups of the IA-automorphism group$\mathrm {IA}_3$of the free group of rank three by using combinatorial group theory and representation theory. In particular, we detect a nontrivial irreducible component in the second cohomology group of$\mathrm {IA}_3$, which is not contained in the image of the cup product map of the first cohomology groups. We also show that the triple cup product of the first cohomology groups is trivial. As a corollary, we obtain that the fourth term of the lower central series of$\mathrm {IA}_3$has finite index in that of the Andreadakis–Johnson filtration of$\mathrm {IA}_3$.

Structure-preserving reduced basis methods for Poisson systems

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with a Poisson manifold structure which encodes the physical properties, symmetries, and conservation laws of the dynamics. The goal is to design reduced basis methods for the general state-dependent degenerate Poisson structure based on a two-step approach. First, via a local approximation of the Poisson tensor, we split the Hamiltonian dynamics into an almost part and the trivial evolution of the Casimir invariants. Second, canonically symplectic reduced basis techniques are applied to the nontrivial component of the dynamics, preserving the local Poisson tensor kernel exactly. The global Poisson structure and the conservation properties of the phase flow are retained by the reduced model in the constant-valued case and up to errors in the Poisson tensor approximation in the state-dependent case. A priori error estimates for the solution of the reduced system are established. A set of numerical simulations is presented to corroborate the theoretical findings.

Maximal moments and uniform modulus of continuity for stable random fields

In this work, we provide sharp bounds on the rate of growth of maximal moments for stationary symmetric stable random fields when the underlying nonsingular group action (or its restriction to a suitable lower rank subgroup) has a nontrivial dissipative component. We also investigate the relationship between this rate of growth and the path regularity properties of self-similar stable random fields with stationary increments, and establish uniform modulus of continuity of such fields. In the process, a new notion of weak effective dimension is introduced for stable random fields and is connected to maximal moments and path properties.

Derived categories of quintic del Pezzo fibrations

We provide a semiorthogonal decomposition for the derived category of fibrations of quintic del Pezzo surfaces with rational Gorenstein singularities. There are three components, two of which are equivalent to the derived categories of the base and the remaining non-trivial component is equivalent to the derived category of a flat and finite of degree 5 scheme over the base. We introduce two methods for the construction of the decomposition. One is the moduli space approach following the work of Kuznetsov on the sextic del Pezzo fibrations and the components are given by the derived categories of fine relative moduli spaces. The other approach is that one can realize the fibration as a linear section of a Grassmannian bundle and apply homological projective duality.

Transferring Orbital Angular Momentum to an Electron Beam Reveals Toroidal and Chiral Order

Orbital angular momentum and torque transfer play central roles in a wide range of magnetic textures and devices including skyrmions and spin-torque electronics(1-4). Analogous topological structures are now also being explored in ferroelectrics, including polarization vortex arrays in ferroelectric/dielectric superlattices(5). Unlike magnetic toroidal order, electric toroidal order does not couple directly to linear external fields. To develop a mechanism that can control switching in polarization vortices, we utilize a high-energy electron beam and show that transverse currents are generated by polar order in the ballistic limit. We find that the presence of an electric toroidal moment in a ferro-rotational phase transfers a measurable torque and orbital angular momentum to the electron beam. Furthermore, we find that the complex polarization patterns, observed in these heterostructures, are microscopically chiral with a non-trivial axial component of the polarization. This chirality opens the door for the coupling of ferroelectric and optical properties.

The roles of social economic status and undernutrition in regional disparities of the under‐five mortality rate in Vietnam

From 2005 to 2017, the prevalence of mortality in Vietnamese children under five years old showed large regional disparities. In 2017, mortality in the wealthiest region was 12.6‰, whereas the most disadvantaged region it was three times as high, at 36‰. This study aims to identify factors affecting regional disparities of the under-five mortality rate (U5MR) in Vietnam. We applied Structural Equation Modelling to estimate the degree and the pathway through which undernutrition and socio-economic status (SES) contributed to the under-five mortality disparities. SES is estimated as a common latent factor of three socio-economic measures, that is, education, poverty and income. The direct effect of SES on U5MR is at 2.16 through the underweight pathway, which is 5 times higher than the effect of underweight on U5MR. Through the stunting channel, this direct impact is 1.43, nearly twice as high as the impact of the stunting rate. SES also has an indirect effect on U5MR through these undernutrition pathways. In total, we estimate that an increase in SES index will make the U5MR increase by 2.73‰. Among the three indicators of SES, poverty conveys the strongest signal of a considerable change in SES, thus to a subsequent change in U5MR. Among two types of undernutrition, the effect of stunting on U5MR is dominant, more than 3 times as high as that of underweight. These findings have important implications for socio-economic and health interventions: those that strongly focus on the reduction of regional poverty and stunting rates would be effective in bridging the regional gap in the U5MR in Vietnam.

