Curvature Properties Research Articles

Influence of thiophene and furan π–bridge on the properties of poly(benzodithiophene-alt-bis(π–bridge)pyrrolopyrrole-1,3-dione) for organic solar cell applications

A new polymer, P(BDT-fPPD), which incorporates 4,8-bis(2-ethylhexyloxy)benzo[1,2-b:4,5-bʹ]dithiophene (BDT) and 4,6-bis(furan-2-yl)-2,5-dioctylpyrrolo [3,4-c]pyrrole-1,3(2H,5H)-dione (fPPD, furan π–bridged PPD) units, was prepared. The optoelectrical, crystalline, charge transport, backbone curvature, and photovoltaic properties of P(BDT-fPPD) were thoroughly studied. P(BDT-fPPD) was also compared to the polymer P(BDT-tPPD), comprising BDT and 4,6-bis(thiophen-2-yl)-2,5-dioctylpyrrolo [3,4-c]pyrrole-1,3(2H,5H)-dione (tPPD, thiophene π–bridged PPD) units. This study demonstrates that the π–bridges, such as thiophene and furan, attached between the BDT and pyrrolo [3,4-c]pyrrole-1,3(2H,5H)-dione (PPD) units greatly altered the properties of the resulting polymers. In particular, the backbone curvature of P(BDT-fPPD) was significantly different from that of P(BDT-tPPD), which resulted in P(BDT-fPPD) having a higher bandgap energy (Eg), deeper HOMO level, and higher crystallinity, but lower carrier mobility (μh) and relatively poor power conversion efficiency (PCE) compared to P(BDT-tPPD). For P(BDT-fPPD), the Eg, HOMO, μh, and PCE were determined as 2.20 eV, −5.44 eV, 1.19 × 10−5 cm−2 V−1 s−1, and 2.62%, respectively. The corresponding values for P(BDT-tPPD) were 2.11 eV, −5.39 eV, 2.95 × 10−4 cm−2 V−1 s−1 and 5.29%, respectively. Interestingly, the inclusion of a small amount of P(BDT-tPPD) in the PTB7-Th:PC70BM blend enhanced the PCE of the resulting ternary organic solar cells (OSCs), whereas the insertion of P(BDT-fPPD) lowered the PCE of the ternary OSCs. The lower mobility and PCE obtained for P(BDT-fPPD) are mainly attributed to its poor blending with PC70BM.

Estimating Monotone Concave Stochastic Production Frontiers

Recent research shows that the search for Bayesian estimation of concave production functions is a fruitful area of investigation. In this article, we use a flexible cost function that satisfies globally the monotonicity and curvature properties to estimate features of the production function. Specification of a globally monotone concave production function is a difficult task which is avoided here by using the first-order conditions for cost minimization from a globally monotone concave cost function. The problem of unavailable factor prices is bypassed by assuming structure for relative prices in the first-order conditions. The new technique is shown to perform well in a Monte Carlo experiment as well as in an empirical application to rice farming in India.

Recurrent curvature over four-dimensional homogeneous manifolds

Recurrent curvature properties are considered on four-dimensional pseudo-Riemannian homogeneous manifolds with non-trivial isotropy, and also on some geometric manifolds.

Some results on almost η-Ricci-Bourguignon solitons

We determine a formula to compute the defining function of a gradient almost Ricci-Bourguignon soliton by means of the potential vector field, providing in this sense two examples. We also give a rigidity result in this case. Moreover, we deduce some curvature properties of solitons with torse-forming potential vector field. Further we generalize some of the results to almost η-Ricci-Bourguignon solitons and prove that a gradient almost Ricci-Bourguignon soliton on a doubly warped product manifold induces gradient almost η-Ricci-Bourguignon solitons on its factor manifolds.

A Note on Solitons with Generalized Geodesic Vector Field

We consider a general notion of an almost Ricci soliton and establish some curvature properties for the case in which the potential vector field of the soliton is a generalized geodesic or a 2-Killing vector field. In this vein, we characterize trivial generalized Ricci solitons.

A Generalized Model for Compliant Passive Bipedal Walking: Sensitivity Analysis and Implications on Bionic Leg Design.

