The Disintegration of a Floating Ferrofluid Layer into an Ordered Drop System in a Vertical Magnetic Field

Magnetic fluids,also known as ferrofluids,are versatile functional materials with a wide range of applications.These applications span from industrial uses such as vacuum seals,actuators,and acoustic devices to medical uses,including serving as contrast agents for magnetic resonance imaging(MRI),delivering medications to specific locations within the body,and magnetic hyperthermia for cancer treatment.The use of a non-wettable immiscible liquid substrate to support a layer of magnetic fluid opens up new possibilities for studying various fluid flows and related instabilities in multi-phase systems with both a free surface and an interface.The presence of two deformable boundaries within a ferrofluid layer significantly reduces the critical magnetic field strength required to transform the layer into an organized system of drops or polygonal figures evolving according to the intensity,frequency and direction of the considered magnetic field.This paper experimentally investigates this problem by assuming a uniform magnetic field perpendicular to the surface.This specific subject has not been previously explored experimentally.The critical magnetic field intensity required to destabilize the ferrofluid layer is determined based on the layer’s thickness and the fluid’s initial magnetic susceptibility.It is demonstrated that the critical magnetic field strength needed to disrupt the initially continuous ferrofluid layer increases with the layer’s thickness.Conversely,an increase in the ferrofluid’s magnetic susceptibility results in a decrease in the critical magnetic field strength.The emerging droplet structures are analyzed in terms of the number of drops,their size,and the periodicity of their arrangement.The number of droplets formed depends on the initial thickness of the layer,the presence or absence of a stable rupture in the upper layer,and the rate at which the magnetic field strength is increased to the critical value.A characteristic viscous time is proposed to evaluate the decomposition of the ferrofluid layer,which depends on the duration of the magnetic field’s application.The experimental data on the instability of a ferrofluid layer on a liquid substrate are compared with the theoretical results from the study of“magnetic fluid sandwich structures”conducted by Rannacher and Engel.This comparison highlights the similarities and differences between experimental observations and theoretical predictions,providing a deeper understanding of the behavior of ferrofluid layers under the influence of magnetic fields.

Dynamic collision avoidance for cooperative fixed-wing UAV swarm based on normalized artificial potential field optimization

Cooperative path planning is an important area in fixed-wing UAV swarm.However,avoiding multiple timevarying obstacles and avoiding local optimum are two challenges for existing approaches in a dynamic environment.Firstly,a normalized artificial potential field optimization is proposed by reconstructing a novel function with anisotropy in each dimension,which can make the flight speed of a fixed UAV swarm independent of the repulsive/attractive gain coefficient and avoid trapping into local optimization and local oscillation.Then,taking into account minimum velocity and turning angular velocity of fixed-wing UAV swarm,a strategy of decomposing target vector to avoid moving obstacles and pop-up threats is proposed.Finally,several simulations are carried out to illustrate superiority and effectiveness.

Comparison of corneal biomechanical properties in normal tension glaucoma patients with different visual field progression speed

AIM：To compare the corneal biomechanical properties difference by ocular response analyzer（ORA） in normal tension glaucoma（NTG） patients with different visual field（VF） progression speed. METHODS：NTG patients with well-controlled Goldmann applanation tonometer（GAT） who routinely consulted Kitasato University Hospital Glaucoma Department between January 2010 and February 2014 were enrolled.GAT and ORA parameters including corneal compensated intraocular pressure（lOPcc）,Goldmann estimated intraocular pressure（lOPg）,corneal hysteresis（CH）,corneal resistance factor（CRF） were recorded.VF was tested by Swedish interactive threshold algorithm（SITA）-standard 30-2 fields.All patients underwent VF measurement regularly and GAT did not exceed 15 mm Hg at any time during the 3y follow up.Patients were divided into four groups according to VF change over 3y,and ORA findings were compared between the upper 25th percentile group（slow progression group） and the lower 25th percentile group（rapid progression group）.RESULTS：Eighty-two eyes of 56 patients were studied.There were 21 eyes（21 patients） each in rapid and slow progression groups respectively.GAT,lOPcc,lOPg,CH,CRF were 12.1＋1.4 mm Hg,15.8±1.8 mm Hg,12.8±2.0 mm Hg,8.4±1.1 mm Hg,7.9±1.3 mm Hg respectively in rapid progression group and 11.5±1.3 mm Hg,13.5±2.1 mm Hg,11.2±1.6 mm Hg,9.3±1.1 mm Hg,8.2±0.9 mm Hg respectively in slow progression group（P=0.214,〈0.001,0.007,0.017,0.413,respectively）.In bivariate correlation analysis,lOPcc,lOPcc-GAT and CH were significant correlated with m△MD（r =-0.292,-0.312,0.228 respectively,P =0.008,0.004,0.039 respectively）.CONCLUSION：Relatively rapid VF progression occurred in NTG patients whose lOPcc are rather high,CH are rather low and the difference between lOPcc and GAT are relatively large.Higher lOPcc and lower CH are associated with VF progression in NTG patients.This study suggests that GAT measures might underestimate the IOP in such patients.

