Initial Phase Distribution Research Articles

Kinetic modeling of the peroxide cross-linking of polymer/monomer blends: From a theoretical model framework to its application for a complex polymer/monomer dispersion system

Multi-functional vinyl monomers, which are highly reactive towards free radicals and are readily graft to polymer chains, ordinarily form a complex cross-linked network with the latter. Initial phase distribution within the polymer matrix is of a great importance for the final user properties of a composite material. Based on the mechanisms of cross-linking process’ reactions, a new theoretical kinetic model framework was developed incorporating blend morphology. The kinetic model was then applied to the cross-linking process’ reactions of various monomer moieties and a chosen complex polymer compound, namely partially hydrogenated poly(acrylonitrile- co-1,3-butadiene) alongside with an organic peroxide. Whereas the blend morphology was determined utilizing field emission scanning electron microscopy, the overall concentration of cross-links’ evolution was monitored through viscoelastic characteristics of the system. The model demonstrated good agreement with experimentally measured data and, moreover; the evolution of concentrations of various crucial species inherent to the cross-linking process were predicted in homogeneous, heterogeneous, and interfacial phase. The most significant advantage of the developed kinetic model is that it may be readily applied to an assortment of polymer/monomer/peroxide systems.

Composite coherence vortices in a radial beam array propagating through atmosphericturbulence along a slant path

The explicit expression for the cross-spectral density of a radial partially coherent beamarray with an initial phase distribution propagating through atmospheric turbulence alonga slant path is derived and used to study the propagation of composite coherence vorticesformed by the radial partially coherent beam array. The dependence of number,position and topological charge of composite coherence vortices on the beam arrayand atmospheric turbulence parameters is illustrated by numerical examples.

径向洛伦兹阵列光束在自由空间的传输特性

The analytical expression for the propagation of a radial Lorentz array beam with an initial phase distribution is derived and used to study the propagation properties of the coherently combined beam in free space. For the case of the radial Lorentz array beam with a certain different initial phase distribution, the intensity profile of the resulting beam becomes a dark-hollow one, whereas for the case of the array beam with an equal initial phase distribution, the center of the intensity profile is a bright spot. The beam width and power in the bucket of the resulting beam depend on the waist width of the Lorentz beamlet, and on the initial phase distribution and radius of the radial array. The results are illustrated by numerical examples. When the radius of the radial array is larger an

PERFORMANCE EVALUATION OF PHASE-ANGLE GRADIENT METHOD FOR PHASE RETRIEVAL BASED ON LOW-FREQUENCY AMPLITUDE-ONLY NEAR-FIELD DATA

The Phase Angle Gradient Method (PAGM) is a recent technique developed for phase retrieval based on amplitude-only measurement data. Preliminary results have shown that the PAGM is able to perform phase retrieval at 100MHz with accurate phase information based on measured fIeld components on three planar surfaces. In this paper, a performance evaluation of the PAGM under different conFigurations is conducted. Phase retrieval based on field measurements for different plane sizes and separations between the planes are studied rigorously. In addition, the PAGM is tested for different initial phase distributions. The results show that the PAGM is capable of retrieving phase information even if the separation between the measurement planes is small in terms of wavelengths.

In situsynchrotron high-energy X-ray diffraction analysis on phase transformations in Ti–Al alloys processed by equal-channel angular pressing

Mixtures of 47-Al and 53-Ti powders (atomic %) have been consolidated using back pressure equal-channel angular pressing starting with both raw and ball-milled powders. In situ synchrotron high-energy X-ray diffraction studies are presented with continuous Rietveld analysis obtained upon a heating ramp from 300 K to 1075 K performed after the consolidation process. Initial phase distributions contain all intermetallic compounds of this system except Al, with distribution maxima in the outer regions of the concentrations (alpha-Ti, TiAl(3)). Upon annealing, the phase evolution and lattice parameter changes owing to chemical segregation, which is in favour for the more equilibrated phases such as gamma-TiAl, alpha(2)-Ti(3)Al and TiAl(2), were followed unprecedentedly in detail. An initial delta-TiH(2) content with a phase transition at about 625 K upon heating created an intermediate beta-Ti phase which played an important role in the reaction chain and gradually transformed into the final products.

