Parabolic Structure Research Articles

Global existence and analyticity of Lp solutions to the compressible fluid model of Korteweg type

We are concerned with a system of equations in Rd(d≥3) governing the evolution of isothermal, viscous and compressible fluids of Korteweg type, that can be used as a phase transition model. In the case of zero sound speed P′(ρ⁎)=0, it is found that the linearized system admits the purely parabolic structure, which enables us to establish the global-in-time existence and Gevrey analyticity of strong solutions in hybrid Besov spaces of Lp-type. Precisely, if the full viscosity coefficient and capillary coefficient satisfy ν¯2≥4κ¯, then the acoustic waves are not available in compressible fluids. Consequently, the prior L2 boundedness on the low frequencies of density and velocity could be improved to the general Lp version with 1≤p<d. The proof mainly relies on new nonlinear Besov (-Gevrey) estimates for product and composition of functions.

How Does Tropical Cyclone Genesis Frequency Respond to a Changing Climate?

AbstractGlobal tropical cyclone (TC) genesis frequency (TCGF) has been documented to decrease or increase linearly in a changing climate. However, our numerical experiments show that the global TCGF exhibits a parabolic relation with spatio‐uniform climate changes in sea surface temperature (SST) from −15 K to 5 K relative to the present climate, with the peak in the 5 K‐cooler climate. The parabolic relation is found in all TC basins except the eastern North Pacific where TCGF keeps increasing with the changing climate. TCGF can be expressed as the product of the frequency of TC seeds and the TC survival rate (SR). Further analysis shows that this parabolic structure in the global TCGF depends on TC seeds rather than the TC SR. The TC SR exhibits an increasing trend with the SST increase, while TC seeds show a consistent change with TCGF, which might be linked to the changes in low‐level relative humidity.

Parabolic opers and differential operators

Parabolic SL(r,C)-opers were defined and investigated in [BDP] in the set-up of vector bundles on curves with a parabolic structure over a divisor. Here we introduce and study holomorphic differential operators between parabolic vector bundles over curves. We consider the parabolic SL(r,C)-opers on a Riemann surface X with given singular divisor S and with fixed parabolic weights satisfying the condition that all parabolic weights at any point $x_i$ in S are integral multiples of $\frac{1}{2N_i+1}$, where $N_i > 1$ are fixed integers. We prove that this space of opers is canonically identified with the affine space of holomorphic differential operators of order r between two natural parabolic line bundles on X (depending only on the divisor S and the weights $N_i$) satisfying the conditions that the principal symbol of the differential operators is the constant function 1 and the sub-principal symbol vanishes identically. The vanishing of the sub-principal symbol ensures that the logarithmic connection on the rank r bundle is actually a logarithmic SL(r, C)-connection.

Motives of moduli spaces of bundles on curves via variation of stability and flips

AbstractWe study the rational Chow motives of certain moduli spaces of vector bundles on a smooth projective curve with additional structure (such as a parabolic structure or Higgs field). In the parabolic case, these moduli spaces depend on a choice of stability condition given by weights; our approach is to use explicit descriptions of variation of this stability condition in terms of simple birational transformations (standard flips/flops and Mukai flops) for which we understand the variation of the Chow motives. For moduli spaces of parabolic vector bundles, we describe the change in motive under wall‐crossings, and for moduli spaces of parabolic Higgs bundles, we show the motive does not change under wall‐crossings. Furthermore, we prove a motivic analogue of a classical theorem of Harder and Narasimhan relating the rational cohomology of moduli spaces of vector bundles with and without fixed determinant. For rank 2 vector bundles of odd degree, we obtain formulae for the rational Chow motives of moduli spaces of semistable vector bundles, moduli spaces of Higgs bundles and moduli spaces of parabolic (Higgs) bundles that are semistable with respect to a generic weight (all with and without fixed determinant).

