Search

We study the strict convexity of the energy function of harmonic maps at their critical points from a Riemann surface to a Riemann surface, or to the product of negatively curved surfaces. When the target is a Riemann surface and when the map is of nonzero degree, we obtain a precise formula for the second derivative of the energy function along a Weil–Petersson geodesic, which implies that the energy function is strictly convex at its critical points. When the target is the product of two surfaces where each projection of the harmonic map is homotopic to a covering map, we also prove the strict convexity of the associated energy function. As an application we prove that the energy function has a unique critical point in these cases. [ABSTRACT FROM AUTHOR]

We obtain a weak formulation of the stationarity condition for the half Dirichlet energy, which can be expressed in terms of a fractional quantity, related to the trace of the Hopf differential of the harmonic extension of the original map. As an application we show that conformal harmonic maps from the disc are precisely the harmonic extensions of stationary points of the half Dirichlet energy on the circle. We also derive a Noether theorem and a Pohozaev identity for stationary points of the half Dirichlet energy. [ABSTRACT FROM AUTHOR]

Let Mn be an embedded closed submanifold of ℝk+1 or a smooth bounded domain in ℝn, where n ≥ 3. We show that the local smooth solution to the heat flow of self-induced harmonic map will blow up at a finite time, provided that the initial map u0 is in a suitable nontrivial homotopy class with energy small enough. [ABSTRACT FROM AUTHOR]

We investigate weighted Lebesgue space estimates for the Bergman projection on a simply connected planar domain via the domain's Riemann map. We extend the bounds which follow from a standard change-of-variable argument in two ways. First, we provide a regularity condition on the Riemann map, which turns out to be necessary in the case of uniform domains, in order to obtain the full range of weighted estimates for the Bergman projection for weights in a Békollè-Bonami-type class. Second, by slightly strengthening our condition on the Riemann map, we obtain the weighted weak-type (1,1) estimate as well. Our proofs draw on techniques from both conformal mapping and dyadic harmonic analysis. [ABSTRACT FROM AUTHOR]

Accurate extraction of Seasonally Inundated Area (SIA) is pivotal for precise delineation of Flood Inundation Area (FIA). Current methods predominantly rely on Water Inundation Frequency (WIF) to extract SIA, which, due to the lack of analysis of dynamic surface water changes, often yields less accurate and robust results. This significantly hampers the rapid and precise mapping of FIA. In the study, based on the Harmonic Models constructed from Long Time-series Surface Water (LTSW) dynamics, an SIA extraction approach (SHM) was introduced to enhance their accuracy and robustness, thereby improving flood mapping. The experiments were conducted in Poyang Lake, a region characterized by active hydrological phenomena. Sentinel-1/2 remote sensing data were utilized to extract LTSW. Harmonic analysis was applied to the LTSW dataset, using the amplitude terms in the harmonic model to characterise the frequency of variation between land and water for the surface units, thus extracting the SIAs. The results reveal that the harmonic model parameters are capable of portraying SIA. In comparison to the commonly used WIF thresholding method for SIA extraction, the SHM approach demonstrates superior accuracy and robustness. Leveraging the SIA extracted through SHM, a higher level of accuracy in FIA extraction is achieved. Overall, the SHM offers notable advantages, including high accuracy, automation, and robustness. It offers reliable reference water extents for flood mapping, especially in areas with active and complex hydrological dynamics. SHM can play a crucial role in emergency response to flood disasters, providing essential technical support for natural disaster management and related departments. [ABSTRACT FROM AUTHOR]

Given a surface M and a fixed conformal class c one defines ƒk.M; c/to be the supremum of the k-th nontrivial Laplacian eigenvalue over all metrics g 2 c of unit volume. It has been observed by Nadirashvili that the metrics achieving ƒk.M; c/are closely related to harmonic maps to spheres. In the present paper, we identify ƒ1.M; c/and ƒ2.M; c/with min-max quantities associated to the energy functional for sphere-valued maps. As an application, we obtain several new eigenvalue bounds, including a sharp isoperimetric inequality for the first two Steklov eigenvalues. This characterization also yields an alternative proof of the existence of maximal metrics realizing ƒ1.M; c/, ƒ2.M; c/, and moreover allows us to obtain a regularity theorem for maximal Radon measures satisfying a natural compactness condition. [ABSTRACT FROM AUTHOR]