Interphase mass transfer in variable aperture fractures: Controlling parameters and proposed constitutive relationships

Interphase mass transfer in variable aperture fractures occurs in many problems where two immiscible fluids are present, such as dissolution of dense nonaqueous phase liquids into groundwater, dissolution of CO2 in deep saline aquifers, and evaporation of trapped water by flowing gas during natural gas production. Typically, one fluid is entrapped by capillary forces and resides in immobilized regions whose distribution and geometry are controlled by the relative influence of capillary, gravitational, and viscous forces within the fracture. For the case of fractures bounded by a low porosity/permeability matrix, interphase mass transfer occurs predominantly owing to diffusive/advective transport from the entrapped phase interface into the phase flowing through the fracture. We explore the relative influence of the initial entrapped phase geometry and mean flowing phase velocities on the dissolution of the entrapped phase. Our systematic simulations use a percolation‐based model of phase invasion and depth‐averaged models of flow, transport, and mass transfer. The invasion model provides a physically based distribution of entrapped phase within the fracture and the mass transfer model implicitly calculates interphase mass transfer from discrete regions of entrapped phase without the need for empirical mass transfer relationships. Results demonstrate behavior across a wide range of initial entrapped phase distributions, with entrapped phase saturations ranging from zero to near the percolation threshold. Interfacial area evolves with a near‐linear dependence on entrapped phase saturation during dissolution in each simulation, and fracture‐scale intrinsic mass transfer rate coefficients exhibit a nonlinear dependence on Peclet number and a negligible dependence on entrapped phase saturation. These observations provide a basis for the development of constitutive relationships that quantify interphase mass transfer in variable aperture fractures as a function of entrapped phase saturation and flow rate; coarse‐grid dissolution simulations using these constitutive relationships demonstrate good agreement with results from the high‐resolution mechanistic simulations.

Studies on propagation of laser beam array with initial phase distributions in a turbulent atmosphere

Based on the coherent superposition principle and the generalized Huygens-Fresnel diffraction integral, the properties of a radial beam array with definite initial phase distributions propagating through a turbulent atmosphere are analytically investigated. It is shown that, when the propagation distance is short, the output intensity distribution will gradually take on a spiral shape, which means an optical vortex. However, under the effect of the atmospheric turbulence, the output vortex property gradually disappears, and changes to a bright-cantered beam without vortex property. Furthermore, the weaker the atmospheric turbulence is, the longer distance the output optical vortex （the center-dark beam） can propagate over.

Robust phase-retrieval for quick whole-body SAR assessment using dual plane amplitude-only data

A robust phase-retrieval method with stable convergence and back-propagation properties for quick experimental whole body specific absorption rate (SAR) assessments is presented. A combination of a fast and coarse method and a more accurate gradient-based method is used to optimise the overall performance. To prevent the solution being trapped in a local minimum, several initial phase distributions are used. An accurate measurement procedure has been developed which reduces measurement time by roughly a factor of 2.5–4 at common mobile communication frequencies compared with a volume scan based procedure.

Formation of optical vortices using coherent laser beam arrays

We present a proposal to generate an optical vortex beam by using the coherent-superposition of multi-beams in a radially symmetric configuration. In terms of the generalized Huygens–Fresnel diffraction integral, we have derived the general propagation expression for the coherent radial arrays of laser beams. Using the derived formulae, we have analyzed the effects of the beamlet number N, the separation distance ρ of the beamlets and the topological charge m on the intensity and phase distributions of the resultant beams. Our simulation results show that optical vortices could be efficiently generated due to the coherent-superposition effect of all beamlets, during the propagation process of the coherent radial array of laser beams with the initial well-organized phase distributions through the free space. In the focusing system, the resultant beam near the focusing plane has the strong rotational effect with the phase helicity.

Influence of morphology on the dynamic mechanical properties of hydrogenated acrylonitrile butadiene elastomer/coagent nanodispersions

AbstractCoagents are vinyl monomers that react with free radicals formed by peroxide dissociation and are either grafted to elastomer chains or homopolymerized within a segregated phase to form a crosslinked network. The initial phase distribution within the elastomer matrix is of great importance for the final user properties of a composite material. In this study, the morphology of blends of each of three different coagents, that is, zinc dimethacrylate (ZDMA), N,N′‐m‐phenylene dimaleimide (HVA‐2), and trimethylolpropane trimethacrylate (TMPTMA) on a reinforcing substrate with dicumyl peroxide and hydrogenated acrylonitrile butadiene elastomer after processing was investigated with scanning electron microscopy. The morphology that evolved during processing was then compared to the results obtained from dynamic mechanical analysis (DMA) of the blends. Dynamic mechanical properties were modeled with a continuous relaxation distribution function, the Williams–Landel–Ferry equation, and the modified Guth–Gold equation. In the case of ZDMA and TMPTMA, a microphase and a nanophase evolved during processing, whereas the HVA‐2 phase in the blends remained well segregated. The volume fraction of the particles under 100 nm in ZDMA and TMPTMA blends ranged from 79 to 89%. The DMA results revealed the reinforcing effect of ZDMA and TMPTMA during the glass‐transition and in the plateau region, whereas HVA‐2 exhibited plasticizer‐like behavior. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008