The anomalous reactions of the geomagnetic horizontal field transfer functions before Tangshan earthquake

We have collected the data of variometers in period from 1972 through 1984 at Changli and Baijiatuan stations. The results calculated from 19 groups of data show: 1) There are no significant anomalies of A, B at Baijiatuan and that of B at Changli, but there are evident anomalous changes for A u, A v at Changli station. This result basically agrees to the a, b calculated using the method of measuring magnetograms, which demonstrates that the anomalies limited in the aftershock area and its neighbouring regions. 2) There are some changes of the inter station transfer functions of C u, C v, F u, F v before Tangshan earthquake, and the changes of the image parts C v, F v are more obvious, which is in agreement with the research results for Hualian earthquake. However, according to the results of Carlisle M =5.0 earthquake by Beamish(1982), the real parts F u, C u change more significantly.

A Normalizing Field Flow Induced Two-Stage Stochastic Homogenization Method for Random Composite Materials

The traditional stochastic homogenization method can obtain homogenized solutions of elliptic problems with stationary random coefficients.However,many random composite materials in scientific and engineering computing do not satisfy the stationary assumption.To overcome the difficulty,we propose a normalizing field flow induced two-stage stochastic homogenization method to efficiently solve the random elliptic problem with non-stationary coefficients.By applying the two-stage stochastic homogenization method,the original elliptic equation with random and fast oscillatory coefficients is approximated as an equivalent elliptic equation,where the equivalent coefficients are obtained by solving a set of cell problems.Without the stationary assumption,the number of cell problems is large and the corresponding computational cost is high.To improve the efficiency,we apply the normalizing field flow model to learn a reference Gaussian field for the random equivalent coefficients based on a small amount of data,which is obtained by solving the cell problems with the finite element method.Numerical results demonstrate that the newly proposed method is efficient and accurate in tackling high dimensional partial differential equations in composite materials with complex random microstructures.

Normal Bases and Their Dual-Bases over Finite Fields

In this paper, we prove the following results： 1） A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2） The normal basis N is self-dual if and only if its multiplication table is symmetric and Tr（α^2） = 1, where α generates N; 3） An optimal normal basis N is self-dual if and only if N is a type-Ⅰ optimal normal basis with q = n = 2 or N is a type-Ⅱ optimal normal basis.

Effects of vertical electric field and compressive strain on electronic properties of bilayer ZrS2

Using first-principles calculations,including Grimme D2 method for van der Waals interactions,we investigate the tuning electronic properties of bilayer zirconium disulfides（ZrS_2/ subjected to vertical electric field and normal compressive strain.The band gap of ZrS_2 bilayer can be flexibly tuned by vertical external electric field.Due to the Stark effect,at critical electric fields about 1.4 V/？,semiconducting-metallic transition presents.In addition,our results also demonstrated that the compressive strain has an important impact on the electronic properties of ZrS_2 bilayer sheet.The widely tunable band gaps confirm possibilities for its applications in electronics and optoelectronics.

On the Existence for Some Special Primitive Elements in Finite Fields

Let F_q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive elementα∈ F_(q^n) such that α + α^(-1)is also primitive or α + α^(-1)is primitive and α is a normal element of F_(q^n) over F_q.

NORMAL VECTOR FIELDS OF IMMERSIONS OF n-MANIFOLDS IN (2n—1)-MANIFOLDS

This paper studies the nonzero normal vector fields of immersions homotopic to a map g: Mn→N2n-1. In the case of the stable normal bundle of g being orientable, rather complete results are obtained.

Ab initio study of vibrational frequencies, force field and normal coordinate analysis of the cis- and trans-isomers of nitrosomethanol

In this paper, the equilibrium geometries of two isomers of the newly found compound ——nitrosomethanol——have been optimized by ab initio SCF MO method with 3-21G basic set by gradient technique. And the second derivatives of potential energy (i. e. the force constant matrix elements) have been calculated analytically. Hence the entire force fields of the two isomers of nitro- somethanol have been obtained theoretically. The theoretical vibrational frequencies and the corres- ponding normal modes were obtained and compared with the experimental values. and the structures of two isomeric forms of nitrosomethanol are established.

Atlas Compatibility Transformation:A Normal Manifold Learning Algorithm

Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.