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京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24737号 / 情博第825号 / 新制||情||138(附属図書館) / 京都大学大学院情報学研究科先端数理科学専攻 / (主査)教授 青柳 富誌生, 教授 田口 智清, 准教授 寺前 順之介 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

A major challenge of developing faster and smaller microelectronic devices is that high flux of heat needs to be removed efficiently to prevent overheating of devices. The conventional way of heat removal using liquid reaches a limit due to low thermal conductivity and limited heat capacity of fluids. Adding solid nanoparticles into fluids has been proposed as a way to enhance thermal conductivity of fluids, but recent results show inconclusive anomalous enhancements in thermal conductivity. A possible way to improve heat transfer is to increase the heat capacity of liquid by adding phase change nanoparticles with large latent heat of fusion into the liquid. Such nanoparticles absorb heat during solid to liquid phase change. However, the colloidal suspension of bare phase change nanoparticles has limited use due to aggregation of molten nanoparticles, irreversible sticking on fluid channels, and dielectric property loss. This dissertation describes a new method to enhance the heat transfer property of a liquid by adding encapsulated phase change nanoparticles (nano-PCMs), which will absorb thermal energy during solid-liquid phase change and release heat during freeze. Specifically, silica encapsulated indium nanoparticles, and polymer encapsulated paraffin (wax) nanoparticles have been prepared using colloidal method, and dispersed into poly-α-olefin (PAO) and water for high temperature and low temperature applications, respectively. The shell, with a higher melting point than the core, can prevent leakage or agglomeration of molten cores, and preserve the dielectric properties of the base fluids. Compared to single phase fluids, heat transfer of nanoparticle-containing fluids have been significantly enhanced due to enhanced heat capacities. The structural integrity of encapsulation allows repeated uses of nanoparticles for many cycles. iv By forming porous semi crystalline silica shells obtained from water glass, supercooling has been greatly reduced due to low energy barrier of heterogeneous nucleation. Encapsulated phase change nanoparticles have also been added into exothermic reaction systems such as catalytic and polymerization reactions to effectively quench local hot spots, prevent thermal runaway, and change product distribution. Specifically, silica-encapsulated indium nanoparticles, and silica encapsulated paraffin (wax) nanoparticles have been used to absorb heat released in catalytic reaction, and to mitigate the gel effect during polymerization, respectively. The reaction rates do not raise significantly owing to thermal buffering using phase change nanoparticles at initial stage of thermal runaway. The effect of thermal buffering depends on latent heats of fusion of nanoparticles, and heat releasing kinetics of catalytic reactions and polymerizations. Micro/nanoparticles of phase change materials will open a new dimension for thermal management of exothermic reactions.

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A recently-proposed modification of the Thurstone-Mosteller method of paired comparisons makes possible the analysis of data involving tied observations. The modification includes the postulating of an angular response law such that the response proportions are scaled with arc sine transforms instead of with normal deviates. In this paper a comparison is made of the arc sine and normal curve scaling procedures in paired comparisons involving ties. This is done by applying both methods to data from to important fields of application. Comparisons are also made on several series of hypothetical data. The criterion of comparison is the goodness of fit between the observations and the expected numbers computed from the solution, as measured by means of a chi-square statistic. Computations of parameter estimates and chi-square statistics are made with the aid of an IBM-650, for which the necessary programs have been written. It is concluded that for data conforming well to the model as proposed, both scaling procedures tend to give results in satisfactory agreement with the observations. There is some evidence that, for the cases considered, the preference, if any, is for the normal curve procedure. / Master of Science

Ph. D.

We study game theoretic ecological models with cyclic competition in the case where the strategies can be mixed or pure. For both projects, reported in [49] and [50], we employ Monte Carlo simulations to study finite systems. In chapter 3 the results of a previously published paper [49] are presented and expanded upon, where we study the extinction time of four cyclically competing species on different lattice structures using Lotka-Volterra dynamics. We find that the extinction time of a well mixed system goes linearly with respect to the system size and that the probability distribution approximately takes the shape of a shifted exponential. However, this is not true for when spatial structure is added to the model. In that case we find that instead the probability distribution takes on a non-trivial shape with two characteristic slopes and that the mean goes as a power law with an exponent greater than one. This is attributed to neutral species pairs, species who do not interact, forming domains and coarsening. In chapter 4 the results of [50] are reported and expanded, where we allow agents to choose cyclically competing strategies out of a distribution. We first study the case of three strategies and find through both simulation and mean field equations that the probability distributions of the agents synchronize and oscillate with time in the limit where the agents probability distributions can be approximated as continuous. However, when we simulate the system on a one-dimensional lattice and the probability distributions are small and discretized, it is found that there is a drastic transition in stability, where the average extinction time of a strategy goes from being a power law with respect to system size to an exponential. This transition can also be observed in space time images with the emergence of tile patterns. We also look into the case of four cyclically competing strategies and find results similar to that of [49], such as the coarsening of neutral domains. However, the transition from power law to exponential for the average extinction time seen for three strategies is not observed, but we do find a transition from one power law to another with a different slope. This work was supported by the United States National Science Foundation through grants DMR-0904999 and DMR-1205309. / Ph. D.