The primary objective of this study is to examine harmonic and generalized magnetic vector fields as mappings from an anti-paraKählerian manifold to its associated tangent bundle, endowed with a ciconia metric. Initially, the conditions under which a vector field is harmonic (or magnetic) concerning a ciconia metric are investigated. Subsequently, the mappings between any given Riemannian manifold and the tangent bundle of an anti-paraKählerian manifold are explored. The paper delves into identifying the circumstances under which vector fields exhibit harmonicity or magnetism within the framework of a ciconia metric. Additionally, it explores the relationships between specific harmonic and magnetic vector fields, particularly emphasizing their behaviour under conformal transformations of metrics. [ABSTRACT FROM AUTHOR]

In response to economic and environmental challenges like sea-level rise, salinity intrusion, groundwater extraction, sand mining, and sinking delta phenomena, the demand for solutions to adapt to changing conditions in riverine environments has increased significantly. High-quality analyses of land use and land cover (LULC) dynamics play a critical role in addressing these challenges. This study introduces a novel high-spatial resolution satellite-based approach to identify sub-seasonal LULC dynamics in the Mekong River Delta (MRD), employing a three-year (2021–2023) Sentinel-1 and Sentinel-2 satellite data time series. The primary obstacle is discerning detailed vegetation dynamics, particularly the seasonality of rice crops, answered through quantile mapping, harmonic regression with Fourier transform, and phenological metrics as inputs to a random forest machine learning classifier. Due to the substantial data volume, Google's cloud computing platform Earth Engine was utilized for the analysis. Furthermore, the study evaluated the relative significance of various input features. The overall accuracy of the classification is 82.6% with a kappa statistic of 0.81, determined using comprehensive reference data collected in Vietnam. While the purely pixel-based approach has limitations, it proves to be a viable method for high-spatial resolution satellite image time series classification of the MRD. [ABSTRACT FROM AUTHOR]

In this paper, we first obtain a refined version of the Bohr inequality of norm-type for holomorphic mappings with lacunary series on the polydisk in $ \mathbb {C}^n $ C n under some restricted conditions. Next, we determine the refined version of the Bohr inequality for holomorphic functions defined on a balanced domain G of a complex Banach space X and take values in the unit disk $ \mathbb {D} $ D . Furthermore, as a consequence of one of these results, we obtain a refined version of the Bohr-type inequality for harmonic functions $ f=h+\bar {g} $ f = h + g ¯ defined on a balanced domain $ G\subset X $ G ⊂ X. All the results are proved to be sharp. [ABSTRACT FROM AUTHOR]

In a geometrically non-linear Cosserat model for micro-polar elastic solids, we prove that critical points of the Cosserat energy functional with an arbitrary large (finite) number of singularities do exist, whereas Cosserat energy minimizers are known to be locally Hölder continuous. To reach that goal, we first develop a technique to insert dipole pairs of singularities into smooth maps while controlling the amount of Cosserat energy needed to do so. We then use this method to force an arbitrary number of singular points into (weak) Cosserat-elastic solids by prescribing smooth boundary data. The boundary data themselves are given in such a way, that they contain no topological obstruction to regularity. Throughout this paper, we often exploit connections between harmonic maps and Cosserat-elastic solids, so that we are able to adapt and incorporate ideas of R. Hardt and F.-H. Lin for harmonic maps with singularities, as well as of F. Béthuel for dipole pairs of singularities. [ABSTRACT FROM AUTHOR]

This note is devoted to developing Morrey regularity theory for the following system of Rivière \begin{equation*} -\Delta u=\Omega \cdot \nabla u+f \qquad \text {in }B^{2}, \end{equation*} under the assumption that f belongs to some Morrey space. Our results extend the L^p regularity theory of Sharp and Topping [Trans. Amer. Math. Soc. 365 (2013), pp. 2317–2339], and also generalize a Hölder continuity result of Wang [Calc. Var. Partial Differential Equations 56 (2017), Paper No. 23, 24] on harmonic mappings. Potential applications of our results are also possible in second order conformally invariant geometrical problems as that of Wang [Calc. Var. Partial Differential Equations 56 (2017), Paper No. 23, 24]. [ABSTRACT FROM AUTHOR]

