Existence and joint continuity of local time of multi-parameter fractional Lévy processes

In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.     

Particle behavior in homogeneous isotropic turbulence

Direct numerical simulations were conducted to investigate the behavior of heavy particles in homogeneous isotropic turbulence. The present study focused on the effect of particle inertia and drift on the autocorrelations of the particle velocity and the fluid seen by particles and the dispersion characteristics of particles. The Lagrangian integral time scale of particles monotonically increased as the magnitude of the particle response time increased, while that of the fluid seen by particles remained relatively constant; it reached a maximum when the particle response time was close to the Kolmolgorov time scale of the flow. Particle dispersion increased as the particle inertia increased for small particles, while for larger particles, it decreased as particle inertia increased; particle eddy diffusion coefficient was maximal, and greater than that of the fluid by about 30%, at the preferential concentration. The concentration field of the particles with τp/τk≈1.0 showed that particles tend to collect in regions of low vorticity (high strain) due to preferential concentration. As the drift velocity of a particle is increased it crosses the paths of fluid elements more rapidly and will tend to lose correlation with its previous velocity faster than a fluid element will. And the correlation of particle velocities along the drift direction is more persistent than that perpendicular to the direction of drift. Simulations also showed that the continuity effect and the crossing-trajectory effect are weakened for particles with infinite inertia.     

DEM simulations of die filling during pharmaceutical tabletting

The flow behaviour of powders from a stationary shoe into a moving die, which mimics the die filling process in a rotary tablet press, was analysed using a discrete element method （DEM）, in which 2D irregular shaped particles were considered. The influence of the particle shape, size and size distribution, the number of particles used in the simulation, the initial height of powder bed in the shoe, and the filling speed on the average mass flow rate and the critical filling speed （the highest speed at which the die can be completely filled） were explored. It has been found that a maximum flow rate is obtained at the critical filling speed for all systems investigated and poly-disperse systems have higher mass flow rates and higher critical filling speeds than mono-disperse systems. In addition, the powder with particles which can tessellate generally has a lower filling rate and a lower critical titling speed.     

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method （DEM） when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.     

DIRECTIONAL DERIVATIVE OF VECTOR FIELD AND REGULAR CURVES ON TIME SCALES

The general idea in this paper is to study curves of the parametric equations where the parameter varies in a so-called time scale, which may be an arbitrary closed subset of the set of all real numbers. We introduce the directional derivative according to the vector fields.     

Hausdorff dimension of set generated by exceptional oscillations of a class of N-parameter Ganssian processes

A class of N-parameter Gaussian processes are introduced,which are more general than the N-parameter Wiener process.The definition of the set generated by exceptional oscillations of a class of these processes is given,and then the Hansdorff di- mension of this set is defined.The Hausdorff dimensions of these processes are studied and an exact representative for them is given,which is similar to that for the two-parameter Wiener process by Zacharie(2001).Moreover,the time set considered is a hyperrectangle which is more general than a hyper-square used by Zacharie(2001).For this more gen- eral case,a Fernique-type inequality is established and then using this inequality and the Slepian lemma,a Lévy's continuity modulus theorem is shown.Independence of incre- ments is required for showing the representative of the Hausdorff dimension by Zacharie (2001).This property is absent for the processes introduced here,so we have to find a different way.     

Application of DEM modified with enlarged particle model to simulation of bead motion in a bead mill

We applied the discrete element method （DEM） of simulation modified by an enlarged particle model to simulate bead motion in a large bead mill. The stainless-steel bead mill has inner diameter of 102 mm and mill length of 198 mm. The bead diameter and filling ratio were fixed respectively at 0.5 mm and 85%. The agitator rotational speed was changed from 1863 to 3261 rpm. The bead motion was monitored experimentally using a high-speed video camera through a transparent mill body. For the simulation, enlarged particle sizes were set as 3-6 mm in diameter. With the DEM modified by the enlarged particle model, the motion of enlarged particles in a mill was simulated.The velocity data of the simulated enlarged particles were compared with those obtained in the experiment. The simulated velocity of the enlarged particles depends on the virtual frictional coefficient in the DEM model. The optimized value of the virtual frictional coefficient can be determined by considering the accumulated mean value. Results show that the velocity of the enlarged particles simulated increases with an increase in the optimum virtual frictional coefficient, but the simulated velocity agrees well with that determined experimentally by optimizing the virtual frictional coefficient in the simulation. The computing time in the simulation decreases with increased particle size.     