THE PARABOLIC STRUCTURE OF GOSPEL PARABLES

The article is devoted to the analysis of the special parabolic structure of the evangelical parables. It is not only about the actual literary understanding of the parabola as a stylistic device, with the help of which foreign language expression is carried out, but also about a mathematical graph – a curved curve, divided at the point of intersection into two symmetrical branches. In the structure of the evangelical parable, these branches can be represented as real-factographic and symbolic interpretive plans, between which there is a direct semantic dependence. All narrative situations that make up the real plan of the parable and are represented by the right branch of the parabola must be interpreted in the same sequence to build a symmetrical left branch. In the article, the parabolic structure of two symmetrical plans is demonstrated on the example of two gospel parables well-known in culture: The Parable of the Prodigal Son [Luk. 15, 11 32] and Proverbs about ten virgins [Matt. 15, 1–11]. Obviously, a similar way of interpretive reading of the Gospel parables can be qualified as a fullfledged hermeneutic technique of analysis of other biblical works.

Modified scaling of thermopower to heat capacity for Cr doped Kondo insulator FeSi near metal to insulator transition

The Low temperature thermopower (S) and heat capacity (C) measurements are investigated for Cr doped FeSi. Metals having simple parabolic band structure whose entropy of free carriers used to scale as S/T proportional to γ, where γ is Sommerfeld coefficient leading to the validity of S/T to γ scaling. However, it is shown that the entropy of free carriers of metals derived from insulators violates such a scaling. Here, we have investigated the compositions which fall in the vicinity of (metal-to-insulator) critical concentration of Fe1-xCrxSi. These compositions are found to agree well with the modified scaling (nS/T vs γ) of thermopower to heat capacity by taking the carrier concentration n into consideration in the zero temperature limit. For higher concentrations of Cr, marked deviations from the scaling are observed probably due to the magnetic contribution such as Schottky effect to the heat capacity at low temperature.

DINAMIKA ŽELjE U „BOŽJIM LjUDIMA“ BORISAVA STANKOVIĆA I „KUĆI MARIJE POMOĆNICE“ IVANA CANKARA

The paper interprets literary ways of shaping the dynamics of desire in the characters of Borisav Stanković’s God’s Children and Ivan Cankar’s The Ward of Mary Help of Christians. The subject of the analysis of the work of the Serbian writer are the modes of the absolutization of desire in the rogue characters of provisional vagabond communities, or, more precisely, the generative-constitutive role of desire and impossibility of its fulfillment. The heroes of Stank- ović’s stories reflect a specific anthropological image, determined by a constant deprivation as a fundamental internal property of the subject. Parabolic structure of the stories plays an important role in the shaping of meaning. When interpreting the work of the Slovenian writer, the focus is on the rogue subjects, too, particularly those excluded from the community. Throughout the analysis, the dynamics of vitalist impulses and death drives is being investigated, as well as the relation between the subjects of such an experience and social norms. At the end of the paper, the similarities and differences of characters’ actions and their meanings in God’s Children and The Ward of Mary Help of Christians are examined.

Generalized parabolic structures over smooth curves with many components and principal bundles over reducible nodal curves

Let Y be a possibly non-connected smooth projective curve, $$y_{1}^{1},y_{2}^{1},\ldots ,y_{1}^{\nu },y_{2}^{\nu }$$ $$2\nu $$ different points of Y, $$r\in \mathbb {N}$$ , $$d\in \mathbb {Z}$$ , $$\delta \in \mathbb {Q}_{>0}$$ , $${\underline{\kappa }}=(\kappa _1,\ldots ,\kappa _{\nu })\in \mathbb {Q}^{\nu }_{\ge 0}$$ and $${\underline{e}}=(e_1,\ldots ,e_{\nu })\in \mathbb {Z}_{\ge 0}^{\nu }$$ with $$e_i \le r$$ . We construct a projective moduli space of $$({\underline{\kappa }},\delta )$$ -(semi)stable singular principal G-bundles of rank r, degree d, with generalized parabolic structure of type $${\underline{e}}$$ supported on the divisors $$D_{1}=y_{1}^{1}+y_{2}^{1},\ldots ,D_{\nu }=y_{1}^{\nu }+y_{2}^{\nu }$$ . In case Y is the normalization of a connected and reducible projective nodal curve X, there exists a closed subscheme coarsely representing the subfunctor corresponding to those bundles that descend to X. We prove that the descent operation gives a bijection between the set of isomorphism classes of singular principal G-bundles of type $${\underline{e}}$$ on X and the set of isomorphism classes of descending singular principal G-bundles with generalized parabolic structures of type $${\underline{e}}$$ satisfying certain condition on Y. If the stable locus is dense inside the moduli space of descending singular principal G-bundles, the descent operation induces a birational, surjective and proper morphism onto the schematic closure of the space of $$\delta $$ -stable singular principal G-bundles of type $${\underline{e}}$$ . This generalizes the known results over irreducible curves.

