Traveling and pinned fronts in bistable reaction-diffusion systems on network

Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erd\"os-R\'enyi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erd\"os-R\'enyi and scale-free networks, the mean-field theory for stationary patterns is constructed

Analysis of relative influence of nodes in directed networks

Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the relative importance of nodes specifically in directed networks. We analyze such a centrality measure called the influence. The influence represents the importance of nodes in various dynamics such as synchronization, evolutionary dynamics, random walk, and social dynamics. We analytically calculate the influence in various networks, including directed multipartite networks and a directed version of the Watts-Strogatz small-world network. The global properties of networks such as hierarchy and position of shortcuts, rather than local properties of the nodes, such as the degree, are shown to be the chief determinants of the influence of nodes in many cases. The developed method is also applicable to the calculation of the PageRank. We also numerically show that in a coupled oscillator system, the threshold for entrainment by a pacemaker is low when the pacemaker is placed on influential nodes. For a type of random network, the analytically derived threshold is approximately equal to the inverse of the influence. We numerically show that this relationship also holds true in a random scale-free network and a neural network.Comment: 9 figure

Household scale slow sand filtration in the Dominican Republic

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2004.Includes bibliographical references (leaves 81-83).Slow sand filtration is a method of water treatment that has been used for hundreds of years. In the past two decades, there has been resurgence in interest in slow sand filtration, particularly as a low-cost, household-scale method of water treatment. During January 2004, the author traveled to the northwestern Dominican Republic to evaluate the performance of BioSand filters installed over the past two years. BioSand filter performance was evaluated based on flow rate, turbidity removal and total coliform removal in communities surrounding the cities of Mao, Puerto Plata and Dajabon. Filter owners were interviewed about general filter use, water storage methods, filter maintenance practices, and water use. Data analysis revealed that even though the majority of filters were removing large portions of both total coliform and E. coli contamination, no filters met the WHO water quality guideline of less than one CFU/100 ml. Analysis also revealed that at low turbidities, turbidity removal and total coliform removal are not correlated. Examination of flow rate and bacterial removal near Puerto Plata revealed that filters with fast flow rates and intermittent chlorination were observed to have the lowest total coliform removal rates. Analysis of storage data revealed that failure to use safe water storage containers leads to recontamination of filtered water. During Spring of 2004, a laboratory was conducted to examine longer-term thermotolerant coliform and turbidity removal. The study compared removal rates between two BioSand filters, one of which was paired with a geotextile prefilter used in the construction of the Peruvian Table Filter. The study revealed that thermotolerant coliform removal rates by the BioSand filter without(cont.) the geotextile stabilized after an initial period of lower bacterial removal efficiency. Thermotolerant coliform removal in the BioSand filter with the geotextile prefilter dropped throughout the experiment, suggesting that pairing a BioSand filter with a prefilter is detrimental to filter performance. Combining the results of the survey analysis and data gathered in the Dominican Republic with the results of the laboratory analysis of Spring 2004 suggests that BioSand filter users in the Dominican Republic should continue to use their filters. If possible, BioSand filter use should be combined with post-filtration chlorination to kill the remaining bacteria. The BioSand filter is a valuable and effective household-scale water treatment method for the Dominican Republic.by Kori S. Donison.M.Eng

