Aspects of Markov Chains and Particle Systems

Thesis (Ph.D.)--University of Washington, 2016-06

Eutectic grains in unmodified and strontium-modified hypoeutectic aluminum-silicon alloys

Additions of strontium to hypoeutectic aluminum-silicon alloys modify the morphology of the eutectic silicon phase from a coarse platelike structure to a fine fibrous structure. Thermal analysis, interrupted solidification, and microstructural examination of sand castings in this work revealed that, in addition to a change in silicon morphology, modification with strontium also causes an increase in the size of eutectic grains. The eutectic grain size increases because fewer grains nucleate, possibly due to poisoning of the phosphorus-based nucleants, that are active in the unmodified alloy. A simple growth model is developed to estimate the interface velocity during solidification of a eutectic grain. The model confirms, independent of microstructural observations, that the addition of 100 ppm strontium increases the eutectic grain size by at least an order of magnitude compared with the equivalent unmodified alloy. The model predicts that the growth velocity varies significantly during eutectic growth. At low strontium levels, these variations may be sufficient to cause transitions between flake and fibrous silicon morphologies depending on the casting conditions. The model can be used to rationally interpret the eutectic grain structure and silicon morphology of fully solidified aluminum-silicon castings and, when coupled with reliable thermal data, can be used to estimate the eutectic grain size.

Accelerating, hyperaccelerating, and decelerating networks

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyperaccelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.

Why many eligible individuals choose not to go on welfare

This article investigates why many eligible for welfare do not participate. We show that on-the-job wage-rising potential is the key factor motivating nonparticipation. Although individuals with very low earnings and little wage-rising potential are typically welfare recipients, those with good wage-rising potential may choose to work, participate in old age, or never participate. Nonparticipation remains the best choice for eligible individuals with large wage-rising potential even if universal old-age social security is available. We will also apply this model to a comprehensive welfare system in Hong Kong.

Income Ranking and convergence with physical and human capital and income equality

This paper presents an overlapping generations model with physical and human capital and income inequality. It shows that inequality impedes output growth by directly harming capital accumulation and indirectly raising the ratio of physical to human capital. The convergence speed of output growth equals the lower of the convergence speeds of the relative capital ratio and inequality, and varies with initial states. Among economies with the same balanced growth rate but different initial income levels, the ranking of income can switch in favor of those starting from low inequality and a low ratio of physical to human capital, particularly if the growth rate converges slowly. (C) 2004 Elsevier B.V. All rights reserved.

Heterogeneous nucleation of Mg-Al alloys

Grain size is one of the most important microstructural characteristics determining the mechanical properties and therefore the service performance of polycrystalline materials. Heterogeneous nucleation involves the addition or in situ formation of potent nuclei in the system to promote nucleation events, leading to a fine grain structure. This paper reports experimental results using graphite and SiC as potential grain refining agents to form in situ nuclei for Mg in Mg-Al alloys, and demonstrates the key role of Al4C3 in grain refilling this important alloy system. This insight will contribute to the design and development of the most cost effective, eco-friendly grain refining agents for Mg-Al alloys. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Modelling predicts positive and negative interactions between three Australian tropical tree species in monoculture and binary mixture

Computer modelling promises to. be an important tool for analysing and predicting interactions between trees within mixed species forest plantations. This study explored the use of an individual-based mechanistic model as a predictive tool for designing mixed species plantations of Australian tropical trees. The 'spatially explicit individually based-forest simulator' (SeXI-FS) modelling system was used to describe the spatial interaction of individual tree crowns within a binary mixed-species experiment. The three-dimensional model was developed and verified with field data from three forest tree species grown in tropical Australia. The model predicted the interactions within monocultures and binary mixtures of Flindersia brayleyana, Eucalyptus pellita and Elaeocarpus grandis, accounting for an average of 42% of the growth variation exhibited by species in different treatments. The model requires only structural dimensions and shade tolerance as species parameters. By modelling interactions in existing tree mixtures, the model predicted both increases and reductions in the growth of mixtures (up to +/- 50% of stem volume at 7 years) compared to monocultures. This modelling approach may be useful for designing mixed tree plantations. (c) 2006 Published by Elsevier B.V.