Many geometry processing techniques require the solution of partial differential equations (PDEs) on manifolds embedded in ℝ2 or ℝ3, such as curves or surfaces. Such manifold PDEs often involve boundary conditions (e.g., Dirichlet or Neumann) prescribed at points or curves on the manifold's interior or along the geometric (exterior) boundary of an open manifold. However, input manifolds can take many forms (e.g., triangle meshes, parametrizations, point clouds, implicit functions, etc.). Typically, one must generate a mesh to apply finite element-type techniques or derive specialized discretization procedures for each distinct manifold representation. We propose instead to address such problems in a unified manner through a novel extension of the closest point method (CPM) to handle interior boundary conditions. CPM solves the manifold PDE by solving a volumetric PDE defined over the Cartesian embedding space containing the manifold and requires only a closest point representation of the manifold. Hence, CPM supports objects that are open or closed, orientable or not, and of any codimension. To enable support for interior boundary conditions, we derive a method that implicitly partitions the embedding space across interior boundaries. CPM's finite difference and interpolation stencils are adapted to respect this partition while preserving second-order accuracy. Additionally, we develop an efficient sparse-grid implementation and numerical solver that can scale to tens of millions of degrees of freedom, allowing PDEs to be solved on more complex manifolds. We demonstrate our method's convergence behavior on selected model PDEs and explore several geometry processing problems: diffusion curves on surfaces, geodesic distance, tangent vector field design, harmonic map construction, and reaction-diffusion textures. Our proposed approach thus offers a powerful and flexible new tool for a range of geometry processing tasks on general manifold representations. [ABSTRACT FROM AUTHOR]

In this paper, we can prove that: (1) Any non-degenerate strongly harmonic map from a compact Finsler manifold with non-negative flag curvature to a Finsler manifold with non-positive flag curvature must be totally geodesic. (2) If (M, F) is a compact Landsberg space with sectional flag curvature, then any non-degenerate strongly harmonic map from (M, F) with non-negative Ricci curvature to a Finsler manifold with non-positive flag curvature must be totally geodesic, which generalizes the result of Eells and Sampson (Amer. J. Math. 86: 106-160, 1964). [ABSTRACT FROM AUTHOR]

In this paper, we first derive a Landau-type theorem and a Bloch-type theorem for the class of meromorphic harmonic mappings. Then we establish two new versions of Bloch-type theorems for certain K-quasiregular meromorphic harmonic mappings in the unit disk. [ABSTRACT FROM AUTHOR]

We derive rigorously the reduced dynamical law for quantized vortex dynamics of the complex Ginzburg-Landau equation on the torus when the core size of vortex ε → 0. The reduced dynamical law of the complex Ginzburg-Landau equation is governed by a mixed flow of gradient flow and Hamiltonian flow which are both driven by a renormalized energy on the torus. Finally, some first integrals and analytic solutions of the reduced dynamical law are discussed. [ABSTRACT FROM AUTHOR]

In this article we consider the following fractional semilinear elliptic equation (-Δ)s u + |x|² u = ωu + |u|²σ in RN, where s ∈ (0, 1), N > 2s, σ ∈ (0, 2s/N-2s) and ω ∈ (0, λ1). By using variational methods we show the existence of a symmetric decreasing ground state solution of this equation. Moreover, we study some continuity and differentiability properties of the ground state level. Finally, we consider a bifurcation type result. [ABSTRACT FROM AUTHOR]

Let \Sigma _H^k(p) be the class of sense-preserving univalent harmonic mappings defined on the open unit disk \mathbb {D} of the complex plane with a simple pole at z=p \in (0,1) that have k-quasiconformal extensions (0\leq k<1) onto the extended complex plane. In this article, we obtain an area theorem for this class of functions. [ABSTRACT FROM AUTHOR]