AYURVEDIC MANAGEMENT OF PSORIASIS - A CASE STUDY

In Ayurveda, all types of skin diseases are described under one umbrella term of Kushtha. Acharyas have described that all Kushthas have Tridosha involvement but the type of Kushtha depends on the predominance of particular Doshas. Eka Kushtha is compared with psoriasis due to its maximum resemblance. Psoriasis is a long-lasting autoimmune disease characterized by patches of abnormal skin. These skin patches are typically red, itchy, and scaly. They may vary in severity from small and localized to extensive, large and spread in complete body. It typically presents with red patches and white scales on the top. Areas of the body most commonly affected are the back of the forearms, shins, around the navel, and the scalp. Psoriasis is generally thought to be a genetic disease which is triggered by environmental factors. Other factors such as local trauma, general illness and stress are also involved. In modern medicine, the cure of this disease is out of question as the cause is unknown. Ayurveda propounds a holistic treatment approach for psoriasis. As per Ayurvedic view point Vata, Pitta and Kapha vitiation are the major contributing pathological factors in the body. The line of treatment of skin diseases are Shodhana and Shamana therapy. Virechana Karma (purgation therapy) followed by internal medications are considered as the best line of management for skin disorders. A case report of 13 year old male child presented with well demarcated raised red scaling silvery patches on trunk and back region, limbs with itching and burning will be presented in the full paper

Collective Phase Sensitivity

The collective phase response to a macroscopic external perturbation of a population of interacting nonlinear elements exhibiting collective oscillations is formulated for the case of globally-coupled oscillators. The macroscopic phase sensitivity is derived from the microscopic phase sensitivity of the constituent oscillators by a two-step phase reduction. We apply this result to quantify the stability of the macroscopic common-noise induced synchronization of two uncoupled populations of oscillators undergoing coherent collective oscillations.Comment: 6 pages, 3 figure

Entrainment of randomly coupled oscillator networks by a pacemaker

Entrainment by a pacemaker, representing an element with a higher frequency, is numerically investigated for several classes of random networks which consist of identical phase oscillators. We find that the entrainment frequency window of a network decreases exponentially with its depth, defined as the mean forward distance of the elements from the pacemaker. Effectively, only shallow networks can thus exhibit frequency-locking to the pacemaker. The exponential dependence is also derived analytically as an approximation for large random asymmetric networks.Comment: 4 pages, 3 figures, revtex 4, submitted to Phys. Rev. Let

Poisoning and fading mechanism of grain refinement in Al-7Si alloy

The poisoning and fading mechanism of grain refinement in Al-7Si alloy has been studied in detail with the conventional (0.01%Ti or B) and higher addition levels of indigenously developed Al-3Ti, Al-5Ti, Al-3B and Al-5Ti- 1B master alloys. Results suggest that on prolonged holding the melt after the conventional addition of grain refiner to Al-7Si alloy, size of the α-Al dendrites increases (fading), which could be due to the dissolution/settling of TiAl3 and AlB2 particles. However, vigorous agitation of the melt after prolonged holding (120s min.), can partly bring back the particles into the liquid melt and acts as heterogeneous nucleating sites to some limited extents (120s min. sample). In addition, the conventional addition (0.2 wt%) of Ti-rich Al-3Ti, Al-5Ti and Al-5Ti-1B master alloy to Al-7Si alloy, the Si from the melt reacts with grain refining constituents (TiAl3) and formation of titanium silicide and coats on the surface of the TiAl3 particles and poisons the effectiveness of the nuclei. However, the higher addition level of these master alloy or B-rich Al-3B master alloys can overcome poisoning effect of Al-7Si alloy

Meconium stained liquor and perinatal outcome

Background: The aim of this study is to know the association between the meconium stained amniotic fluid and its association with the perinatal outcome.Methods: All the patients coming to present hospital for delivery with meconium stained liquor during the study period were included in the study.Results: 163 cases with meconium stained liquor (MSAF) were included in the study, 124(76.1%) and 39(23.9%) had thin and thick MSAF respectively. Among these cases, thick MSAF was more associated with high fetal heart rate (FHR) variability (p value- 0.030), associated with increased rate of operative interference (64.1%; p value- 0.001), abnormal Apgar score (p value-0.003 at 1min and 0.001 at 5min) and increased neonatal intensive care unit (NICU) admission (33.3%; p value - <0.001).Conclusions: Present study showed that thick meconium is associated with more complications like increased operative interference, birth asphyxia, meconium aspiration syndrome, low Apgar score, prolonged NICU stay and overall increased perinatal mortality compared to thin meconium stained liquor. As the gestational age increased the incidence of meconium increased and a greater number of thick meconium had abnormal CTG