Influence of non-uniform inflow on unsteady internal flow characteristics of waterjet pump

Waterjet propulsion has many advantages when operating at high-speed conditions. As a special way of navigation, it is mostly used in high-speed ships and shallow draft ships. In this paper, a mixed-flow waterjet pump was taken as the research object. For the two cases of non-uniform inflow and uniform inflow, a modified RANS/LES method was adopted for unsteady calculation of the whole channel, aiming at investigating the influence mechanism of the non-uniform inflow on the energy performance and pressure pulsation characteristics of the waterjet pump. The hydrodynamic characteristics of the waterjet pump were comprehensively analyzed such as head, efficiency, axial-force, internal flow and pressure pulsation. It is found that the non-uniform inflow will reduce the external characteristics of the waterjet pump and lead to the huge fluctuation of energy performance with time. Low-speed swirls occur locally in the intake duct for non-uniform inflow, in which condition the vorticity is much higher than that for uniform inflow. In terms of the low-speed area, [Formula: see text] and [Formula: see text], the values under non-uniform inflow condition are generally larger than those under uniform flow condition when in the impeller and guide vane zone. The dominant frequencies of pressure pulsation are, respectively, [Formula: see text], 7[Formula: see text] and 4[Formula: see text] in the intake duct, impeller and diffuser, which are almost consitent for the two cases. However, the frequency features are more diverse, and the amplitudes corresponding to the same frequencies are more intense for non-uniform inflow.

On rectifiable measures in Carnot groups: representation

This paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of $$\mathscr {P}$$ P -rectifiable measure. First, we show that in arbitrary Carnot groups the natural infinitesimal definition of rectifiabile measure, i.e., the definition given in terms of the existence of flat tangent measures, is equivalent to the global definition given in terms of coverings with intrinsically differentiable graphs, i.e., graphs with flat Hausdorff tangents. In general we do not have the latter equivalence if we ask the covering to be made of intrinsically Lipschitz graphs. Second, we show a geometric area formula for the centered Hausdorff measure restricted to intrinsically differentiable graphs in arbitrary Carnot groups. The latter formula extends and strengthens other area formulae obtained in the literature in the context of Carnot groups. As an application, our analysis allows us to prove the intrinsic $$C^1$$ C 1 -rectifiability of almost all the preimages of a large class of Lipschitz functions between Carnot groups. In particular, from the latter result, we obtain that any geodesic sphere in a Carnot group equipped with an arbitrary left-invariant homogeneous distance is intrinsic $$C^1$$ C 1 -rectifiable.

Dirichlet Polynomials and Entropy

A Dirichlet polynomial d in one variable y is a function of the form d(y)=anny+⋯+a22y+a11y+a00y for some n,a0,…,an∈N. We will show how to think of a Dirichlet polynomial as a set-theoretic bundle, and thus as an empirical distribution. We can then consider the Shannon entropy H(d) of the corresponding probability distribution, and we define its length (or, classically, its perplexity) by L(d)=2H(d). On the other hand, we will define a rig homomorphism h:Dir→Rect from the rig of Dirichlet polynomials to the so-called rectangle rig, whose underlying set is R⩾0×R⩾0 and whose additive structure involves the weighted geometric mean; we write h(d)=(A(d),W(d)), and call the two components area and width (respectively). The main result of this paper is the following: the rectangle-area formula A(d)=L(d)W(d) holds for any Dirichlet polynomial d. In other words, the entropy of an empirical distribution can be calculated entirely in terms of the homomorphism h applied to its corresponding Dirichlet polynomial. We also show that similar results hold for the cross entropy.

COMPARATIVE STUDY FOR WAVE SPEED ESTIMATION AT A SINGLE AND TWO MEASUREMENT POINTS

Local wave speed is a prognostic detector that allows the analysis of cardiovascular function. Objectives: This study compared wave speed ([Formula: see text] measurements at single-point and two-point techniques. Material and methods: [Formula: see text] were determined from the cepstral analysis of the blood flow velocities, which identified the arrivals times of reflected waves. The blood velocities waveforms were measured by using phase-contrast magnetic resonance (PCMR) for 20 subjects on young and old healthy subjects. Local wave speed was estimated through the arrivals time of reflections waves ([Formula: see text] and the distance separating the measurement site to reflection area ([Formula: see text] or the distance separating the two measurement sites. Results: Our obtained results were in total agreement with reference values reported in the literature. Moreover, the detected results show that there is a high correlation ([Formula: see text]) between the two methods. Conclusion: The analysis of the wave speed variations with advancing age is also achieved out through different regression models.