We develop the thermodynamic formalism for a large class of maps of the interval with indifferent fixed points. For such systems the formalism yields one-dimensional systems with many-body infinite range interactions for which the thermodynamics is well defined while the Gibbs states are not. (Piecewise linear systems of this kind yield the soluble, in a sense, Fisher models.) We prove that such systems exhibit phase transitions, the order of which depends on the behavior at the indifferent fixed points. We obtain the critical exponent describing the singularity of the pressure and analyse the decay of correlations of the equilibrium states at all temperatures. Our technique relies on establishing and exploiting a relationship between the transfer operators of the original map and its suitable (expanding) induced version. The technique allows one to also obtain a version of the Bowen-Ruelle formula for the Hausdorff dimension of repellers for maps with indifferent fixed points, and to generalize Fisher results to some non-soluble models. / Ph. D.

The change in the number of phase transitions for perturbations of finite range interactions is studied. A Monte-Carlo simulation was performed for a translation invariant spin 1/2 ferromagnetic model in Z² with fundamental bonds A = {(0,0);(0,1)} B = {(0,0);(2,0)} C = {(0,0);(0,1);(1,1);(1,0)} The model exhibits one phase transition if the coupling constant J(A) is zero, but two phase transitions were found when J(A) is non zero and small enough. The generalization of this situation is provided by a construction, due to J. Slawny, which through a sequence of progressively smaller perturbations yields models with an arbitrary minimum number of phase transitions. However, such construction requires the existence of interactions with one fundamental bond such that for all values of the coupling constants the Gibbs state is unique even when the interaction is perturbed by an arbitrary finite range perturbation of small enough norm. In this work it is proven that such property is exhibited by some translation invariant systems in Z^ν with finite state space at each point. The proof applies to models with real interactions and whose fundamental bonds are all multiple of a single bond which is of prime order and which is obtained as the product—in the group ring structure of the dual space—of one dimensional bonds whose non trivial projections at each lattice site are unique. The proof is based on the Dobrushin-Pecherski criterion concerning the uniqueness of Gibbs states under perturbations. Such criterion is restated so that only transition functions on sets of simple geometry are involved. In addition, an algebraic characterization is presented for the set of Gibbs states for ferromagnetic systems for which the state space at each lattice site is a compact abelian group. This is a generalization of the theory originally introduced by Slawny for spin 1/2 ferromagnetic models and later extended by Pfister to ferromagnetic models for which the state space at each point is a finite product of tori and finite abelian groups. / Ph. D.

A new physical and mathematical model for the epilepsies is proposed, based on the theory of bond percolation on finite lattices. Within this model, the onset of seizures in the brain is identified with the appearance of spanning clusters of neurons engaged in the spurious and uncontrollable electrical activity characteristic of seizures. It is proposed that the fraction of excitatory to inhibitory synapses can be identified with a bond probability, and that the bond probability is a randomly varying quantity displaying Gaussian statistics. The consequences of the proposed model to the treatment of the epilepsies is explored. The nature of the data on the epilepsies which can be acquired in a clinical setting is described. It is shown that such data can be analyzed to provide preliminary support for the bond percolation hypothesis, and to quantify the efficacy of anti-epileptic drugs in a treatment program. The results of a battery of statistical tests on seizure distributions are discussed. The physical theory of the electroencephalogram (EEG) is described, and extant models of the electrical activity measured by the EEG are discussed, with an emphasis on their physical behavior. A proposal is made to explain the difference between the power spectra of electrical activity measured with cranial probes and with the EEG. Statistical tests on the characteristic EEG manifestations of epileptic activity are conducted, and their results described. Computer simulations of a correlated bond percolating system are constructed. It is shown that the statistical properties of the results of such a simulation are strongly suggestive of the statistical properties of clinical data. The study finds no contradictions between the predictions of the bond percolation model and the observed properties of the available data. Suggestions are made for further research and for techniques based on the proposed model which may be used for tuning the effects of anti-epileptic drugs. / Ph. D.