Deployable Multi-Faceted Reflectarray Antenna in Offset Configuration With Band Enhancement

A multifaceted reflectarray that follows a parabolic cylinder structure is presented to improve the antenna bandwidth compared to a conventional reflectarray. The antenna is suitable to be used in SmallSats since it is low profile and low cost, and can be easily folded and deployed on this kind of platform. To evaluate the characteristics of this solution and the ability to work in different polarizations, two multifaceted demonstrators have been designed, manufactured, and tested. They generate a pencil beam pattern in the Ka-band and are compared to a single-facet offset reflectarray of equivalent aperture size. The multifaceted structure conveniently exploits both the unit cell properties and the geometry to achieve a significant improvement in antenna bandwidth compared to the single-facet version with a better tradeoff between antenna characteristics and performance achieved.

Parabolic completions in gibbon duets may signal appreciation of projectile motion

Most gibbon species produce salient duet calls at daybreak. Duets start with low frequency barks by males, followed by the female great call, and end with a short, and often complex, male-dominated coda. The female great call itself typically climaxes via a crescendoing increase in pitch, tempo, or both and characteristically features bilaterally symmetrical parabolic structures, which can manifest both in the distribution of vocal units over time as well as in frequency. Male codas appear to anticipate and even complete many of these female-initiated parabolas. Employing spectrograms of species-typical great calls from nearly all gibbon species (n = 12), I plotted coordinates of the upper-most frequency of each vocal unit. Using these x = time and y = frequency coordinates (plus x-differences), I tabulated the parabolas with the best possible second order polynomial fits for each species’ great call. Measures of parabolic fit for each call were then compared to quantitative locomotor estimates for each species. All forms of parabolic assessment had positive correlations with leaping bout percentages across species. These results indicate that gibbon duets may function to signal a fundamental understanding of parabolic shapes—presumably useful in landing airborne locomotor (especially leaping) bouts spanning canopy elements—enabling concordant execution of arboreally projectile acrobatics.

Flexoelectric vibration control of parabolic shells

The presented work focuses on the spatially distributed actuation behavior of flexoelectric actuators on a parabolic cylindrical shell panel with simply supported boundary conditions. A flexoelectric actuator with significant electric field gradients could generate actuation forces and control moments to drive or control system oscillations. For an engineering structure with initial excitations, flexoelectric actuators could be employed to achieve vibration control with designed electric inputs. The dynamic equations of the parabolic cylindrical panel laminated with an arbitrary flexoelectric actuator are defined first. The transverse displacement excited by an external mechanical loading and flexoelectric actuators is calculated. Actuation effects and vibration control efficiency contributed by various design parameters including flexoelectric patch thickness and atomic force microscopy (AFM) probe radius are studied. As the purpose of this study is to accelerate the vibration attenuation, the open-loop control usually causes insufficient control or over-actuation effects. Using displacement feedback, velocity feedback, and acceleration feedback, the effectiveness of these three closed-loop control methods is analyzed and evaluated by the modal response. Analyses suggest that the velocity feedback could effectively attenuate oscillations with the lowest voltage input than in the other two cases. Specifically, the system damping ratio can be adjusted with velocity feedback. Lower voltage input could benefit system design and release stress concentrations caused by high electric field gradients. This research provides a basis for vibration control based on flexoelectric parabolic shell structures and provides an optimal choice for the design of flexoelectric drive closed-loop control for parabolic shell structures.

The twistor geometry of parabolic structures in rank two

Let X be a quasi-projective curve, compactified to (Y, D) with $$X=Y-D$$ . We construct a Deligne–Hitchin twistor space out of moduli spaces of framed $$\lambda $$ -connections of rank 2 over Y with logarithmic singularities and quasi-parabolic structure along D. To do this, one should divide by a Hecke-gauge groupoid. Tame harmonic bundles on X give preferred sections, and the relative tangent bundle along a preferred section has a mixed twistor structure with weights 0, 1, 2. The weight 2 piece corresponds to the deformations of the KMS structure including parabolic weights and the residues of the $$\lambda $$ -connection.