The passive behavior of a compliant biped walking model, subject to variations in its design, is investigated. A biped gait model is developed that allows for studying the effects of leg impedance, geometry, foot curvature, and inertial properties on the stable gait performed passively. A set of nondimensional parameters has been produced that fully defines the compass gait behavior, eliminating the dependence of our results on scale. Models emerging from parameter combinations were tested on their ability to perform stable passive walking on slope, and the characteristics of the gait performed in each case were recorded. Investigation of parameter ranges allowed us to draw relationships between various gait characteristics and specific, nondimensional parameter selections. By mapping the changes in system behavior under simple design variations, this work facilitates the selection of design parameters at an early stage of designing bionic walking equipment, including prostheses and exoskeletons.

A study of curvature theory for different symmetry classes of Hamiltonian

We study and present the results of curvature for different symmetry classes (BDI, AIII and A) of model Hamiltonians and also present the transformation of model Hamiltonian from one distinct symmetry class to the other based on the curvature property. We observe the mirror symmetric curvature for the Hamiltonian with BDI symmetry class but there is no evidence of such behaviour for Hamiltonians of AIII symmetry class. We show the origin of torsion and its consequences on the parameter space of topological phase of the system. We find the evidence of torsion for the Hamiltonian of A symmetry class. We present Serret–Frenet equations for all model Hamiltonians in \(\mathbf {R}^3\) space. To the best of our knowledge, this is the first application of curvature theory to the model Hamiltonian of different symmetry classes which belong to the topological state of matter.

Metallic Kähler and nearly metallic Kähler manifolds

In this paper, we construct metallic Kähler and nearly metallic Kähler structures on Riemannian manifolds. For such manifolds with these structures, we study curvature properties. Also, we describe linear connections on the manifold which preserve the associated fundamental [Formula: see text]-form and satisfy some additional conditions and present some results concerning them.

The kinematics of curved profiles mating with a caged idle roller - higher-path curvature analysis

This investigation focuses on the relative motion of a force-closure higher pair mechanism, herein termed caged-roller joint and composed of a cylindrical roller meshing with two slot profiles, carved on different bodies. A distinctive feature of such a mechanism is the pure rolling velocity constraint imposed between its components to limit friction losses. This makes the caged-roller joint an ideal candidate to control the kinematics of high-speed operating devices, such as centrifugal pendulum vibration absorbers.In this paper, a theoretical framework for the motion of caged-roller joint is proposed, employing intrinsic geometry, higher-path curvature and envelope theory. For design-analysis purposes, the correlations between instantaneous invariants, slots profiles curvature properties and pure rolling conditions within the higher pairs have been established. Eventually, the obtained results have been verified for three particular curves profiles, to test their consistency and offer an immediate application.

Simultaneous-integrated evaluation of mechanical–thermal sensory attributes of woven fabrics in considering practical wearing states

Tactile sensations of fabrics are the primary property determining the wearing comfort of clothing; however, comprehensive evaluation of the fabric tactile property by considering the flexural buckling of fabrics under high curvature, hysteresis performance and thermal property has not been fully studied, leading to a clear gap between the existing measurement methods and application requirements. Herein, a simultaneous-integrated testing method, namely the Touch Sensation Tester for Fabrics (TST-F) was introduced to evaluate the mechanical–thermal sensory properties of woven fabrics. The introduced instrument used one device with a single mechanical sensor to test various mechanical properties by constructing different deformations of fabrics, and the thermal property was simultaneously measured using an infrared detector array, achieving an efficient characterization of the mechanical–thermal sensation properties of textiles. The measurement capacity and repeatability of the TST-F were statistically analyzed; the measurement indices and their relation with fabric mechanical–thermal sensation properties were also exhibited. Results showed that the TST-F was promising to characterize fabric touch sensations in terms of bending stiffness, compression softness with wrinkling, stretching tightness and thermal comfort by considering the infrared transmission and heat conductivity of textiles.

