Transient Dynamics in the Random Growth and Reset Model

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.     

Tracking an Auto-Regressive Process with Limited Communication per Unit Time

Samples from a high-dimensional first-order auto-regressive process generated by an independently and identically distributed random innovation sequence are observed by a sender which can communicate only finitely many bits per unit time to a receiver. The receiver seeks to form an estimate of the process value at every time instant in real-time. We consider a time-slotted communication model in a slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to refine estimates of the latest sample and study the following question: Is it better to collect communication of multiple slots to send better refined estimates, making the receiver wait more for every refinement, or to be fast but loose and send new information in every communication opportunity? We show that the fast but loose successive update scheme with ideal spherical codes is universally optimal asymptotically for a large dimension. However, most practical quantization codes for fixed dimensions do not meet the ideal performance required for this optimality, and they typically will have a bias in the form of a fixed additive error. Interestingly, our analysis shows that the fast but loose scheme is not an optimal choice in the presence of such errors, and a judiciously chosen frequency of updates outperforms it.     

Direct contact ultrasound assisted freezing of chicken breast samples

Nowadays, rapid freezing is sought to favor the formation of small ice crystals. Several studies have shown that the application of ultrasounds (US) accelerates the processes of energy and mass transfer when they are applied through immersion systems. However, there are hardly any studies on its application in direct systems without the use of a liquid medium for its transmission. Therefore, the objective of this work was to evaluate the potential of the application of US for improving the freezing process of chicken breast samples. First, the application of intermittent US treatments at different net sonication times of 7, 17, 37, 50 and 67% during the freezing of distilled water samples in a conventional freezer was evaluated. It was observed that net sonication times of 37, 50 and 67% reduced the phase change period by 30.0, 21.4, 27.0%, respectively. The effective freezing time was also reduced by 12.4 and 12.8% by applying net sonication times of 37 and 50%. Considering these results, an intermittent US treatment with a net sonication time of 37% was chosen for chicken breast freezing in an air-forced cooling tunnel at ambient temperatures from −13 to −22 °C. The length of all the freezing phases was reduced upon application of US, leading to an overall process time reduction of approx. 11%. On the other hand, no significant differences were found either in the Water Holding Capacity (WHC) or Cooking Loss (CL) values between control and US assisted frozen chicken breast samples. Furthermore, in vitro experiments showed that US-assisted freezing did not influence protein digestibility of chicken meat samples.This study demonstrates the potential of the application of US by direct contact to favor energy transfer processes during freezing of water and chicken breasts samples. However, its effect on the quality of the frozen products should be further studied.     

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

With the development of information technology, rumors propagate faster and more widely than in the past. In this paper, a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed. The global positivity of the solution process is proved, and further the basic reproductive number R₀ is obtained. When R₀ < 1, the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system, and the rumor tends to extinction; when R₀ > 1, the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system. The results show that the oscillation amplitude is related to the disturbance of the system. In addition, increasing media coverage can effectively reduce the final spread of rumors. Finally, the above results are verified by numerical simulation.     

Combinatorial and approximative analyses in a spatially random division process

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.     

Time-varying human mobility patterns with metapopulation epidemic dynamics

In this paper, explicitly considering the influences of an epidemic outbreak on human travel, a time-varying human mobility pattern is introduced to model the time variation of global human travel. The impacts of the pattern on epidemic dynamics in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals, are investigated by using a mean-field approach. The results show that the pattern does not alter the epidemic threshold, but can slightly lower the final average density of infected individuals as a whole. More importantly, we also find that the pattern produces different impacts on nodes with different degree, and that there exists a critical degree _kc$k_c$. For nodes with degree smaller than _kc$k_c$, the pattern produces a positive impact on epidemic mitigation; conversely, for nodes with degree larger than _kc$k_c$, the pattern produces a negative impact on epidemic mitigation.     

Influence of the surface morphology on the melting of polymer crystals. I. Loops of random length and adjacent reentry

A polymer crystal with a noncrystalline surface layer formed by chain loops of different lengths is considered. It is assumed that the length of each loop can be changed by longitudinal diffusion of the molecule through the crystal lattice. From the condition that the free energy of the system is minimum, the loop length distribution and the average loop length as function of temperature are calculated. In contrast to the results for loops of equal length, for the present model, a substantial thickness of the noncrystalline surface layer and a broad melting range is obtained also for the case of adjacent reentry. In order to get this result one has to take into account that even an “ideal fold” consists of at least four rigidly arranged CH2 groups in energetically unfavored conformation.     

DRDF analysis of wide-angle x-ray scattering of natural rubber

A differential radial distribution function (DRDF) of molten natural rubber (NR) was derived from its wide-angle x-ray scattering (WAXS) data. Three peaks with Bragg spacings 4.85, 2.31, and 1.23 Å corresponding, respectively, to interchain, C₁-C₃ and C₁ -C₂ distances are present in the corrected WAXS curve. The derived DRDF, which is shown to be greatly improved than the ones published so far, contains six peaks located at 1.51, 2.48, 3.98, 5.68, 10.65, and 15.25 Å. Maximum contributions of intramolecular atomic distances to the radial distribution peaks were estimated and compared with the experimental results. The comparison shows that the first three peaks are intramolecular in origin and the remaining peaks are predominantly due to intermolecular regularities. A periodicity of an approximately constant interval of 5.26 Å is found between the intermolecular peaks and is attributable to the organizations of more or less parallel chain segments in the material. This finding provided additional evidence for the presence of local lateral ordering to the extent of about 30 Å in molten-state natural rubber.     

Polycrystalline silicon films prepared by metal-induced crystallisation using pre- and post-deposited aluminium on amorphous silicon

We report on the successful fabrication of polycrystalline silicon films by aluminium-induced crystallisation (AIC) of Radio frequency (rf) plasma-enhanced chemical vapour deposited (PECVD) a-Si films. The effects of annealing at different temperatures (300 and 400°C), below the eutectic temperature of the Si–Al binary system, on the crystallisation process have been studied. This work emphasises the important role of the position of the Al layer with respect to the Si layer on the crystallisation process. The properties of the crystallised films were characterised using X-ray diffraction, Raman spectroscopy, ellipsometry, field-emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM). With an increase in the annealing temperature, it was found that the degree of crystallisation of annealed a-Si/Al and Al/a-Si films increased. The results showed that the arrangement where the Al was on top of the a-Si had a more prominent effect on crystallisation enhancement than when Al was below the a-Si. The interfacial layer between the Al and a-Si film is crucial because it influences the layer-exchange process during annealing. The oxide layer formed between the Al and the a-Si layers greatly retards the crystallisation process in the case of the Al/Si arrangement. Our investigations suggest that polycrystalline Si films formed by AIC can be used as a seed layer in solar cell fabrication.