In this article, we make use of convex analytic functions Ha(z) = [1/(1 - a)] log[(1 - az)/(1 - z)], a - ℝ, |a| ≤ 1, a ≠ 1 and starlike analytic functions Lb(z) = z/[(1 - bz)(1 - z)], b - ℝ, |b| ≤ 1, to construct univalent harmonic functions by means of a transformation on some normalized univalent analytic functions. Besides exploring mapping properties of harmonic functions so constructed, we establish sufficient conditions for their harmonic convolutions or Hadamard products to be locally univalent and sense preserving, univalent and convex in some direction. [ABSTRACT FROM AUTHOR]

We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane. [ABSTRACT FROM AUTHOR]

Some theorems of Liouville type are given for such P-harmonic maps when target manifold have conformal vector field or convex function or have non-positive sectional curvature. [ABSTRACT FROM AUTHOR]

We investigate stability conditions related to the existence of solutions of the Hull–Strominger system with prescribed balanced class. We build on recent work by the authors, where the Hull–Strominger system is recasted using non-Hermitian Yang–Mills connections and holomorphic Courant algebroids. Our main development is a notion of harmonic metric for the Hull–Strominger system, motivated by an infinite-dimensional hyperKähler moment map and related to a numerical stability condition, which we expect to exist for families of solutions. We illustrate our theory with an infinite number of continuous families of examples on the Iwasawa manifold. [ABSTRACT FROM AUTHOR]

For a harmonic diffeomorphism between the Poincaré disks, Wan [J. Differential Geom. 35 (1992), pp. 643–657] showed the equivalence between the boundedness of the Hopf differential and the quasi-conformality. In this paper, we will generalize this result from quadratic differentials to r-differentials. We study the relationship between bounded holomorphic r-differentials/(r-1)-differential and the induced curvature of the associated harmonic maps from the unit disk to the symmetric space SL(r,\mathbb R)/SO(r) arising from cyclic/subcyclic Higgs bundles. Also, we show the equivalence between the boundedness of holomorphic differentials and having a negative upper bound of the induced curvature on hyperbolic affine spheres in \mathbb {R}^3, maximal surfaces in \mathbb {H}^{2,n} and J-holomorphic curves in \mathbb {H}^{4,2}. Benoist-Hulin and Labourie-Toulisse have previously obtained some of these equivalences using different methods. [ABSTRACT FROM AUTHOR]

In this paper, we study a higher order Kirchhoff problem with variable exponent of type M∫Ω|Dru|m(x)m(x)dxΔm(x)ru=f(x,u)inΩ,Dαu=0,on∂Ω,for eachα∈ℝNwith|α|≤r−1,$$ \left\{\begin{array}{ll}M\left({\int}_{\Omega}\frac{{\left&#x0007C;{\mathcal{D}}_ru\right&#x0007C;}&#x0005E;{m(x)}}{m(x)} dx\right){\Delta}_{m(x)}&#x0005E;ru&#x0003D;f\left(x,u\right)& \mathrm{in}\kern0.30em \Omega, \\ {}{D}&#x0005E;{\alpha }u&#x0003D;0,\kern0.30em & \mathrm{on}\kern0.30em \mathrm{\partial \Omega },\kern0.30em \mathrm{for}\ \mathrm{each}\kern0.4em \alpha \in {\mathrm{\mathbb{R}}}&#x0005E;N\kern0.4em \mathrm{with}\kern0.4em \mid \alpha \mid \le r-1,\end{array}\right. $$where Ω⊂ℝN$$ \Omega \subset {\mathrm{\mathbb{R}}}&#x0005E;N $$ is a smooth bounded domain, r∈ℕ∗,m∈C(Ω‾),1

In this paper a new generalized norm is defined and Riesz type inequalities for harmonic functions on the unit disk are discussed by applying it. Also sharp constants are obtained for certain special values considered in the reverse case of the standard Riesz inequality. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the Riesz theorem for harmonic quasiregular mappings for a special case (when p = 2) in the unit disc. Our results improve similar results in this field and are proved with milder conditions. Moreover, we prove another variant forms of Riesz inequality for harmonic quasiregular functions. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness of weak solutions of the heat flow of half-harmonic maps, which was first introduced by Wettstein as a half-Laplacian heat flow and recently studied by Struwe using more classical techniques. On top of its similarity with the two dimensional harmonic map flow, this geometric gradient flow is of interest due to its links with free boundary minimal surfaces and the Plateau problem, leading Struwe to propose the name Plateau flow, which we adopt throughout. We obtain uniqueness of weak solutions of this flow under a natural condition on the energy, which answers positively a question raised by Struwe. [ABSTRACT FROM AUTHOR]