Tailoring Local Hysteresis in Small Clusters of Dipolar Interacting Magnetic Nanoparticles

Using first-principle calculations and kinetic Monte Carlo simulation, we study the local and averaged hysteresis in tiny clusters of [Formula: see text] magnetic nanoparticles (MNPs) or [Formula: see text]-mers. We also analyze the variation of local dipolar field acting on the constituent nanoparticles as a function of the external magnetic field. The dipolar interaction is found to promote chain-like arrangement in such a cluster. Irrespective of cluster size, the local hysteresis response depends strongly on the corresponding dipolar field acting on a nanoparticle. In a small [Formula: see text]-mer, there is a wide variation in local hysteresis as a function of nanoparticle position. On the other hand, the local hysteresis is more uniform for larger [Formula: see text]-mer, except for MNPs at the boundary. In the case of superparamagnetic nanoparticle and weak dipolar interaction, the local hysteresis loop area [Formula: see text] is minimal and depends weakly on the [Formula: see text]-mer size. While for ferromagnetic counterpart, [Formula: see text] is considerably large even for weakly interacting MNPs. The value of [Formula: see text] is found to be directly proportional to the dipolar field acting on the nanoparticle. The dipolar interaction and [Formula: see text]-mer size also enhance the coercivity and remanence. There is always an increase in [Formula: see text] with cluster size and dipolar interaction strength. Similarly, the averaged hysteresis loop area [Formula: see text] also depends strongly on the [Formula: see text]-mer size, particle size and dipolar interaction strength. [Formula: see text] and [Formula: see text] always increase with [Formula: see text]-mer size and dipolar interaction strength. Interestingly, the value of [Formula: see text] saturates for [Formula: see text] and considerable dipolar interaction irrespective of particle size. We believe that this work would help understand the intricate role of dipolar interaction on hysteresis and the organizational structure of MNPs and their usage in drug delivery and hyperthermia applications.

A New Construction of Holditch Theorem for Homothetic Motions in C p

In this study, the planar kinematics has been studied in a generalized complex plane which is a geometric representation of the generalized complex number system. Firstly, the planar kinematic formulas with one parameter for homothetic motions in the generalized complex plane have been mentioned briefly. Then, the Steiner area formula given areas of the trajectories drawn by the points taken in a generalized complex plane have been obtained during the one-parameter planar homothetic motion. Finally, the Holditch theorem, which gives the relationship between these areas of trajectories, has been expressed for homothetic motions in a generalized complex plane. So, this theorem obtained in this study is the most general form of all Holditch theorems obtained so far.

Synthesis of Novel g-C3N4/NH2-MIL-88B(Fe) Composite Photocatalysis for Efficient Ciprofloxacin Degradation Under Simulated Sunlight Irradiation

The presence of the antibiotics in the wastewater has posed a huge risk to aquatic life and human health. It is a great significance to develop an effective technology to treat the antibiotics-containing wastewater. In this study, a series of g-C3N4/NH2-MIL-88B(Fe) composite photocatalysts are synthesized through a simple one-step method. The structure and optical properties of prepared photocatalysts are detected by X-ray diffraction (XRD), field emission scanning electron microscope (FESEM), transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), UV–Vis absorption spectra (UV–Vis DRS), photoluminescence (PL) spectroscopy and transient photocurrent techniques, respectively. FESEM and TEM show that MOF is uniformly dispersed in petaloid g-C3N4. The uniform dispersion of Fe-MOFs in the heterojunction composites increases the specific surface area ([Formula: see text] of g-C3N4, which results in a great adsorption property for the nanocomposite. The capture experiment shows that [Formula: see text]O[Formula: see text] and h[Formula: see text] are the main active substances in ciprofloxacin (CIP) degradation. These prepared composite photocatalysts exhibit excellent CIP photodegradation activity under visibly light irradiation with an apparent rate constant of 0.0127[Formula: see text]min[Formula: see text] (3.74 times as the rate of single component). The remarkable catalytic performance can be ascribed to the fact that the g-C3N4/NH2-MIL-88B(Fe) heterojunction inhibits the recombination of photoinduced electron–hole pairs and improved the visible light absorption.

An area formula for the triangle of residual centroids and its generalizations

In this paper we consider an inscribed triangle XY Z to a triangle ABC and we establish a relation between the area of these two triangles and the area of the triangle determined by the centroids of the residual triangles AZY, BXZ and CY X. Moreover we generalize this relation to the case of a general barycenter instead of centroid and also to quadrilaterals.

Irreducible first Brillouin zone for two-dimensional magnonic crystals with asymmetric complex lattices

Two-dimensional (2D) magnonic crystal (MC) with an asymmetric complex basis is proposed in this paper, and its band structures are calculated in the whole area of the first Brillouin zone (BZ). This kind of MCs is composed of two different atoms in the unit cell, and the symmetry of the unit cell is broken due to changes in the position of the second atom, so the irreducible part of the BZ is no longer the small area [Formula: see text] for square lattice, and it must be expanded to the whole first BZ. Only by investigating the whole first BZ, can we get the true full band-gap for this kind of MCs.