bluuebunny/crossref_metadata_2025 huggingface dataset:
A Multi-Scale Modeling Approach to Simulate Intergranular Crack Propagation in Textured Polycrystalline Materials
Authors: Arafin Muhammad A. , Lu Jian , Szpunar Jerzy
Published: December 2011

In this paper, a multiscale modeling approach has been developed to simulate the intergranular crack propagation in textured polycrystalline materials. Embedded Atom Method (EAM) and Molecular Dynamics (MD) simulations were carried out to determine the energy and fracture strength of different types of grain boundaries in Ni3Al. Subsequently, the atomistic model has been integrated with the microstructure based model of crack propagation using the Voronoi-Markov Chain-Monte Carlo approach. The model has been utilized to evaluate the crack length for various scenarios and reasonable results are obtained.
Texture Evolution along the Layer Thickness in a Fe-3%Si Steel under Electropulsing Treatment
Authors: Wang Xin Li , Zhao Hong Ming , Dai Wen Bin , Zhao Xiang
Published: December 2011

Effects of electric current densities on recrystallization texture evolution in cold-rolled Fe-3%Si steel were investigated by using a high current density electropulsing treatment. Results showed that the orientation density of α fiber and  fiber varied with the specimen thickness during current passing. However, with the current density increasing, the difference from layer thickness almost vanished. In addition, Goss component texture was the final sharper one but no relation with the specimen thickness at 9.96kAmm-2. By the texture evolution analysis, it was found that the preferred nucleation always occurred in the surface layer due to the high storied energy coursed by previous cold rolling. Combined with the corresponding microstructures, it could be found that though there was an apparent texture evolution along specimen thickness, the microstructure had no change with thickness. In addition, due to the application of electropulsing, the recrystallization nucleation was greatly increased.
Mesoscopic EBSD Analysis and Mesomechanical Behavior of Ridging or Roping in AA6XXX Alloys
Authors: Qin Ling , Seefeldt Marc , Bennett Tricia A. , Petrov Roumen H. , van Houtte Paul
Published: December 2011

Aluminium alloys for car body manufacturing often show a specific type of band-shaped surface roughening upon stretching, called “ridging” or “roping”. Experimental research as well as modelling attempts have indicated that the evolving surface roughness profiles cannot be understood based on banding of individual surface texture components, like cube or Goss, only. Therefore, it is proposed to study banding on the “mesoscopic” level of texture banding rather than on the “microscopic” one of orientation banding. In mechanical terms, such patterning in the texture would lead to patterning in, for instance, the Lankford coefficient (r-value), so that the mechanical response can be calculated on an intermediate length scale. The present contribution presents a method for calculating r-value patterning from Electron Backscatter diffraction (EBSD) orientation maps. In a first test case of a strongly ridging AA6xxx sheet, indeed patterning in the r-value is found which corresponds to reported patterning of the surface roughness.
Effect of Modes of Rolling on Mechanical Properties, Texture and Ballistic Performance of Al-7017 Alloy
Authors: Jena Pradipta Kumar , Mondal Chandan , Siva Kumar K. , Singh A.K.
Published: December 2011

This study describes the influence of texture and associated mechanical properties on ballistic performance of Aluminium-7017 alloy in two different (unidirectional and clock) hot rolling conditions. The change in texture has been explained in terms of β fiber in hot rolled and T6 tempered condition. A marginal variation in strength and hardness is observed with changing the mode of rolling, whereas Charpy impact values are found to be varying considerably. Results show that the unidirectional rolled material exhibits improved ballistic performance than that of the clock rolled plate. This has been attributed to different textures present in both the plates.
Effect of Roll Diameter and Modes of Rolling on Evolution of Texture in High Purity Aluminum
Authors: Mondal Chandan , Rao A.C. Umamaheshwer , Tagore G.R.N. , Singh Ashok Kumar
Published: December 2011

Present work describes the development of texture in high purity aluminum under different modes of deformation by rolling using two different roll diameters, namely 300 and 610 mm. It has been observed that the change in both the roll diameter as well as the modes of rolling has a marked influence on the evolution of texture as well as the characteristics of a- and β-fibres. The results are discussed in terms of the effects of roll gap geometry and the relevant stress conditions that affect the strain path of crystallite rotation.
Ferroelastic Domains and Anisotropy in Lead Free Piezoelectrics
Authors: Li Bin Zhi , Fancher Chris , Blendell John E. , Garcia R. Edwin , Bowman Keith J.
Published: December 2011

Our research investigates the correlations between domain texture and microstructural features, including crystallographic texture in bulk and thin film polycrystalline materials to understand the development of piezoelectric and other anisotropic properties in a number of rapidly evolving lead free piezoelectric materials. We investigate approaches to understanding polarization distributions by starting from polarization measurements. In addition, 2D and 3D microstructural simulations are carried out in all types of ferroelectrics to rationalize and then engineer their equilibrium and kinetic response. This paper discusses recent findings associated with bulk piezoelectricity, phase stability, and ferroelastic and ferroelectric domain motion for materials such as Ba(Ti0.8Zr0.2)O3-x(Ba0.7Ca0.3)TiO3 (BZT-BCT) and Bi0.5Na0.5TiO3 (BNT). Conventional and synchrotron-based x-ray diffraction, electron and optical microscopy and piezoelectric characterization techniques are employed to assess texture, both as a function of poling and temperature. The coupling between microstructure and the inherent directional biases fundamental to piezoelectric and ferroelectric performance enable consideration of orientation and anisotropy in systems with unique constraints.
Effect of AlN on Microstructure and Mechanical Properties of Mg-Al-Zn Alloy
Authors: Liu Peng , Geng Hao Ran , Wang Zhen Qing , Zhu Jian Rong , Pan Fu Sen , Dong Xiao Bin
Published: December 2011