Clusters and Switchers in Globally Coupled Photochemical Oscillators

We experimentally investigate the transition to synchronization in a population of photochemical oscillators with weak global coupling. Above a critical coupling strength the oscillators join a one-phase group or two-phase clusters. The number of oscillators in each cluster depends on the initial phase distribution, and irregular switching of oscillators between clusters is observed. The fully synchronized state emerges above a second critical coupling strength. In agreement with earlier theory, the experiments demonstrate the importance of population heterogeneity in cluster multistability.

Water behavior in serpentine micro-channel for proton exchange membrane fuel cell cathode

The behavior of water in the air–water flow inside a serpentine channel for a proton exchange membrane (PEM) fuel cell was investigated using the FLUENT software package. The volume-of-fluid (VOF) model was adopted to track the dynamic air–water interface. Five cases with varying initial water phase distribution corresponding to different fuel cell operating conditions were numerically simulated to obtain a better understanding of water behavior inside a serpentine micro-channel. Results show that the bend area of a serpentine flow channel has significant effects on the flow field, which in turn affects the air–water flow and water liquid distribution inside the channel or along the interior channel surfaces. The simulation results also indicate that water flooding could occur in the “after-bend” section of a micro-channel. For the case with larger amount of water in the two-phase flow, the simulation shows that the “after-bend” water distribution might block the reactant supply to reaction sites and, in some extreme situations, might block the reactant transport inside the flow channel, thus decreasing fuel cell performance.

Helico-conical optical beams: a product of helical and conical phase fronts

Helico-conical optical beams, different from higher-order Bessel beams, are generated with a parallel-aligned nematic liquid crystal spatial light modulator (SLM) by multiplying helical and conical phase functions leading to a nonseparable radial and azimuthal phase dependence. The intensity distributions of the focused beams are explored in two- and threedimensions. In contrast to the ring shape formed by a focused optical vortex, a helico-conical beam produces a spiral intensity distribution at the focal plane. Simple scaling relationships are found between observed spiral geometry and initial phase distributions. Observations near the focal plane further reveal a cork-screw intensity distribution around the propagation axis. These light distributions, and variations upon them, may find use for optical trapping and manipulation of mesoscopic particles.

A spatio-temporal simulation model of the response of solid tumours to radiotherapy in vivo: parametric validation concerning oxygen enhancement ratio and cell cycle duration

Advanced bio-simulation methods are expected to substantially improve radiotherapy treatment planning. To this end a novel spatio-temporal patient-specific simulation model of the in vivo response of malignant tumours to radiotherapy schemes has been recently developed by our group. This paper discusses recent improvements to the model: an optimized algorithm leading to conformal shrinkage of the tumour as a response to radiotherapy, the introduction of the oxygen enhancement ratio (OER), a realistic initial cell phase distribution and finally an advanced imaging-based algorithm simulating the neovascularization field. A parametric study of the influence of the cell cycle duration Tc, OER, OERβ for the beta LQ parameter on tumour growth, shrinkage and response to irradiation under two different fractionation schemes has been made. The model has been applied to two glioblastoma multiforme (GBM) cases, one with wild type (wt) and another one with mutated (mt) p53 gene. Furthermore, the model has been applied to a hypothetical GBM tumour with α and β values corresponding to those of generic radiosensitive tumours. According to the model predictions, a whole tumour with shorter Tc tends to repopulate faster, as is to be expected. Furthermore, a higher OER value for the dormant cells leads to a more radioresistant whole tumour. A small variation of the OERβ value does not seem to play a major role in the tumour response. Accelerated fractionation proved to be superior to the standard scheme for the whole range of the OER values considered. Finally, the tumour with mt p53 was shown to be more radioresistant compared to the tumour with wt p53. Although all simulation predictions agree at least qualitatively with the clinical experience and literature, a long-term clinical adaptation and quantitative validation procedure is in progress.