Nonplanar ion-acoustic solitons and shocks with superthermal trapped electrons and transverse perturbations

The formation and propagation of nonlinear ion-acoustic (IA) waves are studied in an unmagnetized cold viscous plasma, comprising the inertial ions and superthermal trapped electrons in cylindrical geometry with transverse perturbations. The well-known reductive perturbation method is employed to derive cylindrical trapped Kadomtsev Petviashvili Burgers (CTKPB) and cylindrical trapped Kadomtsev Petviashvili (CTKP) equations with and without dissipation effects, respectively. The exact solutions of CTKPB and CTKP equations are obtained for the first time by utilizing the dependent variable transformation. The soliton and shock structures are found to be significantly affected by the plasma parameters including the trapping efficiency parameter β, the superthermality parameter κ, viscosity µ 0 and the geometrical effects. Importantly, the geometrical effects and transverse perturbations alter the shape of solitons and shocks, resulting into the parabolic nonlinear structures. These structures become more parabolic at later times due to an interplay of transverse and time coordinates (η, τ). The results of the present study might be helpful to understand the characteristics of IA structures in space plasmas, such as auroral regions, where energetic trapped electrons have been observed.

Precision estimation of large space-borne parabolic antenna support structure

An accuracy analysis approach – mosaic equivalence approach which is based on the principle of approximate structure substitution, to a large complex spatial mechanism with three-dimensional (3D) paired bearings support joint (PBS-joint) clearance is presented to effectively estimate the support structure precision of large parabolic space-borne antenna. The analysis suggests when all the PBS-joints equipped with Metric 628/6 bearings in standard clearance, the surface precision of support structure can obtain relatively high accuracy with a 99.73% probability that root mean square (RMS) was kept in (0.3275, 0.7673) mm and peak-to-valley (PV) was kept in (0.8806, 1.8178) mm. The solution of deviation configuration under a large complex spatial mechanism using the proposed mosaic equivalence approach can be transformed into that under a mosaiced structure of its simple sub-mechanisms. As a result, the high-dimensional coupling between the deviation configuration decision variables can be effectively avoided. Besides, the constraint equations of large complex mechanisms with the PBS-joint 3D clearance can be simplified. This method lays a foundation for reducing the manufacturing cost and risk of large-diameter, high-precision satellite antennas. It has essential engineering value.

Random vibration and structural reliability of composite hyperbolic–parabolic membrane structures under wind load

The paper presents the random vibration and structural reliability of composite hyperbolic–parabolic membrane structures under wind load. First, the non-linear random vibration equation of the hyperbolic–parabolic membrane structures is established by the moment-free theory of thin shells, von Karman’s large deflection theory, and the potential flow theory. The results of random dynamic responses are obtained with the Fokker Planck Kolmogorov equation method (FPK) solving the equation. Then, the structural performance function of composite membrane structures is established based on the Displacement First Passage Failure Criteria (DFPFC) and the results of random dynamic responses. Furthermore, the reliability index (RI) of the performance function is calculated by the JC method. Finally, the theoretical model proposed is validated by experimental investigation utilizing the Monte Carlo sampling method (MCS). Additionally, the influence of wind speed, pretension force, and rise–span ratio on hyperbolic–parabolic membrane structure reliability is analyzed. The paper can provide important references for the design and analysis of membrane structures.

Zero-electron-mass limit of the compressible Navier–Stokes–Poisson equations with well/ill-prepared initial data

In this study, we consider the viscous compressible Navier–Stokes–Poisson equations, which consist of the balance laws for electron density and moment, and a Poisson equation for the electrostatic potential. The limit of vanishing electron mass of this system with both well/ill-prepared initial data on the whole space is rigorously justified within the framework of local smooth solution. We first make use of the symmetric hyperbolic–parabolic structure of the compressible Navier–Stokes–Poisson equation to obtain uniform estimate in the short time, by which we show uniform existence of local classical solution to the compressible Navier–Stokes–Poisson equation in $\mathbb {R}^d(d\geq 1)$. Further, with uniform estimate of time derivatives, we show the zero-electron-mass limit of the solutions for the compressible Navier–Stokes–Poisson equation with well-prepared initial data in $\mathbb {R}^d(d\geq 1)$ by using Aubin's lemma. A detailed spectral analysis on the linearized system is done so that we are able to prove the zero-electron-mass limit of the solutions with ill-prepared initial data in $\mathbb {R}^d(d\geq 3)$, where the convergence occurs away from the time $t=0$. Finally, note that the dissipation mechanism for the linearized compressible Navier–Stokes–Poisson system is different from that of the compressible Euler equations in Grenier (Commun. Partial Diff. Eqns.21 (1996), 363–394); Grenier (Commun. Pure Appl. Math.50 (1997), 821–865); Ukai (J. Math. Kyoto Univ.26 (1986), 323–331), or that of the compressible Euler–Poisson equations in Ali and Chen (Nonlinearity24 (2011), 2745–2761), since its eigenvalues are somehow similar to that of heat equation, and the fundamental solution contains a part behaving like the heat kernel, thus a big difficulty is the singularity of the heat kernel at $t=0$.