Effects of AlN addition on the microstructure and mechanical properties of as-cast Mg-Al-Zn magnesium alloy were investigated using optical microscopy (OM), scanning electron microscopy (SEM), X-ray diffraction (XRD) and tensile testing. Five different samples were made with different amounts of AlN(0wt%, 0.12wt%, 0.30wt%, 0.48wt%, 0. 60wt%). The results show that the phases of as-cast alloy are composed of α-Mg,β-Mg17Al12. The addition of AlN suppressed the precipitation of the β-phase. And, with the increase of AlN content, the microstructure of β-phase was changed from the reticulum to fine grains. When AlN content was up to 0.48wt% in the alloy, the β-phase became most uniform distribution. After adding 0.3wt% AlN to Al-Mg-Zn alloy, the average alloy grain size reduced from 102μm to 35μm ,the tensile strength of alloy was the highest. The average tensile strength increased from 139MPa to 169.91MPa, the hardness increased from 77.7HB to 98.4HB, but the elongation changes indistinctively. However, when more amount of AlN was added, the average alloy grain size did not reduce sequentially and increased to 50μm by adding 0.6wt% AlN and the β-phase became a little more. Keywords: Al-Mg-Zn alloy; AlN; β-Mg17Al12; Tensile strength
Investigation of Precipitated Hardening Layer Performance on Machined NAK80 Steel Surface
Authors: Yang Xin Chun , Wang Hong Jun
Published: December 2011

The surface integrity of NAK80 steel by grinding and electrical discharge machining (EDM) was studied in this paper. Microhardness, 3D topography and surface roughness of machined surface precipitation hardening layer were measured respectively. And the residual stress of the machined steel surface was measured with X-ray diffraction. Further experiments indicated that, compared with EDM, grinding method can obtain better surface integrity, and lower stress concentration sensitivity of NAK80 steel. But when machining the parts with complex shapes, EDM has the unparalleled advantages to grinding method.
Study on Diffusion Processes of Water and Proton in PEM Using Molecular Dynamics Simulation
Authors: Chen Lei , Tao Wen Quan
Published: December 2011

In this paper a molecular dynamics calculation model for the Nafion 117 membrane is constructed by Materials Studio (MS) software platform to study its micro-structure and transport properties. Based on the calculation model, cell structures of different water content of Nafion 117 membrane are obtained and the predicted density values of simulated cell are in good agreement with experimental data. Meanwhile, the diffusion processes of water molecules and hydrogen ions in the membrane are studied, respectively. The predicted diffusion coefficients of both water molecules and hydrogen ions increase with the water content, which agrees well with the variation trend of experimental data. The reasons for the deviation between numerical results and the experiment values in literature are analyzed.
Study on FEM Numerical Simulation Method for the Welding Distortion
Authors: Lu Yao Hui , Wu Xing Wen , Zeng Jing , Wu Ping Bo
Published: December 2011

The control of welding distortion during assembly process is very important. At present, there are mainly two numerical simulation methods for the welding distortion which are thermo-elastic-plastic finite element method and its simplified approach of inherent strains. At first, taking T-joint as an example, the welding distortions were computed using two methods mentioned above. Based on thermo-elastic-plastic finite element method, welding process was simulated by life and death element, moving heat source and transient state thermal field etc. Then, the welding distortion was calculated by inherent strains method after thermo-elastic-plastic computation. It was concluded from the comparison that the simulation results by using the two methods are consistent. Therefore, the inherent strains method can be conveniently and economically applied to prediction of structural welding distortion in engineering. Applied the inherent strains method, welding deformation was predicted for the bogie frame side beam of high speed train. According to the deformation results from the finite element analysis, the welding deformation of the bogie frame side beam was lager than the tolerance of quality and in reasonable agreement with the experimentally determined distortion values. The work in this paper indicated that the inherent strains method was effective to predict the welding deformation so as to control the welding quality in large complex structures, such as the bogie frame of railway vehicle. Key words: welding distortion; thermo-elastic-plastic method; inherent strains approach; numerical simulation; bogie frame;
A Study on Mathematical Model of Deformation Force for Tube Nosing with Conical Die
Authors: Chu Liang , Wang Qing Wei , Bi Yan , Bi Da Sen
Published: December 2011

Based on analyzing the stress-strain characters of material in nosing deformation zone, and considering two influencing factors, i.e. material thickness variation and material work-hardening, according to ignoring and considering the influence of additional bending stress at the entrance of die, and the different forms of work-hardening of metal materials, a new set of mathematical models of deformation force calculated for tube nosing with conical die are set up by utilizing slab method that belongs to one of the theoretic methods solving the problems of metal plastic forming. Furthermore, the scope of the application of every mathematical model of deformation force calculated for tube nosing with conical die is classified from conical die semi-angle and work-hardening of metal material point of view in theory.
Comparison of Warm Deformation Behavior between Quenched and Annealed ASTM 1045 Steel
Authors: Zhao Xin , Yang Xiao Ling , Jing Tian Fu
Published: December 2011