By studying cohomology classes that are related with n-harmonic morphisms and F-harmonic maps, we augment and extend several results on Fharmonic maps, harmonic maps in [1, 3, 15], p-harmonic morphisms in [23], and also revisit our previous results in [10, 11, 29] on Riemannian submersions and nharmonic morphisms which are submersions. The results, for example Theorem 3.2 obtained by utilizing the n-conservation law (2.6), are sharp. [ABSTRACT FROM AUTHOR]

As the Cantor-derived medium-entropy alloys (MEAs), FeNiCoMn and FeNiCrMn quaternaries in both equiatomic and non-equiatomic compositions were investigated by density functional theory combined with the quasiharmonic Debye–Grüneisen approximation using the special-quasirandom structure model. The structural properties, magnetic properties, and thermodynamics and phase stability were explored in detail. The temperature stabilization effect of lattice vibration, configurational mixing entropy, and thermal electronic excitation was discussed. Also FeNiCoPd and FeNiCrPd quaternaries, in which Mn was replaced by Pd, were considered in the same framework in order to highlight the similarities and differences between these Mn- and Pd-MEAs. The phase stability competition between homogeneous and inhomogeneous states in terms of both size and chemical ordering was revealed for four groups of FeNiCoMn, FeNiCoPd, FeNiCrMn, and FeNiCrPd MEAs. [ABSTRACT FROM AUTHOR]

In this paper, first we prove a nonexistence theorem for α‐harmonic mappings between Riemannian manifolds. Second, the instability of nonconstant α‐harmonic maps is studied with regard to the Ricci curvature criterion of their codomain. Then, we estimate the Morse index for measuring the degree of instability of some particular α‐harmonic maps. Furthermore, the notion of α‐stable manifolds and its applications are considered. Finally, we investigate the α‐stability of any compact Riemannian manifolds admitting a nonisometric conformal vector field and any Einstein Riemannian manifold under certain assumptions on the smallest positive eigenvalue of its Laplacian operator on functions. [ABSTRACT FROM AUTHOR]

In this paper we study the harmonic map heat flow on the euclidean space R d and we show an unconditional uniqueness result for maps with small initial data in the homogeneous Besov space B ˙ p , ∞ d p (R d) where d < p < ∞. As a consequence we obtain decay rates for solutions of the harmonic map flow of the form ‖ ∇ u (t) ‖ L ∞ (R d) ≤ C t − 1 2 . Additionally, under the assumption of a stronger spatial localization of the initial conditions, we show that the temporal decay happens in a self-similar way. We also explain that similar results hold for the biharmonic map heat flow and the semilinear heat equation with a power-type nonlinearity. [ABSTRACT FROM AUTHOR]

The relationship between convexity and symmetry is widely recognized. In fuzzy theory, both concepts exhibit similar behavior. It is crucial to remember that real and interval-valued mappings are special instances of fuzzy-number-valued mappings ( F - N - V - M s ), as fuzzy theory relies on the unit interval, which is crucial to resolving problems with interval analysis and fuzzy number theory. In this paper, a new harmonic convexities class of fuzzy numbers has been introduced via up and down relation. We show several Hermite–Hadamard ( H ⋅ H ) and Fejér-type inequalities by the implementation of fuzzy Aumann integrals using the newly defined class of convexities. Some nontrivial examples are also presented to validate the main outcomes. [ABSTRACT FROM AUTHOR]