∗-Conformal η-Ricci soliton on Sasakian manifold

In this paper, we study ∗-Conformal [Formula: see text]-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting ∗-Conformal [Formula: see text]-Ricci soliton. We obtain some significant results on ∗-Conformal [Formula: see text]-Ricci soliton in Sasakian manifolds satisfying [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text], where [Formula: see text] is Pseudo-projective curvature tensor. The conditions for ∗-Conformal [Formula: see text]-Ricci soliton on [Formula: see text]-conharmonically flat and [Formula: see text]-projectively flat Sasakian manifolds have been obtained in this paper. Lastly we give an example of five-dimensional Sasakian manifolds satisfying ∗-Conformal [Formula: see text]-Ricci soliton.

Manipulating Berry curvature of SrRuO3 thin films via epitaxial strain

Berry curvature plays a crucial role in exotic electronic states of quantum materials, such as the intrinsic anomalous Hall effect. As Berry curvature is highly sensitive to subtle changes of electronic band structures, it can be finely tuned via external stimulus. Here, we demonstrate in SrRuO3 thin films that both the magnitude and sign of anomalous Hall resistivity can be effectively controlled with epitaxial strain. Our first-principles calculations reveal that epitaxial strain induces an additional crystal field splitting and changes the order of Ru d orbital energies, which alters the Berry curvature and leads to the sign and magnitude change of anomalous Hall conductivity. Furthermore, we show that the rotation of the Ru magnetic moment in real space of a tensile-strained sample can result in an exotic nonmonotonic change of anomalous Hall resistivity with the sweeping of magnetic field, resembling the topological Hall effect observed in noncoplanar spin systems. These findings not only deepen our understanding of anomalous Hall effect in SrRuO3 systems but also provide an effective tuning knob to manipulate Berry curvature and related physical properties in a wide range of quantum materials.

A note on some properties of 4-dimensional walker metrics

This paper is devoted to examine a special case of Walker metric on a 4-dimensional manifold, and some of its curvature properties are studied, e.g., conditions for a Walker metric to be Einstein or locally conformally flat. Finally, a necessary and sufficient condition for a function c(x, y, z, t) of Walker metric of 4-dimensional manifold to have vector field X on M to be a Killing vector field, is constructed.

On Ricci curvature of metric structures on [formula omitted]-manifolds

We study the properties of Ricci curvature of g-manifolds with particular attention paid to higher dimensional abelian Lie algebra case. The relations between Ricci curvature of the manifold and the Ricci curvature of the transverse manifold of the characteristic foliation are investigated. In particular, sufficient conditions are found under which the g-manifold can be a Ricci soliton or a gradient Ricci soliton. Finally, we obtain a amazing (non-existence) higher dimensional generalization of the Boyer-Galicki theorem on Einstein K-manifolds for a special class of abelian g-manifolds.

Curvature Properties of Generalized pp-Wave Metrics

The main objective of the present paper is to investigate the curvature properties of generalized pp-wave metrics. It is shown that a generalized pp-wave spacetime is Ricci generalized pseudosymmetric, 2-quasi-Einstein and generalized quasi-Einstein in the sense of Chaki. As a special case it is shown that pp-wave spacetime is semisymmetric, semisymmetric due to conformal and projective curvature tensors, R-space by Venzi and satisfies the pseudosymmetric type condition P ⋅ P = −13Q(S,P). Again we investigate the sufficient condition for which a generalized pp-wave spacetime turns into pp-wave spacetime, pure radiation spacetime, locally symmetric and recurrent. Finally, it is shown that the energy-momentum tensor of pp-wave spacetime is parallel if and only if it is cyclic parallel. Again the energy momentum tensor is Codazzi type if it is cyclic parallel but the converse is not true as shown by an example. Finally, we make a comparison between the curvature properties of the Robinson-Trautman metric and generalized pp-wave metric.