The warm deformation behavior of as-quenched and as-annealed ASTM 1045 steel was studied by isothermal compression testing on a Gleeble3500 machine. The temperature range was 550-700°C and the strain rate range 0.001-0.1s-1. Transmission electron microscopy (TEM) was used to study the microstructures associated with the observed deformation phenomenons. The results show that the flow stress of quenched specimens is higher than that of annealed ones at 550°C when strain rates are greater than 0.001s-1. However, at 600-700°C and strain rate of 0.001s-1, the whole flow curves of quenched specimens are below that of annealed ones. Under the rest conditions, the flow stress of quenched specimens is higher at the beginning of compression and then the opposite is true after the strain is greater than a critical value. The microstructure examination proves that the dynamic recrystallization easily occurs in quenched specimens during warm compression, which results in the above phenomenons. Keywords: warm deformation, flow stress, steel, quenching, annealing
Numerical Simulation of Al Ball Forming Process in Skew Rolling
Authors: Shi Xiao Min , Wang Bao Jian
Published: December 2011

According to the equation of pass surface in skew rolling, the characteristic curves are obtained by VC++ programming, a three-dimensional model of the roller is constructed by using of modeling function of Pro/E software, it is done for numerical simulation of Φ21.6mm Al ball forming process in skew rolling by means of ANSYS6.0 software, the stress and strain distributions are obtained in this simulation. It provides the important foundation for the design of dies and making clear the cause of the rolled piece inner defect. Key words: Skew rolling; Numerical simulation; Pro/E modeling; Al ball
Numerical Simulation of Seamless Tube’s Stretch Reducing Process
Authors: Li Jun Hong , Yu Hui
Published: December 2011

The stretch reducing process is the last hot deformation process of the hot-rolled seamless steel tube’s production. Its role is to decrease the tube’s diameter under the large tension and expand the range of product specifications. But the stretch reducing process often results in wall thickness tolerance at the head and end of the tube. In order to solve the problem, a 3D elastic-plastic finite element analysis model was established to simulate the stretch reducing process of φ159 unit. Based on this, the tube’s wall thickness distribution was studied and the parameters of sharpen rolling process was put forward. Numerical simulation results indicate that with the parameters of sharpen rolling process, the length of wall thickness tolerance was shorten and the rate of finished products was proved.
Effect of the Die and Tool Structure on Continuous Extrusion Expansion Forming of Copper
Authors: Yun Xin Bing , Chen Xu , Zhao Ying , Fan Zhi Xin , Song Bao Yun
Published: December 2011

Continuous extrusion expansion deforming is an advanced forming process for manufacturing copper bus-bar, die and tool structure is important effect factor of deformation. Based on the characteristics of the forming process, the model of rigid-plastic finite element (FE) on DEFORMT is established and the numerical simulation of continuous extrusion expansion forming process of the copper bus-bar is carried, The metal flow regularity and the mean-square deviation of velocity (SDV) with the different structure of expansion chamber and port hole and die assembled pattern is analyzed. The result show that when using the drum expansion chamber, the trapezium of port hole without transition surface and the die fitted in reverse, the variance of flow velocity is the minimum and deformation is the most homgeneous, the SDV is 0.62. The simulation results provide a theoretical direction for optimization design of die and tool structure of the continuous extrusion expansion forming. Keywords: copper bus-bar, continuous extrusion expansion deforming, die and tool structure optimization, numerical simulation
Numerical Simulation and Experiment Research on Temperature Field of Steel Slab in Walking Beam Furnace
Authors: Chen Chao , Ding Cui Jiao , Ouyang De Gang , Liu Zhan Zeng , Song Zhong Hua , Chen Sheng , Yang Chao
Published: December 2011

This paper presents a study of the temperature fields of steel slab in a walking beam furnace. To simulate the temperature distribution in the slab of heating-up process in heating furnace, a two-dimensional mathematical model was developed. The heat transfer in the furnace was very complex, so the model was developed on the assumptions that the temperature of each section of the furnace was unchangeable, the slab moved in the furnace in even velocity, the heat transfer between the slab and the walking beam was out of consideration, the longitudinal heat conduction of the slab and the effect of the scale on the heat conduction were neglected. The equations were calculated by the finite difference method. A black box experiment research was carried out to measure the temperature history of the slab as it passed through the furnace. The comparison of the calculated results with the measured results showed that the model worked well for simulating the temperature distribution of the slab in walking beam furnace. With this developed model, the optimizing of hot rolling and heating processes of steel slab can be investigated in the future.
Research of Ti2AlC/TiAl (Nb, B) Composites Based on Multi-Fractal Spectrum
Authors: Wen Ming , Yue Yun Long , Zhang Hai Tao , Li Yang
Published: December 2011

Spark plasma sintering (SPS) technology was used in-situ to fabricate the Ti2AlC/TiAl (Nb, B) composites. And the composites were treated by rapid heat treatment. which had many advantages, such as heating-up quickly, short holding time and relatively slow cooling. The hidden relationship between images could be reflected by Multi-fractal spectrum, which also could show irregularity apparently. In this paper, the SEM images which fabricated after rapid heat treatment were researched by multifractals. And the parameter was calculated by MATLAB through anglicizing the multi-fractal spectrum theory. There was only small fluctuate between lnχq (r) and lnr when r=0.00625, and lnχq (r) and lnr had well linear relationship in spite of the value of q. After the rapid heat treatment at T=1403 K, the correlation coefficient between τ (q) and q reached 99.99% . The trend of D (q) and q turned to be gently, and the fracture appeared uniformity, and these SEM images were single fractures. τ (q) and q show nonlinear relationship in q∈[-3,-1], and there was one observe steep.The clock shape relationship between the α and f (α) revealed good symmetry of spectrum, wider spectral width, uneven distribution of the fracture, multi-fractal feature clearly, and obvious characteristic of multi-fractal. Key words: multi-fractal spectrum, rapid heating heat treatment, fractal dimension
Finite Element Analysis and Optimization for the High Voltage Disconnector Self-Elastic Contact Base on ANSYS Workbench
Authors: Liu Wei Feng , Zhang Yan Min , Song Ke Xing , Zhao Pei Feng , Zhang Li
Published: December 2011