Martingales with jumps on Riemannian manifolds and harmonic maps with respect to Markov processes are discussed in this paper. Discontinuous martingales on manifolds were introduced in Picard (Séminaire de Probabilités de Strasbourg 25:196–219, 1991). We obtain results about the convergence of martingales with finite quadratic variations on Riemannian submanifolds of higher-dimensional Euclidean space as t → ∞ and as t → 0 . Furthermore, we apply the result about martingales with jumps on submanifolds to harmonic maps with respect to Markov processes such as fractional harmonic maps. [ABSTRACT FROM AUTHOR]

On a complete Calabi‐Yau manifold M$M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon‐Hein. We prove this result by proving a Liouville‐type theorem for harmonic 1‐forms, which follows from a new local L2$L^2$ estimate of the exterior derivative. [ABSTRACT FROM AUTHOR]

For an irreducible representation |$\rho :\pi _{1}(\Sigma _{g})\to \textrm{GL}(n,\mathbb{C})$|⁠ , there is an energy functional |$\textrm{E}_{\rho }: {{\mathcal{T}}}_{g}\to \mathbb{R}$|⁠ , defined on Teichmüller space by taking the energy of the associated equivariant harmonic map into the symmetric space |$\textrm{GL}(n,\mathbb{C})/\textrm{U}(n)$|⁠. It follows from a result of Toledo that |$\textrm{E}_{\rho }$| is plurisubharmonic, that is, its Levi form is positive semi-definite. We describe the kernel of this Levi form, and relate it to the |$\mathbb{C}^{*}$| action on the moduli space of Higgs bundles. We also show that the points in |$ {{\mathcal{T}}}_{g}$| where strict plurisubharmonicity fails (i.e. this kernel is non-zero) are critical points of the Hitchin fibration. When |$n\geq 2$| and |$g\geq 3$|⁠ , we show that for a generic choice |$(S,\rho)$|⁠ , the map |$\textrm{E}_{\rho }$| is strictly plurisubharmonic. We also describe the kernel of the Levi form for |$n=1$|⁠. [ABSTRACT FROM AUTHOR]

We prove the existence of nonconstant harmonic maps of optimal regularity from an arbitrary closed manifold (M n , g) of dimension n > 2 to any closed, non-aspherical manifold N containing no stable minimal two-spheres. In particular, this gives the first general existence result for harmonic maps from higher-dimensional manifolds to a large class of positively curved targets. In the special case of the round spheres N = S k , k ⩾ 3 , we obtain a distinguished family of nonconstant harmonic maps M → S k of index at most k + 1 , with singular set of codimension at least 7 for k sufficiently large. Furthermore, if 3 ⩽ n ⩽ 5 , we show that these smooth harmonic maps stabilize as k becomes large, and correspond to the solutions of an eigenvalue optimization problem on M , generalizing the conformal maximization of the first Laplace eigenvalue on surfaces. [ABSTRACT FROM AUTHOR]

For degree ± 1 harmonic maps from R 2 (or S 2 ) to S 2 , Bernand-Mantel et al. (Arch Ration Mech Anal 239(1):219–299, 2021) recently establish a uniformly quantitative stability estimate. Namely, for any map u : R 2 → S 2 with degree ± 1 , the discrepancy of its Dirichlet energy and 4 π can linearly control the H ˙ 1 -difference of u from the set of degree ± 1 harmonic maps. Whether a similar estimate holds for harmonic maps with a higher degree is unknown. In this paper, we prove that a similar quantitative stability result for a higher degree is true only in a local sense. Namely, given a harmonic map, a similar estimate holds if u is already sufficiently near to it (modulo Möbius transforms) and the bound in general depends on the given harmonic map. More importantly, we thoroughly investigate an example of the degree 2 case, which shows that it fails to have a uniformly quantitative estimate like the degree ± 1 case. This phenomenon shows the striking difference between degree ± 1 ones and higher degree ones. Finally, we also conjecture a new uniformly quantitative stability estimate based on our computation. [ABSTRACT FROM AUTHOR]

We study singularity formation for the heat flow of harmonic maps from R d . For each d ≥ 4 , we construct a compact, d-dimensional, rotationally symmetric target manifold that allows for the existence of a corotational self-similar shrinking solution (shortly shrinker) that represents a stable blowup mechanism for the corresponding Cauchy problem. [ABSTRACT FROM AUTHOR]