Hamiltonian chaos and differential geometry of configuration space–time

This paper tackles Hamiltonian chaos by means of elementary tools of Riemannian geometry. More precisely, a Hamiltonian flow is identified with a geodesic flow on configuration space–time endowed with a suitable metric due to Eisenhart. Until now, this framework has never been given attention to describe chaotic dynamics. A gap that is filled in the present work. In a Riemannian-geometric context, the stability/instability of the dynamics depends on the curvature properties of the ambient manifold and is investigated by means of the Jacobi–Levi-Civita (JLC) equation for geodesic spread. It is confirmed that the dominant mechanism at the ground of chaotic dynamics is parametric instability due to curvature variations along the geodesics. A comparison is reported of the outcomes of the JLC equation written also for the Jacobi metric on configuration space and for another metric due to Eisenhart on an extended configuration space–time. This has been applied to the Hénon–Heiles model, a two-degrees of freedom system. Then the study has been extended to the 1D classical Heisenberg XY model at a large number of degrees of freedom. Both the advantages and drawbacks of this geometrization of Hamiltonian dynamics are discussed. Finally, a quick hint is put forward concerning the possible extension of the differential–geometric investigation of chaos in generic dynamical systems, including dissipative ones, by resorting to Finsler manifolds.

Almost Paracontact Almost Paracomplex Riemannian Manifolds with a Pair of Associated Schouten–van Kampen Connections

Two correlated Schouten–van Kampen affine connections on an almost paracontact almost paracomplex Riemannian manifold are introduced and investigated. The considered manifolds are characterized by virtue of the presented non-symmetric connections. Curvature properties of the studied connections are obtained. A family of examples on a Lie group are given in confirmation of the obtained results.

Surface and curvature properties of charged strangelets in compact objects

Droplets of absolutely stable strange quark matter (strangelets) immersed in a lepton background may be the energetically preferred composition of strange star crusts and may also constitute the interior of a new class of stellar objects known as strangelet dwarfs. In this work we calculate the surface tension $\ensuremath{\sigma}$ and the curvature coefficient $\ensuremath{\gamma}$ of charged strangelets as a function of the baryon number density, the temperature, the chemical potential of trapped neutrinos, the strangelet size, the electric potential, and the electric charge at their boundary. Strange quark matter in chemical equilibrium and with global electric charge neutrality is described within the MIT bag model. We focus on three different astrophysical scenarios, namely, cold strange stars, protostrange stars, and postmerger strange stars, characterized by the temperature and the amount of neutrinos trapped in the system. Finite-size effects are implemented within the multiple reflection expansion framework. We find that $\ensuremath{\sigma}$ decreases significantly as the strangelet's boundary becomes more positively charged. This occurs because $\ensuremath{\sigma}$ is dominated by the contribution of $s$ quarks which are the most massive particles in the system. Negatively charged $s$-quarks are suppressed in strangelets with a large positive electric charge, diminishing their contribution to $\ensuremath{\sigma}$ and resulting in smaller values of the total surface tension. We also verify that the more extreme astrophysical scenarios, with higher temperatures and higher neutrino chemical potentials, allow higher positive values of the strangelet's electric charge at the boundary and consequently smaller values of $\ensuremath{\sigma}$. In contrast, $\ensuremath{\gamma}$ is strongly dominated by the density of light ($u$ and $d$) quarks and is quite independent of the charge-per-baryon ratio, the temperature and neutrino trapping. We discuss the relative importance of surface and curvature effects as well as some astrophysical consequences of these results.

On the attractor for a semilinear wave equation with variable coefficients and nonlinear boundary dissipation

<p style='text-indent:20px;'>Long time behavior of a semilinear wave equation with variable coefficients with nonlinear boundary dissipation is considered. It is shown that the existence of global and compact attractors depends on the curvature properties of a Riemannian metric given by the variable coefficients.</p>

$$\zeta $$-Ricci Soliton on Real Hypersurfaces of Nearly Kaehler 6-Sphere with SSMC

The main intention of this paper is to study the real hypersurfaces in nearly Kaehler $$\mathbb {S}^{6}$$ endowed with a semi-symmetric metric connection. We characterize the real hypersurfaces of the nearly Kaehler $$\mathbb {S}^{6}$$ admitting semi-symmetric metric connection, and investigate the curvature properties of these submanifolds. Moreover, it is shown that a real hypersurface is congruent to an open segment of a totally-geodesic hypersphere or a tube over an almost complex curve in $$\mathbb {S}^{6}$$ if such a connected real hypersurface of nearly Kaehler $$\mathbb {S}^{6}$$ is an $$\zeta $$ -Ricci soliton with the potential vector field $$\xi $$ .