Developing a reliable engineering product requires huge amount of resources and knowledge. Often a huge amount of resources were wasted in trying to test products and understanding its reliability performances. Consequently, it takes obvious advantages of resources to develop a reliable engineering product using convenient and fast process in the fierce industrial competition. This paper optimized the structure of high voltage disconnector self-elastic contacts based on ANSYS Workbench. The parts are made of Cu-Cr alloy, the physical property is decided by the content of alloys, and the mechanical property is mainly decided by physical dimensions of self-elastic contacts which include section thickness, corner radius and middle groove width. The traditional design method for self-elastic contacts is tryout design which wastes huge amount of resources and knowledge and it is comparatively uneconomical. Using ANSYS workbench, the finite element model of the self-elastic contact was established, and the finite element analysis was carried out. Design spaces and sensitivity of the response variables, which were related to strength, stiffness and mass, were synthetically analyzed based on design of experiment and physical dimensions of self-elastic contact were optimized by the Optimizer DesignXplorer. After optimization, the self-elastic contact meets service conditions accurately, and the service life is evidently prolonged. Optimization results show that this structure optimization method based on ANSYS workbench is effective in the contact structure design and the capabilities to optimize multi-objective conﬂicting goals are highlighted. Keywords: Self-elastic contact; FEA; Optimization; ANSYS Workbench
Preparation of Activated Carbon of Lignin from Straw Pulping by Chemical Activation Using Potassium Carbonate
Authors: Jin Xiao Juan , Yu Zhi Ming , Yan Gao Jiang , Yu Wu
Published: December 2011

Activated carbons were prepared through chemical activation of lignin from straw pulping precursor using potassium carbonate as the chemical agent. Effects of activated temperature, K2CO3/lignin ratio and the activated time on the yield, Iodine number of activated carbon were investigated. Experimental results indicated that the optimum conditions were as follow: activated temperature 800°C, K3CO3(40% concentration) /lignin ratio 5: l, activated time 50min. These conditions allowed us to obtain a BET surface area of 1104 m2/g, including the external or non-microporous surface of 417 m2/g，Amount of methylene blue adsorption, Iodine number and the yield of activated carbon prepared under optimum conditions were 10.6mL/0.lg,1310 mg/g and 19.75%, respectively.
Investigating the Influence of the Power Supply Type upon the Weld Joints Properties and Health Characteristics of the Manual Arc Welding
Authors: Ilyaschenko D.P. , Chinakhov D.A.
Published: December 2011

The given work considers the influence of the power supply type (diode rectifier ВД-306 and upon new generation inverter Nebula-315) upon the chemical composition, microstructure, mechanical properties of the weld joints and health characteristics of the manual arc welding process.
Numerical Simulation of MIG Welding Arc with Longitudinal Magnetic Field
Authors: Wang Qi Wei , Zhu Sheng , Yin Feng Liang , Liang Yuan Yuan , Wang Xiao Ming
Published: December 2011

In the study three dimensions finite element mathematical model of MIG welding with longitudinal magnetic field was established. By ANSYS FEA software the temperature and other physical characteristics of the arc were obtained including the distributions of current density and arc pressure on the anode surface. The simulated results show that when the additional longitudinal magnetic field was introduced into welding process, the temperature of arc decreased remarkably and peak value of temperature changed from 16 950K to 13 700K at a welding current of 120A. Under the action of longitudinal magnetic field, on the one hand, heat flux density and current density at the anode surface decrease in the arc core and rise at the edge of arc, on the other hand, arc pressure decrease and arc potential increase. Keywords: Numerical simulation; MIG welding arc; magnetic field
Strain-Rate Relationship of Aluminum Matrix Composites Predicted by Johnson-Cook Model
Authors: Zhu De Zhi , Chen Wei Ping , Li Yuan Yuan
Published: December 2011

Strain-rate sensitivities of 55-65vol.% aluminum 2024-T6/TiB2composites and the corresponding aluminum 2024-T6 matrix were investigated using split Hopkinson pressure bar. Results showed that 55-65vol.% aluminum 2024-T6/TiB2composites exhibited significant strain-rate sensitivities, which were three times higher than that of the aluminum 2024-T6 matrix. The strain-rate sensitivity of the aluminum 2024-T6 matrix composites rose obviously with reinforcement content increasing (up to 60%), which agreed with the previous researches. The aluminum 2024-T6/TiB2composites showed hybrid fracture characteristics including particle cracking and aluminum alloy softening under dynamic loading. The flow stresses predicted by Johnson-Cook model increased slowly when the reinforcement volume fraction ranged in 10%-40%. While the reinforcement volume fraction was over 40%, the flow stresses of aluminum matrix composites increased obviously and the strains dropped sharply. Keywords: Composite materials; Dynamic compression; Stress-strain relationship
Preparation of Al Foam Sandwiches and Analyzing on the Interface Solidification Microstructure
Authors: Wang Lu Cai , You Xiao Hong , Wang Fang , Wu Jian Guo
Published: December 2011