Čech systems that induce approximate inverse systems

In previous work we showed that if a paracompact Hausdorff space contains a nontrivial component, then none of the Čech systems of the nerves of its open covers can be an approximate (inverse) system. This extended a theorem of the first author who, in answering a question of S. Mardešić, proved this result in the restricted case that the given Hausdorff space was arc-like (and hence is nontrivial, compact and connected). We will demonstrate that the same is true for a nonempty discrete space: none of the Čech systems of the nerves of its open covers can be an approximate (inverse) system. In our main theorem, we are going to show in contradistinction that the completely opposite phenomenon occurs in the case that the space in question is strongly 0-dimensional (meaning that it has covering dimension 0) and has a limit point by proving that at least one of its Čech systems can support the structure of an approximate system. We will also show that such a space can be written as the inverse limit, in the classical sense, of an inverse system of discrete spaces.

Topographic and coastline influences on surf Eddies

Rip currents arise from the momentum flux associated with depth-induced breaking of incident surface gravity waves on beaches with irregular bottom topography. In 3D simulations with an idealized topographic configuration, uniform density, and a steady incident wave field, a striking enhancement of transient surf eddy variability occurs over irregular topography compared to smooth topography, especially at nearly normal incident wave angles. Alternatively, with highly oblique incident waves, transient shear instability is observed over smooth topography whereas for irregular topography, standing rip eddies are generated. In the presence of larger-scale coastline variations, mega-rip circulations emerge, and they are especially strong for embayments. In all cases with significant transient surf-eddy activity, the eddy-induced mean horizontal transport is a non-trivial component of the total mean transport, and sometimes it is much larger than the gravity-wave Stokes drift. Typically the transport by the eddy-induced flow partially cancels the Eulerian transport by the time- and/or alongshore-averaged currents, but not by enough to reverse the “residual” pattern of total transport.

The low fee entry strategy and first mover advantage in the ETF market

Academic literature struggles to explain investors’ attitude towards fees and expenses charged by mutual funds. In general, investors have been found to exhibit a puzzling lack of interest in this non-trivial component of their total return, raising questions of rationality of real-world investor behavior. An emergence of exchange-traded funds (ETFs), their rapid proliferation in the past decades and distinct features, such as more simple expense structure, present a valuable opportunity to contribute to the debate surrounding the pricing of funds. To better understand the expense policy/fund flows dynamics, the authors first test a conjecture that later entrants in the ETF markets face a disadvantage in competition for fund flows. Then, they test whether competitive pressure can be successfully overcome by lowering expenses charged to ETF investors. The results suggest that, though it is not necessary to be a first entrant in a fund category to enjoy competitive advantage, an earlier market entry is beneficial for attracting fund flows. It is also found that later entrants’ to the ETF market successfully use the strategy of reducing their expense ratios. Firms with lower net expense ratios obtain greater investment, as evidenced by greater capitalization and market share, supporting our intuition that investors may acknowledge the merits of low-cost ETFs.

Environmental Gating and Galvanic Effects in Single Crystals of Organic-Inorganic Halide Perovskites.

Understanding the impact of environmental gaseous on the surface of organometal halide perovskites (OMHPs) couples to the electronic and ionic transport is critically important. Here, we explore the transport behavior and origins of the gas sensitivity in MAPbBr3 single crystals (SCs) devices using impedance spectroscopy and current relaxation measurements. Strong resistive response occurs when crystals are exposed to different environments. It was shown that SC response to the environment is extremely different at the surface as compared to the bulk due to the disorder surface chemistry. The nonlinear transport properties studied using ultrafast Kelvin probe force microscopy (G-KPFM) to unravel spatio-temporal charge dynamics at SC/electrode interface. The relaxation processes observed in pulse relaxation and G-KPFM measurements along with gas sensitivity of crystals suggest the presence of a triple-phase boundary between environment, electrode, and crystal. Results indicate that the environment is a nontrivial component in the operation of OMHP devices which is reminiscent of fuel cell systems. Furthermore, the triple-phase boundary can play a significant role in the transport properties of OMHPs due to the possibility of the redox processes coupled to the concentration of bulk ionic species. Although instrumental for understanding the device characteristics of perovskites, our studies suggest a new opportunity of coupling the redox chemistry of the Br2-Br- pair that defines the bulk ionic conductivity of MAPbBr3 with the redox chemistry of gaseous (or liquid) environment via a suitable electrocatalytic system to enable new class of energy storage devices and gas sensors.