In this paper, first, we recall the notion of Clairaut Riemannian map (CRM) F using a geodesic curve on the base manifold and give the Ricci equation. We also show that if base manifold of CRM is space form then leaves of (k e r F ∗) ⊥ become space forms and symmetric as well. Secondly, we define Clairaut semi-invariant Riemannian map (CSIRM) from a Riemannian manifold (M , g M) to a Kähler manifold (N , g N , P) with a non-trivial example. We find necessary and sufficient conditions for a curve on the base manifold of semi-invariant Riemannian map (SIRM) to be geodesic. Further, we obtain necessary and sufficient conditions for a SIRM to be CSIRM. Moreover, we find necessary and sufficient condition for CSIRM to be harmonic and totally geodesic. In addition, we find necessary and sufficient condition for the distributions D 1 ¯ and D 2 ¯ of (k e r F ∗) ⊥ (which are arisen from the definition of CSIRM) to define totally geodesic foliations. Finally, we obtain necessary and sufficient conditions for (k e r F ∗) ⊥ and base manifold to be locally product manifold D 1 ¯ × D 2 ¯ and (r a n g e F ∗) × (r a n g e F ∗) ⊥ , respectively. [ABSTRACT FROM AUTHOR]

This study utilized one-dimensional implicit particle-in-cell/Monte Carlo collision simulations to investigate the impact of different harmonic numbers and magnetic field strengths on capacitive-coupled argon plasma. Under the conditions of a pressure of 50 mTorr and a voltage of 100 V, simulations were conducted for magnetic field strengths of 0 and 100 G, magnetic field gradients of 10–40, 10–60, 10–80, 10–100, and 100–10 G, as well as discharge scenarios with harmonic numbers ranging from 1 to 5. Through in-depth analysis of the results, it was observed that the combined effect of positive magnetic field gradients and harmonic numbers can significantly enhance plasma density and self-bias properties to a greater extent. As the magnetic field gradient increases, the combined effect also increases, while an increase in harmonic numbers weakens the combined effect. Furthermore, this combined effect expands the range of control over ion bombardment energy. This provides a new research direction for improving control over ion energy and ion flux in capacitive-coupled plasmas. [ABSTRACT FROM AUTHOR]

We investigate resonant third-harmonic generation in near-zero index thin films driven out-of-equilibrium by intense optical excitation. Adopting the Landau weak coupling formalism to incorporate electron–electron and electron–phonon scattering processes, we derive a novel set of hydrodynamic equations accounting for collision-driven nonlinear dynamics in sodium. By perturbatively solving hydrodynamic equations, we model third-harmonic generation by a thin sodium film, finding that such a nonlinear process is resonant at the near-zero index resonance of the third-harmonic signal. Thanks to the reduced absorption of sodium, we observe that third-harmonic resonance can be tuned by the impinging pump radiation angle, efficiently modulating the third-harmonic generation process. Furthermore, owing to the metallic sodium response at the pump optical wavelength, we find that the third-harmonic conversion efficiency is maximised at a peculiar thin film thickness where evanescent back-reflection provides increased field intensity within the thin film. Our results are relevant for the development of future ultraviolet light sources, with potential impact for innovative integrated spectroscopy schemes. [ABSTRACT FROM AUTHOR]

Ground-penetrating radars (GPR) based on a variety of techniques have been proposed to improve the performance of buried target (e.g., landmines, threat devices) detection. However, the small radar cross section (RCS) of small electronic devices poses difficulties for target detection, especially when they are buried in lossy and inhomogeneous media. This paper presents a novel buried nonlinear target detection method based on the decomposition of the time-reversal operator (DORT) that uses a multistatic system to overcome the limitations of conventional GPR. Using harmonic radar, which detects the harmonic responses scattered from electronic devices, and DORT processing, which enables focusing/imaging of the detected target, the detection performance is verified by conducting simulation and measurements. The overall results demonstrate that the proposed method achieves accurate detection of buried targets with small RCS. [ABSTRACT FROM AUTHOR]