Al Foam Sandwiches (AFS) has been created by a process of hot pressing Al-TiH2 precursor (core) made by cold pressing together with steel sheet, and then foaming. The microstructure and composition of Al-Fe interface has been analyzed by SEM and Element Linescanning Electron Microscopy (ELEM). The experiment and analysis show that during hot pressing process, firm mechanical bonding is formed between steel sheet and core, during foaming, the intermetallic compound FeAl3 and eutectic structure (FeAl3+Al) were formed by diffuse of Fe and Al elements each other at the interface, which gave a rise to a good metallurgical bonding interface between sheet and core.
Histamine H4 Receptor Optimizes T Regulatory Cell Frequency and Facilitates Anti-Inflammatory Responses within the Central Nervous System
Authors: del Rio Roxana , Noubade Rajkumar , Saligrama Naresha , Wall Emma H. , Krementsov Dimitry N. , Poynter Matthew E. , Zachary James F. , Thurmond Robin L. , Teuscher Cory
Published: December 2011

Histamine is a biogenic amine that mediates multiple physiological processes, including immunomodulatory effects in allergic and inflammatory reactions, and also plays a key regulatory role in experimental allergic encephalomyelitis, the autoimmune model of multiple sclerosis. The pleiotropic effects of histamine are mediated by four G protein-coupled receptors, as follows: Hrh1/H1R, Hrh2/H2R, Hrh3/H3R, and Hrh4/H4R. H4R expression is primarily restricted to hematopoietic cells, and its role in autoimmune inflammatory demyelinating disease of the CNS has not been studied. In this study, we show that, compared with wild-type mice, animals with a disrupted Hrh4 (H4RKO) develop more severe myelin oligodendrocyte glycoprotein (MOG)35\x{2013}55-induced experimental allergic encephalomyelitis. Mechanistically, we also show that H4R plays a role in determining the frequency of T regulatory (TR) cells in secondary lymphoid tissues, and regulates TR cell chemotaxis and suppressor activity. Moreover, the lack of H4R leads to an impairment of an anti-inflammatory response due to fewer TR cells in the CNS during the acute phase of the disease and an increase in the proportion of Th17 cells.
Cauchy problem for semilinear parabolic equations with initial data in $H^s_p(\mathbb R^n)$
Authors: Ribaud Francisco
Published: December 2011

We study local and global Cauchy problems for the Semilinear Parabolic Equations

\partial_tU – \Delta U = P(D)F(U)

with initial data in fractional Sobolev spaces

H^s_p(\mathbb R^n)

. In most of the studies on this subject the initial data

U_0(x)

belongs to Lebesgue spaces

L^p(\mathbb R^n)

or to supercritical fractional Sobolev spaces

H^s_p(\mathbb R^n) (s > n/p)

. Our purpose is to study the intermediate cases (namely for

0 < s < n/p)

. We give some mapping properties for functions with polynomial growth on subcritical

H^s_p(\mathbb R^n)

spaces and we show how to use them to solve the local Cauchy problem for data with low regularity. We also give some results about the global Cauchy problem for small initial data.
Hardy space $H^1$ associated to Schrödinger operator with potential satisfying reverse Hölder inequality
Authors: Dziubański Jacek , Zienkiewicz Jacek
Published: December 2011

Let

\lbrace T_t\rbrace_{t>0}

be the semigroup of linear operators generated by a Schrödinger operator

–A = \Delta –V

where

V

is a nonnegative potential that belongs to a certain reverse Hölder class. We define a Hardy space

H^1_A

be means of a maximal function associated with the semigroup

\lbrace T_t\rbrace_{t>0}

. Atomic and Riesz transforms characterizations of

H^1_A

are shown.
Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off
Authors: Villani Cédric
Published: December 2011

We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function

f \in L^1(\mathbb R^N)

yields a control of

\sqrt f

in Sobolev norms as soon as

f

is locally bounded below. Under this additional assumption of lower bound our result is an improvement of a recent estimate given by P.L. Lions and is optimal in a certain sense.
Absolute values of BMOA functions
Authors: Dyakonov Konstantin M.
Published: December 2011

The paper contains a complete characterization of the moduli of BMOA functions. These are described explicitly by a certain Muckenhoupt-type condition involving Poisson integrals. As a consequence, it is shown that an outer function with BMO modulus need not belong to BMOA. Some related results are obtained for the Bloch space.
Construction of functions with prescribed Hölder and chirp exponents
Authors: Jaffard Stéphane
Published: December 2011

We show that the Hölder exponent and the chirp exponent of a function can be prescribed simultaneously on a set of full measure, if they are both lower limits of continuous functions. We also show that this result is optimal: In general Hölder and chirp exponents cannot be prescribed outside a set of Hausdorff dimension less than one. The direct part of the proof consists in an explicit construction of a function determined by its orthonormal wavelet coefficients; the optimality is the direct consequence of a general method we introduce in order to obtain lower bounds on the dimension of some fractal sets.
An elliptic semilinear equation with source term involving boundary measures: the subcritical case
Authors: Bidaut-Véron Marie-Françoise , Vivier Laurent
Published: December 2011

We study the boundary behaviour of the nonnegative solutions of the semilinear elliptic equation in a bounded regular domain

\Omega

of

\mathbb R^N

(

N≥2

),

\begin{cases}
{\Delta u+u^q = 0}, &\text{in }\Omega,\\
u=\mu, &\text{on }\partial \Omega,
\end{cases}

where

1 < q < (N+1) / (N-1)

and

\mu

is a Radon measure on

\partial \Omega

. We give a priori estimates and existence results. They lie on the study of the superharmonic functions in some weighted Marcinkiewicz spaces.
On ovals on Riemann surfaces
Authors: Gromadzki Grzegorz
Published: December 2011