Noisy random Boolean formulae:a statistical physics perspective

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

Gold nanoparticles decorated with oligo(ethylene glycol) thiols:kinetics of colloid aggregation driven by depletion forces

We have studied the kinetics of the phase-separation process of mixtures of colloid and protein in solutions by real-time UV-vis spectroscopy. Complementary small-angle X-ray scattering (SAXS) was employed to determine the structures involved. The colloids used are gold nanoparticles functionalized with protein resistant oligo(ethylene glycol) (OEG) thiol, HS(CH(2))(11)(OCH(2)CH(2))(6)OMe (EG6OMe). After mixing with protein solution above a critical concentration, c*, SAXS measurements show that a scattering maximum appears after a short induction time at q = 0.0322 angstrom(-1) stop, which increases its intensity with time but the peak position does not change with time, protein concentration and salt addition. The peak corresponds to the distance of the nearest neighbor in the aggregates. The upturn of scattering intensities in the low q-range developed with time indicating the formation of aggregates. No Bragg peaks corresponding to the formation of colloidal crystallites could be observed before the clusters dropped out from the solution. The growth kinetics of aggregates is followed in detail by real-time UV-vis spectroscopy, using the flocculation parameter defined as the integral of the absorption in the range of 600-800 nm wavelengths. At low salt addition (<0.5 M), a kinetic crossover from reaction-limited cluster aggregation (RLCA) to diffusion-limited cluster aggregation (DLCA) growth model is observed, and interpreted as being due to the effective repulsive interaction barrier between colloids within the depletion potential. Above 0.5 M NaCl, the surface charge of proteins is screened significantly, and the repulsive potential barrier disappeared, thus the growth kinetics can be described by a DLCA model only.

Drivers of peak sales for pharmaceutical brands

Peak sales are an important metric in the pharmaceutical industry. Specifically, managers are focused on the height-of-peak-sales and the time required achieving peak sales. We analyze how order of entry and quality affect the level of peak sales and the time-to-peak-sales of pharmaceutical brands. We develop a growth model that includes these two variables as well as control variables for own and competitive marketing activities. We find that early entrants achieve peak sales later, and they have higher peak-sales levels. High-quality brands achieve peak sales earlier, and their peak-sales levels are higher. In addition, quality has a moderating effect on the order of entry effect on time-to-peak-sales. Our results indicate that late entrants have longer expected time-to-peak-sales when they introduce a brand with high quality.

Lie-szimmetriák egy közgazdasági alkalmazása (An economic application of the Lie symmetries)

Ebben a tanulmányban ismertetjük a Nöther-tétel lényegi vonatkozásait, és kitérünk a Lie-szimmetriák értelmezésére abból a célból, hogy közgazdasági folyamatokra is alkalmazzuk a Lagrange-formalizmuson nyugvó elméletet. A Lie-szimmetriák dinamikai rendszerekre történő feltárása és viselkedésük jellemzése a legújabb kutatások eredményei e területen. Például Sen és Tabor (1990), Edward Lorenz (1963), a komplex kaotikus dinamika vizsgálatában jelent®s szerepet betöltő 3D modelljét, Baumann és Freyberger (1992) a két-dimenziós Lotka-Volterra dinamikai rendszert, és végül Almeida és Moreira (1992) a három-hullám interakciós problémáját vizsgálták a megfelelő Lie-szimmetriák segítségével. Mi most empirikus elemzésre egy közgazdasági dinamikai rendszert választottunk, nevezetesen Goodwin (1967) ciklusmodelljét. Ennek vizsgálatát tűztük ki célul a leírandó rendszer Lie-szimmetriáinak meghatározásán keresztül. / === / The dynamic behavior of a physical system can be frequently described very concisely by the least action principle. In the centre of its mathematical presentation is a specic function of coordinates and velocities, i.e., the Lagrangian. If the integral of the Lagrangian is stationary, then the system is moving along an extremal path through the phase space, and vice versa. It can be seen, that each Lie symmetry of a Lagrangian in general corresponds to a conserved quantity, and the conservation principle is explained by a variational symmetry related to a dynamic or geometrical symmetry. Briey, that is the meaning of Noether's theorem. This paper scrutinizes the substantial characteristics of Noether's theorem, interprets the Lie symmetries by PDE system and calculates the generators (symmetry vectors) on R. H. Goodwin's cyclical economic growth model. At first it will be shown that the Goodwin model also has a Lagrangian structure, therefore Noether's theorem can also be applied here. Then it is proved that the cyclical moving in his model derives from its Lie symmetries, i.e., its dynamic symmetry. All these proofs are based on the investigations of the less complicated Lotka Volterra model and those are extended to Goodwin model, since both models are one-to-one maps of each other. The main achievement of this paper is the following: Noether's theorem is also playing a crucial role in the mechanics of Goodwin model. It also means, that its cyclical moving is optimal. Generalizing this result, we can assert, that all dynamic systems' solutions described by first order nonlinear ODE system are optimal by the least action principle, if they have a Lagrangian.