Guiding particles along arbitrary trajectories by circular Pearcey-like vortex beams

A type of circular Pearcey-like vortex beam (CPLVB) is introduced numerically and experimentally, combining the properties of self-acceleration and abruptly autofocusing in the off-axis position. The interplay between the spiral phase and the modulated phase of arbitrary predesigned trajectories assists the beam to present a special shape which is suitable for manipulating and guiding particles along arbitrary trajectories. The beam propagating along the hyperbolic, hyperbolic secant trajectories generates a twisting hollow guide channel, and a parabolic bottlelike structure is constructed when the beam accelerates along the parabolic trajectory. Furthermore, the generation of the CPLVB, stable trapping, and rotation motion of micron-sized particles and transport of light-absorbing particles in air are realized in the experiment. Our results may bring about possibilities for wave front control, optical guidance, and manipulation of particles.

An ultra-high sensitivity fluorescence sensor based on fluorescence technology

An ultra-high sensitivity fluorescence sensor with 1 ng/L-level detection limit was developed for water treatment applications, in which fluorescent tracing method is applied by using PTSA (1, 3, 6, 8-pyrenetetrasulfonic acid, sodium salt) to indicate the concentration of water treatment agents. This sensor consists of an optical part for fluorescence excitation and detection, as well as a signal processing and control circuit. The optical part employs a compound parabolic concentrator structure and achieves 6-fold increase in the collected fluorescence intensity. The circuit handles the determination procedures such as LED emission modulation, detector signal processing and concentration determination of water treatment agents. For PTSA with ultrapure water in ultra-low concentration range of 0 – 0.1 μg/L, a detection limit of 7 ng/L is demonstrated. The sensor has benefits of low cost, high accuracy and ease of deployment, which is promising for real-time detection of water treatment agents concentration in industrial cooling water circulation system.

Thermoelectric properties of semiconducting materials with parabolic and pudding-mold band structures

By a combination of semi-analytical Boltzmann transport and first-principles calculations, we systematically investigate thermoelectric properties of semiconducting (gapped) materials by varying the degrees of polynomials in their energy dispersion relations, in which either the valence or conduction energy dispersion depends on the wave vector raised to the power of two, four, and six. Within the relaxation time approximation, we consider various effects such as band gaps, dimensionalities, and dispersion powers to understand the conditions that can give the optimal thermoelectric efficiency or figure of merit (ZT). Our calculations show that the so-called pudding-mold band structure produces larger electrical and thermal conductivities than the parabolic band, but no significant difference is found in the Seebeck coefficients of the pudding-mold and parabolic bands. Tuning the band gap of the material to an optimum value simultaneously with breaking the band symmetry, the largest ZT is found in a combination of two-contrasting polynomial powers in the dispersion relations of valence and conduction bands. This band asymmetry also shifts the charge neutrality away from the undoped level and allows optimal ZT to be located at a smaller chemical potential. We expect this work to trigger high-throughput calculations for screening of potential thermoelectric materials combining various polynomial powers in the energy dispersion relations of semiconductors. We give preliminary screening results for bulk PtS2 and FeAs2 compared with Si, where we indicate that the former two have better thermoelectric performance than the latter.

Analytic Langlands correspondence for PGL_2 on {mathbb {P}}^1 with parabolic structures over local fields

We continue to develop the analytic Langlands program for curves over local fields initiated in our earlier papers, following a suggestion of Langlands and a work of Teschner. Namely, we study the Hecke operators which we introduced in those papers in the case of a projective line with parabolic structures at finitely many points for the group PGL_2. We establish most of our conjectures in this case.