We prove that

k

(

k ≥ 9

) non-conjugate symmetries of a Riemann surface of genus

g

have at most

2g-2+2^{r-3}(9-k)

ovals in total, where

r

is the smallest positive integer for which

k≤2^{r-1}

. Furthermore we prove that for arbitrary

k≥9

this bound is sharp for infinitely many values of

g

.
Jacobi-Eisenstein series of degree two over Cayley numbers
Authors: Eie Minking
Published: December 2011

We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi Eisenstein series which forms the orthogonal complement of the vector space of Jacobi cusp forms of degree two over Cayley numbers. The construction is based on a group representation arising from the transformation formula of a set of theta series.
Unicité dans $L^3 (\mathbb R^3)$ et d'autres espaces fonctionnels limites pour Navier-Stokes
Authors: Furioli Giulia , Lemarié-Rieusset Pierre Gilles , Terraneo Elide
Published: December 2011

The main result of this paper is the proof of uniqueness for mild solutions of the Navier-Stokes equations in

L^3 (\mathbb R^3)

. This result is extended as well to some Morrey-Campanato spaces.
Square functions of Calderón type and applications
Authors: Hofmann Steve , Lewis John L.
Published: December 2011

We establish

L^2

and

L^p

bounds for a class of square functions which arises in the study of singular integrals and boundary value problems in nonsmooth domains. As an application we present a simplified treatment of a class of parabolic smoothing operators which includes the caloric single layer potential on the boundary of certain minimally smooth noncylindrical domains.
Dynamical instability of symmetric vortices
Authors: Almeida Luís , Guo Yan
Published: December 2011

Using the Maxwell-Higgs model we prove that linearly unstable symmetric vortices in the Ginzburg-Landau theory are dynamically unstable in the

H^1

norm (which is the natural norm for the problem).
Independence of time and position for a random walk
Authors: Ackermann Christophe , Lorang Gérard , Roynette Bernard
Published: December 2011

Given a real-valued random variable

X

whose Laplace transform is analytic in a neighbourhood of 0, we consider a random walk

{(S_{n},n\geq 0)}

, starting from the origin and with increments distributed as

X

. We investigate the class of stopping times

T

which are independent of

S_{T}

and standard, i.e.

(S_{n\wedge T},n\geq 0)

is uniformly integrable. The underlying filtration

(\mathcal{F}_{n},n\geq 0)

is not supposed to be natural. Our research has been deeply inspired by [7], where the analogous problem is studied, but not yet solved, for the Brownian motion. Likewise, the classification of all possible distributions for

S_{T}

remains an open problem in the discrete setting, even though we manage to identify the solutions in the special case where

T

is a stopping time in the natural filtration of a Bernoulli random walk and

\min T \le 5

. Some examples illustrate our general theorems, in particular the first time where

|S_{n}|

(resp. the age of the walk or Pitman's process) reaches a given level

a\in\mathbb{N}^{\ast}

. Finally, we are concerned with a related problem in two dimensions. Namely, given two independent random walks

(S_{n}^{\prime},n\geq 0)

and

(S_{n}^{\prime\prime},n\geq 0)

with the same incremental distribution, we search for stopping times

T

such that

S_{T}^{\prime}

and

S_{T}^{\prime\prime}

are independent.
Équation anisotrope de Navier-Stokes dans des espaces critiques
Authors: Paicu Marius
Published: December 2011

We study the tridimensional Navier-Stokes equation when the value of the vertical viscosity is zero, in a critical space (invariant by the scaling). We shall prove local in time existence of the solution, respectively global in time when the initial data is small compared with the horizontal viscosity.
Taille des valeurs de fonctions $L$ de carrés symétriques au bord de la bande critique
Authors: Royer Emmanuel , Wu Jie
Published: December 2011

For each weight

k

and level

N

square free and without small prime factors, we prove the existence of primitive forms

f_+

and

f_-

of weight

k

and level

N

such that

L(1,\operatorname{sym}^2f_+)\gg_{k}[\log\log(3N)]^{3}

and

L(1,\operatorname{sym}^2f_-)\ll_{k}[\log\log(3N)]^{-1}.

The result comes from a delicate study of the moments of

L(1,\operatorname{sym}^2 f)

. This study gives also results for squarefree levels but with small prime factors. It provides counterexamples to the equivalence between harmonic and natural means.
Extreme cases of weak type interpolation
Authors: Pustylnik Evgeniy
Published: December 2011

We consider quasilinear operators

T

of
joint weak type

(a,b;p,q)

(in the sense of [Bennett, Sharpley: Interpolation of operators, Academic Press, 1988]) and study their properties on spaces

L_{\varphi,E}

with the norm

\|\varphi(t)f^*(t) \|_{\tilde E}

, where

\tilde E

is arbitrary rearrangement-invariant space with respect to the measure

dt/t

. A space

L_{\varphi,E}

is said to be “close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to

1/a

or to

1/p

. For all possible kinds of such “closeness”, we give sharp estimates for the function

\psi(t)

so as to obtain that every

T:L_{\varphi,E}\to L_{\psi,E}

.
Quasiconformal dimensions of self-similar fractals
Authors: Tyson Jeremy T. , Wu Jang-Mei
Published: December 2011