A fizikai matematika legújabb eredményei mint a közgazdaság-tudomány lehetséges vizsgálati eszközei (The newest results of physical mathematics as the possible investigation tools of economics)

A közgazdaság-tudomány számos problémája a fizika analóg modelljeinek segítségével nyert megoldást. A közgazdászok körében erőteljesen megoszlanak a vélemények, hogy a közgazdasági modellek mennyire redukálhatók a fizika, vagy más természettudományok eredményeire. Vannak,akik pontosan ezzel magyarázzák,hogy a mai mainstream közgazdasági elmélet átalakult alkalmazott matematikává,ami a gazdasági kérdéseket csak a társadalom-tudományi vonatkozásaitól eltekintve képes vizsgálni. Mások, e tanulmányszerzője is, viszont úgy vélekednek, hogy a közgazdasági problémák egy része, ahol lehetőség van a mérésre, jól modellezhetők a természettudományok technikai arzenáljával. A másik része, amelyekben nem lehet mérni,s tipikusan ilyenek a társadalomtudományi kérdések, ott sokkal komplexebb technikákra lesz szükség. Etanulmány célkitűzése, hogy felvázolja a fizika legújabb, az irreverzibilis dinamika, a relativitáselmélet és a kvantummechanika sztochasztikus matematikai összefüggéseit, amelyekből a közgazdászok választhatnak egy-egy probléma megfogalmazásában és megoldásában. Például az időoperátorok pontos értelmezése jelentős fordulatot hozhat a makroökonómiai elméletekben; vagy az eddigi statikus egyensúlyi referencia pontokat felválthatják a dinamikus,időben változó sztochasztikus egyensúlyi referenciafüggvények, ami forradalmian új megvilágításba helyezhet számos társadalomtudományi, s főleg nemegyensúlyi közgazdasági kérdést.A termodinamika és a biológiai evolúció fogalmait és definícióit Paul A. Samuelson (1947) már adaptálta a közgazdaságtanban, viszont a kvantummechanika legújabb eredményeit, az időoperátorokat stb. nem érintette. E cikk azokat a legújabb fizikai, kémiai és biológiai matematikai összefüggéseket foglalja össze,amelyek hasznosak lehetnek a közgazdasági modellek komplexebb megfogalmazásához. ___________________ The aim of this paper is to out line the newest results of physics,i.e.,the stochastic mathematical relations of relativity theory and quantum mechanics as well as irreversible dynamics which can be applied for some economic problems.For example,the correct interpretation of time operators using for the macroeconomic theories may provide a serious improvement in approach to the reality.The stochastic dynamic equilibrium reference functions will take over the role of recent static equilibrium reference points,which may also reveal some nonequilibrium questions of macroeconomics.The concepts and definitions of thermodynamics and biological evolution have been adopted in economics by Paul A. Samuelson, but he did not concern the newest results of quantum mechanics, e.g., the time operators. Now we do it.In addition, following Samuelson,we show that von Neumann growth model cannot be explained as a peculiar extension of thermodynamic irreversibility.