FORMATION OF MICRO-POROUS SPHERICAL PARTICLES OF CALCIUM SILICATE （XONOTLITE）IN DYNAMIC HYDROTHERMAL PROCESS

Stiming during hydrothermal synthesis plays an important role in the formation of porous spherical xonotlite particles.The size of spherical particles formed during dynamic hydrothermal process is related to the size of minimum vortices in the reaction slurry,which is determined by stirring speed.The kinetics of growth of xonotlite particless is de-termined by measuring the apparent viscosity of the reactant slurry at various reaction time and reaction temperatures.It is found that the growth of particles follows the contracting-volume equation.and the activation energies for nucleation and growth are 104 and 123 kJ-mol,respectively.     

PRODUCTION OF PIGMENT NANOPARTICLES USING A WET STIRRED MILL WITH POLYMERIC MEDIA

Pigment nanoparticles with a size range of 10-100 nm were produced from large agglonmerates via a stirred media mill operating in the wet-batch mode and using polymeric media,The effects of several operating variables such as the surfactant concentration,polystyrene media loading.and media size on the pigment size distribution of the product were studied.The process dynamics was also investigated.Dynamic light scattering and electron microscopy were used as the characerization techniques.The polymeric grinding media are found to be effective for the production of pigment nanoparticles.The experimental results suggest the existence of an optimum media size and surfactant concentration,A population balance model of the process reveals a transition from first-order breakage kinetice for rela-large agglomerates split in a first-order kinetics,with a delay period,for the smaller particles.The model implies that large agglomerates split in a first-order fashion whereas the breakage of individual naoparticles may depend on induced fatigue of the particles.     

Rotational dynamics of bottom-heavy rods in turbulence from experiments and numerical simulations

We successfully perform the three-dimensional tracking in a turbulent fluid flow of small axisymmetrical particles that are neutrally-buoyant and bottom-heavy, i.e., they have a non-homogeneous mass distribution along their symmetry axis. We experimentally show how a tiny mass inhomogeneity can affect the particle orientation along the preferred vertical direction and modify its tumbling rate. The experiment is complemented by a series of simulations based on realistic Navier–Stokes turbulence and on a point-like particle model that is capable to explore the full range of parameter space characterized by the gravitational torque stability number and by the particle aspect ratio. We propose a theoretical perturbative prediction valid in the high bottom-heaviness regime that agrees well with the observed preferential orientation and tumbling rate of the particles. We also show that the heavy-tail shape of the probability distribution function of the tumbling rate is weakly affected by the bottom-heaviness of the particles.     

Hausdorff dimension of set generated by exceptional oscillations of a class of N-parameter Gaussian processes

A class of N-parameter Gaussian processes are introduced, which are more general than the N-parameter Wiener process. The definition of the set generated by exceptional oscillations of a class of these processes is given, and then the Hausdorff dimension of this set is defined. The Hausdorff dimensions of these processes are studied and an exact representative for them is given, which is similar to that for the two-parameter Wiener process by Zacharie （2001）. Moreover, the time set considered is a hyperrectangle which is more general than a hyper-scluare used by Zacharie （2001）. For this more general case, a Fernique-type inequality is established and then using this inequality and the Slepian lemma, a Levy＇s continuity modulus theorem is shown. Independence of increments is required for showing the representative of the Hausdorff dimension by Zacharie （2001）. This property is absent for the processes introduced here, so we have to find a different way.     

An experimental study on fracture mechanical behavior of rock-like materials containing two unparallel fissures under uniaxial compression

Strength and deformability characteristics of rock with pre-existing fissures are governed by cracking behavior. To further research the effects of pre-existing fissures on the mechanical properties and crack coalescence process, a series of uniaxial compression tests were carried out for rock-like material with two unparallel fissures.In the present study, cement, quartz sand, and water were used to fabricate a kind of brittle rock-like material cylindrical model specimen. The mechanical properties of rock-like material specimen used in this research were all in good agreement with the brittle rock materials. Two unparallel fissures(a horizontal fissure and an inclined fissure) were created by inserting steel during molding the model specimen.Then all the pre-fissured rock-like specimens were tested under uniaxial compression by a rock mechanics servocontrolled testing system. The peak strength and Young's modulus of pre-fissured specimen all first decreased and then increased when the fissure angle increased from 0?to 75?.In order to investigate the crack initiation, propagation and coalescence process, photographic monitoring was adopted to capture images during the entire deformation process.Moreover, acoustic emission(AE) monitoring technique was also used to obtain the AE evolution characteristic of prefissured specimen. The relationship between axial stress, AE events, and the crack coalescence process was set up: when a new crack was initiated or a crack coalescence occurred, thecorresponding axial stress dropped in the axial stress–time curve and a big AE event could be observed simultaneously.Finally, the mechanism of crack propagation under microscopic observation was discussed. These experimental results are expected to increase the understanding of the strength failure behavior and the cracking mechanism of rock containing unparallel fissures.     