The Sierpinski gasket and other self-similar fractal subsets of

\mathbb R^d

,

d\ge 2

, can be mapped by quasiconformal self-maps of

\mathbb R^d

onto sets of Hausdorff dimension arbitrarily close to one. In

\mathbb R^2

we construct explicit mappings. In

\mathbb R^d

,

d\ge 3

, the results follow from general theorems on the equivalence of invariant sets for iterated function systems under quasisymmetric maps and global quasiconformal maps. More specifically, we present geometric conditions ensuring that (i) isomorphic systems have quasisymmetrically equivalent invariant sets, and (ii) one-parameter isotopies of systems have invariant sets which are equivalent under global quasiconformal maps.
Oscillations of Hecke eigenvalues at shifted primes
Authors: Zhao Liangyi
Published: December 2011

In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twisted with an exponential sums whose amplitude is

\sqrt{n}

at prime arguments.
Transition operators on co-compact $G$-spaces
Authors: Saloff-Coste Laurent , Woess Wolfgang
Published: December 2011

We develop methods for studying transition operators on metric spaces that are invariant under a co-compact group which acts properly. A basic requirement is a decomposition of such operators with respect to the group orbits. We then introduce "reduced" transition operators on the compact factor space whose norms and spectral radii are upper bounds for the

L^p

-norms and spectral radii of the original operator. If the group is amenable then the spectral radii of the original and reduced operators coincide, and under additional hypotheses, this is also sufficient for amenability. Further bounds involve the modular function of the group. In this framework, we prove among other things that the bottom of the spectrum of the Laplacian on a co-compact Riemannian manifold is 0 if and only if the group is amenable and unimodular. The same result holds for Euclidean simplicial complexes. On a geodesic, proper metric space with co-compact isometry group action, the averaging operator over balls with a fixed radius has norm equal to 1 if and only if the group is amenable and unimodular. The technique also allows explicit computation of spectral radii when the group is amenable.
A geometry on the space of probabilities II. Projective spaces and exponential families
Authors: Gzyl Henryk , Recht Lázaro
Published: December 2011

In this note we continue a theme taken up in part I, see [Gzyl and Recht: The geometry on the class of probabilities I: The finite dimensional case. Rev. Mat. Iberoamericana 22 (2006), 545-558.], namely to provide a geometric interpretation of exponential families as end points of geodesics of a non-metric connection in a function space. For that we characterize the space of probability densities as a projective space in the class of strictly positive functions, and these will be regarded as a homogeneous reductive space in the class of all bounded complex valued functions. We shall develop everything in a generic

\mathcal{C}^*

-algebra setting, but shall have the function space model in mind.
Special Toeplitz operators on strongly pseudoconvex domains
Authors: Čučković Željko , McNeal Jeffery D.
Published: December 2011

Toeplitz operators on strongly pseudoconvex domains in

\mathbb{C}^n

, constructed from the Bergman projection and with symbol equal to a positive power of the distance to the boundary, are considered. The mapping properties of these operators on

L^p

, as the power of the distance varies, are established.
Recouvrements, derivation des mesures et dimensions
Authors: Assouad Patrice , Quentin de Gromard Thierry
Published: December 2011

Let

X

be a set with a symmetric kernel

d

(not necessarily a distance). The space

(X,d)

is said to have the weak (resp. strong) covering property of degree

\leq m

[briefly \textbf{prf}

(m)

(resp. \textbf{prF}

(m)

)], if, for each family

\mathcal{B}

of closed balls of

(X,d)

with radii in a decreasing sequence (resp. with bounded radii), there is a subfamily, covering the center of each element of

\mathcal{B}

, and of order

\leq m

(resp. spliting into

m

disjoint families). Since Besicovitch, covering properties are known to be the main tool for proving derivation theorems for any pair of measures on

(X,d)

. Assuming that any ball for

d

belongs to the Baire

\sigma

-algebra for

d

, we show that the \textbf{prf} implies an almost sure derivation theorem. This implication was stated by D. Preiss when

(X,d)

is a complete separable metric space. With stronger measurability hypothesis (to be stated later in this paper), we show that the \textbf{prf} restricted to balls with constant radius implies a derivation theorem with convergence in measure. We show easily that an equivalent to the \textbf{prf}

(m+1)

(resp. to the \textbf{prf}

(m+1)

restricted to balls with constant radius) is that the Nagata-dimension (resp. the De Groot-dimension) of

(X,d)

is

\leq m

. These two dimensions (see J.I. Nagata) are not lesser than the topological dimension; for

\mathbb{R}^n

with any given norm (

n > 1

), they are

> n

. For spaces with nonnegative curvature

\geq 0

(for example for

\mathbb{R}^n

with any given norm), we express these dimensions as the cardinality of a net; in these spaces, we give a similar upper bound for the degree of the \textbf{prF} (generalizing a result of Furedi and Loeb for

\mathbb{R}^n

) and try to obtain the exact degree in

\mathbb{R}

and

\mathbb{R}^2

.
Multi-parameter paraproducts
Authors: Muscalu Camil , Pipher Jill , Tao Terence , Thiele Christoph
Published: December 2011

We prove that the classical Coifman-Meyer theorem holds on any polydisc

\mathbf{T}^d

of arbitrary dimension

d\geq 1

.
Infinite groups with many permutable subgroups
Authors: Ballester-Bolinches Adolfo , Kurdachenko L. A. , Otal J. , Pedraza T.
Published: December 2011

A subgroup

H

of a group

G

is said to be

permutable in

G

, if

HK = KH

for every subgroup

K

of

G

. A result due to Stonehewer asserts that every permutable subgroup is ascendant although the converse is false. In this paper we study some infinite groups whose ascendant subgroups are permutable (