Accurately characterizing the thermomechanical parameters of nanoscale systems is essential for understanding their performance and building innovative nanoscale technologies due to their distinct behaviours. Fractional thermal transport models are commonly utilized to correctly depict the heat transfer that occurs in these nanoscale systems. The current study presents a novel mathematical thermoelastic model that incorporates a new fractional differential constitutive equation for heat conduction. This heat equation is useful for understanding the effects of thermal memory. An application of a fractional-time Atangana–Baleanu (AB) derivative with a local and non-singular kernel was utilized in the process of developing the mathematical model that was suggested. To deal with effects that depend on size, nonlocal constitutive relations are introduced. Furthermore, in order to take into consideration, the viscoelastic behaviour of the material at the nanoscale, the fractional Kelvin–Voigt model is utilized. The proposed model is highly effective in properly depicting the unusual thermal conductivity phenomena often found in nanoscale devices. The study also considered the mechanical deformation, temperature variations, and viscoelastic characteristics of the functionally graded (FG) nanostructured beams. The consideration was made that the material characteristics exhibit heterogeneity and continuous variation across the thickness of the beam as the nanobeam transitions from a ceramic composition in the lower region to a metallic composition in the upper region. The complicated thermomechanical features of simply supported viscoelastic nanobeams that were exposed to harmonic heat flow were determined by the application of the model that was constructed. Heterogeneity, nonlocality, and fractional operators are some of the important variables that contribute to its success, and this article provides a full study and illustration of the significance of these characteristics. The results that were obtained have the potential to play a significant role in pushing forward the design and development of tools, materials, and nanostructures that have viscoelastic mechanical characteristics and graded functions. [ABSTRACT FROM AUTHOR]

Robot Exploration can be used to autonomously map an area or conduct search missions in remote or hazardous environments. Using multiple robots to perform this task can improve efficiency for time-critical applications. In this work, a distributed method for multi-robot exploration using a Harmonic Map Transformation (HMT) is presented. We employ SLAM to construct a map of the unknown area and utilize map merging to share terrain information amongst robots. Then, a frontier allocation strategy is proposed to increase efficiency. The HMT is used to safely navigate the robots to the frontiers until the exploration task is complete. We validate the efficacy of the proposed strategy via tests in simulated and real-world environments. Our method is compared to other recent schemes for multi-robot exploration and is shown to outperform them in terms of total path distance. [ABSTRACT FROM AUTHOR]

The long-distance ship target turns into a small spot in an infrared image, which has the characteristics of small size, weak intensity, limited texture information, and is easily affected by noise. Moreover, the presence of heavy sea clutter, including sun glints that exhibit local contrast similar to small targets, negatively impacts the performance of small-target detection methods. To address these challenges, we propose an effective detection scheme called fusion gray gradient clutter suppression (FGGCS), which leverages the disparities in grayscale and gradient between the target and its surrounding background. Firstly, we designed a harmonic contrast map (HCM) by using the two-dimensional difference of Gaussian (2D-DoG) filter and eigenvalue harmonic mean of the structure tensor to highlight high-contrast regions of interest. Secondly, a local gradient difference measure (LGDM) is designed to distinguish isotropic small targets from background edges with local gradients in a specific direction. Subsequently, by integrating the HCM and LGDM, we designed a fusion gray gradient clutter suppression map (FGGCSM) to effectively enhance the target and suppress clutter from the sea background. Finally, an adaptive constant false alarm threshold is adopted to extract the targets. Extensive experiments on five real infrared maritime image sequences full of sea glints, including a small target and sea–sky background, show that FGGCS effectively increases the signal-to-clutter ratio gain (SCRG) and the background suppression factor (BSF) by more than 22% and 82%, respectively. Furthermore, its receiver operating characteristic (ROC) curve has an obviously more rapid convergence rate than those of other typical detection algorithms and improves the accuracy of small-target detection in complex maritime backgrounds. [ABSTRACT FROM AUTHOR]

This paper delves into the global existence of weak solutions for a three-dimensional magnetoelastic interaction model. This model combines a fractional harmonic map heat flow with an evolution equation for displacement. By using the Faedo-Galerkin method, we successfully establish the global existence of weak solutions for this coupled system. [ABSTRACT FROM AUTHOR]