Circulation intensity and axial dispersion of non-cohesive solid particles in a V-blender via DEM simulation

In this study, discrete element method （DEM） was employed to simulate the movement of non-cohesive mono-dispersed particles in a V-blender along with particle-particle and particle-boundary interactions. To validate the model, DEM results were successfully compared to positron emission particle tracking （PEPT） data reported in literature. The validated model was then utilized to explore the effects of rotational speed and fill level on circulation intensity and axial dispersion coefficient of non-cohesive particles in the V-blender. The results showed that the circulation intensity increased with an increase in the rotational speed from 15 to 60 rpm. As the fill level increased from 20% to 46%, the circulation intensity decreased, reached its minimum value at a fill level of 34% for all rotational speeds, and did not change significantly at fill levels greater than 34%. The DEM results also revealed that the axial dispersion coefficient of particles in the V-blender was a linear function of the rotational speed. These trends were in good agreement with the experimentallv determined values reported bv previous researchers.     

CHARACTERISTIC DIMENSIONLESS NUMBERS IN MULTl-SCALE AND RATE-DEPENDENT PROCESSES

Multi-scale modeling of materials properties and chemical processes has drawn great attention from science and engineering. For these multi-scale and rate-dependent processes, how to characterize their trans-scale for-mulation is a key point. Three questions should be addressed:How do multi-sizes affect the problems?How are length scales coupled with time scales?How to identify emergence of new structure in process and its effect?For this sake, the macroscopic equations of mechanics and the kinetic equations of the microstructural transforma-tions should form a unified set that be solved simultaneously.As a case study of coupling length and time scales, the trans-scale formulation of wave-induced damage evolution due to mesoscopic nucleation and growth is discussed. In this problem, the trans-scaling could be reduced to two inde-pendent dimensionless numbers: the imposed Deborah number De=(ac)/(LV) and the intrinsic Deborah num-ber D = (nNc5)/V* ,where a. L, c, V and nN are wave speed, sample size, micr     

Effect of wall rougheners on cross-sectional flow characteristics for non-spherical particles in a horizontal rotating cylinder

Discrete-element-method （DEM） simulations have been performed to investigate the cross-sectional flow of non-spherical particles in horizontal rotating cylinders with and without wall rougheners. The non-spherical particles were modeled using the three-dimensional super-quadric equation. The influence of wall rougheners on flow behavior of grains was studied for increasing particle blockiness. Moreover, for approximately cubic particles （squareness parameters [555]）, the rotational speed, gravitational acceleration and particle size were altered to investigate the effect of wall rougheners under a range of operating conditions. For spherical and near-spherical particles （approximately up to the squareness parameters [344]）, wall rougheners are necessary to prevent slippage of the bed against the cylinder wall. For highly cubic particle geometries （squareness parameters larger than [3441）, wall rougheners resulted in a counter-intuitive decrease in the angle of repose of the bed. In addition, wall rougheners employed in this study were demonstrated to have a higher impact on bed dynamics at higher rotational speeds and lower gravitational accelerations. Nevertheless, using wall rougheners had a comparatively small influence on particle-flow characteristics for a bed composed of finer grains.     

Effects of nozzle and fluid properties on the drop formation dynamics in a drop-on-demand inkjet printing

The droplet formation dynamics of a Newtonian liquid in a drop-on-demand(DOD) inkjet process is numerically investigated by using a volume-of-fluid(VOF) method.We focus on the nozzle geometry, wettability of the interior surface, and the fluid properties to achieve the stable droplet formation with higher velocity. It is found that a nozzle with contracting angle of 45° generates the most stable and fastest single droplet, which is beneficial for the enhanced printing quality and high-throughput printing rate. For this nozzle with the optimal geometry, we systematically change the wettability of the interior surface, i.e., different contact angles. As the contact angle increases, pinch-off time increases and the droplet speed reduces. Finally, fluids with different properties are investigated to identify the printability range.     