AP

-groups). We show that the structure of radical hyperfinite

AP

-groups behave as that of finite soluble groups in which the relation
to be a permutable subgroup
is transitive (

PT

-groups).
Toeplitz operators on Bergman spaces with locally integrable symbols
Authors: Taskinen Jari , Virtanen Jani
Published: December 2011

Given a calibrated Riemannian manifold

\overline{M}

with parallel calibration

\Omega

of rank

m

and

M

an orientable m-submanifold with parallel mean curvature

H

, we prove that if

\cos\theta

is bounded away from zero, where

\theta

is the

\Omega

-angle of

M

, and if

M

has zero Cheeger constant, then

M

is minimal. In the particular case

M

is complete with

Ricci^M\geq 0

we may replace the boundedness condition on

\cos\theta

by

\cos\theta\geq Cr^{-\beta}

, when

r\rightarrow+\infty

, where

0 < \beta < 1

and

C > 0

are constants and

r

is the distance function to a point in

M

. Our proof is surprisingly simple and extends to a very large class of submanifolds in calibrated manifolds, in a unified way, the problem started by Heinz and Chern of estimating the mean curvature of graphic hypersurfaces in Euclidean spaces. It is based on an estimation of

\|H\|

in terms of

\cos\theta

and an isoperimetric inequality. In a similar way, we also give some conditions to conclude

M

is totally geodesic. We study some particular cases.
A convolution estimate for two-dimensional hypersurfaces
Authors: Bejenaru Ioan , Herr Sebastian , Tataru Daniel
Published: December 2011

Given three transversal and sufficiently regular hypersurfaces in

\mathbb{R}^3

it follows from work of Bennett-Carbery-Wright that the convolution of two

L^2

functions supported of the first and second hypersurface, respectively, can be restricted to an

L^2

function on the third hypersurface, which can be considered as a nonlinear version of the Loomis-Whitney inequality. We generalize this result to a class of

C^{1,\beta}

hypersurfaces in

\mathbb{R}^3

, under scaleable assumptions. The resulting uniform

L^2

estimate has applications to nonlinear dispersive equations.
Contact properties of codimension 2 submanifolds with flat normal bundle
Authors: Nuño Ballesteros Juan José , Romero Fuster María Carmen
Published: December 2011

Given an immersed submanifold

M^n\subset\mathbb{R}^{n+2}

, we characterize the vanishing of the normal curvature

R_D

at a point

p \in M

in terms of the behaviour of the asymptotic directions and the curvature locus at

p

. We relate the affine properties of codimension 2 submanifolds with flat normal bundle with the conformal properties of hypersurfaces in Euclidean space. We also characterize the semiumbilical, hypespherical and conformally flat submanifolds of codimension 2 in terms of their curvature loci.
Aronson-Bénilan type estimate and the optimal Hölder continuity of weak solutions for the 1-D degenerate Keller-Segel systems
Authors: Sugiyama Yoshie
Published: December 2011

We consider the Keller-Segel system of degenerate type (KS)

_m

with

m > 1

below. We establish a uniform estimate of

\partial_x^2 u^{m-1}

from below. The corresponding estimate to the porous medium equation is well-known as an Aronson-Bénilan type. We apply our estimate to prove the optimal Hölder continuity of weak solutions of (KS)

_m

. In addition, we find that the set

D(t):=\{ x \in \mathbb{R}; u(x,t) > 0\}

of positive region to the solution

u

is monotonically non-decreasing with respect to

t

.
The Jet of an Interpolant on a Finite Set
Authors: Fefferman Charles , Israel Arie
Published: December 2011

We study functions

F \in C^m (\mathbb{R}^n)

having norm less than a given constant

M

, and agreeing with a given function

f

on a finite set

E

. Let

\Gamma_f (S,M)

denote the convex set formed by taking the

(m-1)

-jets of all such

F

at a given finite set

S \subset \mathbb{R}^n

. We provide an efficient algorithm to compute a convex polyhedron

\tilde{\Gamma}_f (S,M)

, such that $$ \Gamma_f (S,cM) \subset \tilde{\Gamma}_f (S,M) \subset \Gamma_f (S,CM),

where

c

and

C

depend only on

m

and

n$.
A proof of hypoellipticity for Kohn’s operator via FBI
Authors: Chinni Gregorio
Published: December 2011

A new proof of both analytic and

C^{\infty}

hypoellipticity of Kohn's operator is given using FBI techniques introduced by J. Sjöstrand. The same proof allows us to obtain both kind of hypoellipticity at the same time.
The center of a Leavitt path algebra
Authors: Aranda Pino Gonzalo , Crow Kathi
Published: December 2011

In this paper the center of a Leavitt path algebra is computed for a wide range of situations. A basis as a

K

-vector space is found for

Z(L(E))

when

L(E)

enjoys some finiteness condition such as being artinian, semisimple, noetherian and locally noetherian. The main result of the paper states that a simple Leavitt path algebra

L(E)

is central (i.e. the center reduces to the base field

K

) when

L(E)

is unital and has zero center otherwise. Finally, this result is extended, under some mild conditions, to the case of exchange Leavitt path algebras.
Harmonic polynomials and tangent measures of harmonic measure
Authors: Badger Matthew
Published: December 2011

We show that on an NTA domain if each tangent measure to harmonic measure at a point is a polynomial harmonic measure then the associated polynomials are homogeneous. Geometric information for solutions of a two-phase free boundary problem studied by Kenig and Toro is derived.