The effect of the reproductivity's velocity on the biodiversity of a theoretical ecosystem

Climate change has a great impact on the build and the work of natural ecosystems. Disappearance of some population or growth of the number in some species can be already caused by little change in temperature. A Theoretical Ecosystem Growth Model was investigated in order to examine the effects of various climate patterns on the ecological equilibrium. This paper examines the diversity of a theoretical ecosystem on the grounds of changing in temperature-climate patterns. Simulations were made from the simplest case to the more complex exercise to explain harder questions. Daily temperature values were calculated according to various functions. The effect of existing climate patterns (historical or future daily temperatures) was analysed where temperature values were from various climatic zones. In this paper it is examined what kind of environmental conditions result larger diversity related to the velocity of reproduction.

Characterizing Internet worm spatial-temporal infection structures

Since the Morris worm was released in 1988, Internet worms continue to be one of top security threats. For example, the Conficker worm infected 9 to 15 million machines in early 2009 and shut down the service of some critical government and medical networks. Moreover, it constructed a massive peer-to-peer (P2P) botnet. Botnets are zombie networks controlled by attackers setting out coordinated attacks. In recent years, botnets have become the number one threat to the Internet. The objective of this research is to characterize spatial-temporal infection structures of Internet worms, and apply the observations to study P2P-based botnets formed by worm infection. First, we infer temporal characteristics of the Internet worm infection structure, i.e., the host infection time and the worm infection sequence, and thus pinpoint patient zero or initially infected hosts. Specifically, we apply statistical estimation techniques on Darknet observations. We show analytically and empirically that our proposed estimators can significantly improve the inference accuracy. Second, we reveal two key spatial characteristics of the Internet worm infection structure, i.e., the number of children and the generation of the underlying tree topology formed by worm infection. Specifically, we apply probabilistic modeling methods and a sequential growth model. We show analytically and empirically that the number of children has asymptotically a geometric distribution with parameter 0.5, and the generation follows closely a Poisson distribution. Finally, we evaluate bot detection strategies and effects of user defenses in P2P-based botnets formed by worm infection. Specifically, we apply the observations of the number of children and demonstrate analytically and empirically that targeted detection that focuses on the nodes with the largest number of children is an efficient way to expose bots. However, we also point out that future botnets may self-stop scanning to weaken targeted detection, without greatly slowing down the speed of worm infection. We then extend the worm spatial infection structure and show empirically that user defenses, e.g. , patching or cleaning, can significantly mitigate the robustness and the effectiveness of P2P-based botnets. To counterattack, we evaluate a simple measure by future botnets that enhances topology robustness through worm re-infection.

Helicopter-borne sea ice thickness measurements in the Storfjord, Spitsbergen from flight HEM_STJ06_01

Results from electromagnetic induction surveys of sea-ice thickness in Storfjorden, Svalbard, reveal large interannual ice-thickness variations in a region which is typically characterized by a reoccurring polynya. The surveys were performed in March 2003, May 2006 and March 2007 with helicopter- and ship-based sensors. The thickness distributions are influenced by sea-ice and atmospheric boundary conditions 2 months prior to the surveys, which are assessed with synthetic aperture radar (SAR) images, regional QuikSCAT backscatter maps and wind information from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis dataset. Locally formed thin ice from the Storfjorden polynya was frequently observed in 2003 and 2007 (mean thickness 0.55 and 0.37 m, respectively) because these years were characterized by prevailing northeasterly winds. In contrast, the entire fjord was covered with thick external sea ice in 2006 (mean thickness 2.21 m), when ice from the Barents Sea was driven into the fjord by predominantly southerly winds. The modal thickness of this external ice in 2006 increased from 1.2 m in the northern fjord to 2.4 m in the southern fjord, indicating stronger deformation in the southern part. This dynamically thickened ice was even thicker than multi-year ice advected from the central Arctic Ocean in 2003 (mean thickness 1.83 m). The thermodynamic ice thickness of fast ice as boundary condition is investigated with a one-dimensional sea-ice growth model (1DICE) forced with meteorological data from the weather station at the island of Hopen, southeast of Storfjorden. The model results are in good agreement with the modal thicknesses of fast-ice measurements in all years.