Application of ultrafiltration and stable isotopic amendments to field studies of mercury partitioning to filterable carbon in lake water and overland runoff

Results from pilot studies on colloidal phase transport of newly deposited mercury in lake water and overland runoff demonstrate that the combination of ultrafiltration, and stable isotope amendment techniques is a viable tool for the study of mercury partitioning to filterable carbon. Ultrafiltration mass balance calculations were generally excellent, averaging 97.3, 96.1 and 99.8% for dissolved organic carbon (DOC), total mercury (Hg T), and methylmercury (MeHg), respectively. Sub nanogram per liter quantities of isotope were measurable, and the observed phase distribution from replicate ultrafiltration separations on lake water agreed within 20%. We believe the data presented here are the first published colloidal phase mercury data on lake water and overland runoff from uncontaminated sites. Initial results from pilot-scale lake amendment experiments indicate that the choice of matrix used to dissolve the isotope did not affect the initial phase distribution of the added mercury in the lake. In addition there was anecdotal evidence that native MeHg was either recently produced in the system, or at a minimum, that this ‘old’ MeHg partitions to the same subset of DOC that binds the amended mercury. Initial results from pilot-scale overland runoff experiments indicate that less than 20% of newly deposited mercury was transported in the filterable fraction (<0.7 μm). There is some indication of colloidal phase enrichment of mercury in runoff compared to the phase distribution of organic carbon, but the mechanism of this enrichment is unclear. The phase distribution of newly deposited mercury can differ from that of organic carbon and native mercury, suggesting that the quality of the carbon (available ligands), not the quantity of carbon, regulates partitioning. Further characterization of DOC is needed to clarify the underlying mechanisms.

Synchronous Phase Clustering in a Network of Neurons with Spatially Decaying Excitatory Coupling

Synchronization is studied in a spatially-distributed network of weekly-coupled, excitatory neurons of Hodgkin–Huxley type. All neurons are coupled to each other synaptically with a fixed time delay and a coupling strength inversely proportional to the distance between two neurons. We found that a robust, noise-resistant phase clustering state occurred regardless of the initial phase distribution. This has not been shown in previous studies where similar clustering states were found only when the coupling was inhibitory. The spatial distribution of neurons in each synchronous cluster is determined by the spatial distribution of the coupling strength. Phase-interaction properties of the model neurons in the network are used to explain why such a clustering state can be robust.

A New Method for Phase Retrieval in the Optical System

In this letter, a new recursive algorithm to implement phase retrieval from two intensities in the two-dimensional Fourier transform domain is presented. In terms of the cascading property and additivity of the order of the fractional Fourier transform, a set of convolution equations is exactly derived. Applying recursive algorithm, these equations can be easily solved. This approach simplifies significantly computational manipulations comparing with conventional iterative algorithms and does not need initial phase distribution.

INVERSE PROBLEM OF A LASER AMPLIFIER SYSTEM CONTAINING A SPATIAL FILTER

Starting from the Frantz-Nodvik equation and Huygens-Fresnel diffraction integral and using the fast Fourier transform and successive iteration method, we studied the inverse problem of a laser amplifier system containing a spatial filter, i-e-, to find the initial input temporal pulse profile, am-plitude and phase distributions from the required output temporal, spatial pulse profile and fluence, as well as the given amplifier and spatial filter parameters-

Odd and even two-dimensional dark spatial solitons

The formation of two-Dimensional (2D) odd dark spatial solutions is analyzed numerically at an initial helical dark-beam phase distribution. Experimental results are presented for the first time confirming the existence of two-dimensional optical even dark solitons (ring dark solitons). Several aspects of the evolution of input 1D and 2D odd/even dark beams are compared qualitatively.

Microwave inverse free-electron-laser accelerator using a small "phase window"

We analyze, by numerical simulation, an inverse free-electron-laser accelerator for the purpose of accelerating electrons from 1.5 MeV to about 20 MeV in a 1.5 m long undulator (\ensuremath{\sim}13 MeV/m). The initial phase distribution of injected electrons is chosen to lie in a small ``phase window'' from -\ensuremath{\pi}/8 to -3\ensuremath{\pi}/8 so that all the electrons can be trapped in the accelerating bucket. In this case, there is little particle spread in phase space and the electron energy spectrum is a narrow spike.