Large scale manufacture of magnetic polymer particles using membranes and microfluidic devices

Magnetic polymer particles have found applications in diverse areas such as biomedical treatments, diagnosis and separation technology. These applications require the particles to have controlled sizes and narrow size distributions to gain better control and reproducibility in use. This paper reviews recent developments in the preparation of magnetic polymer particles at nano- and micro-scales by encapsulating magnetic components with dissolved or in situ formed polymers. Particle manufacture using emulsification and embedment methods produces magnetic polymer particles at micro-scale dimensions. However, the production of particles in this range using conventional emulsification methods affords very limited control over particle sizes and polydispersity. We report on alternative routes using membrane and microfluidics emulsification techniques, which have a capability to produce monodisperse emulsions and polymer microspheres （with coefficients of variation of less than 10%） in the range from submicrometer to a few 100 μm. The performance of these manufacturing methods is assessed with a view to future applications.     

A review of research on nanoparticulate flow undergoing coagulation

Nanoparticulate flows occur in a wide range of natural phenomena and engineering applications and, hence,have attracted much attention. The purpose of the present paper is to provide a review of the research conducted over the last decade. The research covered relates to the Brownian coagulation of monodisperse and polydisperse particles, the Taylor-series expansion method of moment, and nanoparticle distributions due to coagulation in pipe and channel flow,jet flow, and the mixing layer and in the process of flame synthesis and deposition.     

Influence of interparticle interactions on the kinetics of self-assembly and mechanical strength of nanoparticulate aggregates

Computer simulations based on Discrete Element Method have been performed in order to investigate the influence of interparticle interactions on the kinetics of self-assembly and the mechanical strength of nanoparticle aggregates. Three different systems have been considered. In the first system the interaction between particles has been simulated using the JKR （Johnson, Kendall and Roberts） contact theory, while in the second and third systems the interaction between particles has been simulated using van der Waals and electrostatic forces respectively. In order to compare the mechanical behaviour of the three systems, the magnitude of the maximum attractive force between particles has been kept the same in all cases. However, the relationship between force and separation distance differs from case to case and thus, the range of the interparticle force. The results clearly indicate that as the range of the interparticle force increases, the self-assembly process is faster and the work required to produce the mechanical failure of the assemblies increases by more than one order of magnitude.     

CHARACTERISTIC DIMENSIONLESS NUMBERS IN MULTI—SCALE AND RATE—DEPENDENT PROCESSES

Multi-scale modeling of materials properties and chemical processes has drawn great attention from science and engineering. For these multi-scale and rate-dependent processes, how to characterize their trans-scale formulation is a key point. Three questions should be addressed:*How do multi-sizes affect the problems? *How are length scales coupled with time scales?*How to identify emergence of new structure in process and its effect? For this sake, the macroscopic equations of mechanics and the kinetic equations of the microstructural transformations should form a unified set that be solved simultaneously. As a case study of coupling length and time scales, the trans-scale formulation of wave-induced damage evolution due to mesoscopic nucleation and growth is discussed. In this problem, the trans-scalina could be reduced to two independent dimensionless numbers:the imposed Deborah number De*(ac)^*/(LV^*) and the intrinsic Deborah number D^*=(nN^*C^*5)/V^*,where a,L,c^*,V^* and nN^* are wave speed, sample size, microcrack size, the rate of micro-crack growth and the rate of microcrack nucleation density, respectively. Clearly, the dimensionless number De^*(ac^*)/(LV^*) includes length and time scales on both meso- and macro- levels and governs the proqressive process.Whereas, the intrinsic Deborah number D^* indicates the characteristic transition of microdamage to macroscopic rupture since D“ is related to the criterion of damage localization, which is a precursor of macroscopic rupture. This case study may highlight the scaling in multi-scale and rate-dependent problems.Then, more generally, we compare some historical examples to see how trans-scale formulations were achieved and what are still open now. The comparison of various mechanisms governing the enhancement of meso-size effects reminds us of the importance of analyzing multi-scale and rate-dependent processes case by case. For multi-scale and rate-dependent processes with chemical reactions and diffusions, there seems to be a need of trans-scale formulation of coupling effect of multi-scales and corresponding rates. Perhaps, two trans-scale effects may need special attention. One is to clarify what dimensionless group is a proper trans-scale formulation in coupled multiscale and rate-dependent processes with reactions and diffusion. The second is the effect of emergent structures and its lenath scale effect.