THERMODYNAMIC LAWS OF BILLIARDS-LIKE MICROSCOPIC HEAT CONDUCTION MODELS

In this thesis, we study the mathematical model of one-dimensional microscopic heat conduction of gas particles, applying both both analytical and numerical approaches. The macroscopic law of heat conduction is the renowned Fourier’s law J = −k∇T, where J is the local heat flux density, T(x, t) is the temperature gradient, and k is the thermal conductivity coefficient that characterizes the material’s ability to conduct heat. Though Fouriers’s law has been discovered since 1822, the thorough understanding of its microscopic mechanisms remains challenging [3] (2000). We assume that the microscopic model of heat conduction is a hard ball system. The model consists of hard disks contained in a long and thin tube. A large number of moving disks interact with each other and the external environment through elastic collisions. The dynamics of hard ball systems is a billiard-like system, which is equivalent to billiard systems in the sense of isometry [8] (1982). Billiard systems were firstly studied by Birkhoff [2] (1927), while the more interesting study of chaotic vi billiard was initiated by Sinai [40] (1970). However, most known results of chaotic billiards are for one-particle models. Only some limited rigorous results are available for hard ball systems that consists more than one particles [38] (2003). Meanwhile, the stochastic models of heat conduction have been emerging and has attracted increasing attention because they are more tractable for both rigorous and numerical studies since 1980s such as [15] (1982). This motivates us to numerically investigate (1) the macroscopic thermodynamic properties of the hard ball system and (2) the connection of the billiards-like model to more mathematically tractable stochastic models. The study of this thesis constitutes of three parts as follows. Tube model The first part is the numerical study of a billiards-like microscopic heat conduction model called the tube model, which constitutes of a large number of hard disks undergoing elastic collisions and following Hamiltonian dynamics in a long thin tube on the plane. The left-most and right-most boundaries are thermalized such that a disk collides with a virtual in-coming particle with random velocity immediately when hitting the thermalized boundary. We simulate the microscopic dynamics of this system by an efficient event-driven algorithm and record all the needed microscopic time series data of the dynamics. Several key macroscopic transport properties of this system, including the diffusion coefficient and the thermal conductivity, are numerically investigated. In addition, we numerically verified that particle trajectories resemble Wiener processes. Those transport properties are macroscopic characteristics of the system, and they are statistical quantities of the microscopic dynamics. We find that those transport properties of the tube model largely mimic those of ideal gas. But some differences due to issues like non-zero particle size can also be observed. Localization model Secondly, we discuss the localized version of the tube model, called the locally confined particle system. On one side, it is difficult to study the dynamics when a large number of gas molecules moving and interacting in a tube. vii On the other side, the mean free path of a gas molecule is very short [14](1988), By the above two reasons, naturally we can introduce a model that “localizes” gas molecules into a chain of cells to simplify the dynamics, such that particles cannot leave their own cell, but particles in adjacent cells can collide through a “gate”. This billiard-like microscopic heat conduction model is generalized from the model proposed by Bunimovich et al. [4] (1992). Note that to explore the dynamics of this localized system, we do not connect any heat bath with the chain in this part, then the dynamics is a measure-preserving system with Liouville measure as the invariant measure. For simplicity we consider the case of the chain with two cells. A key feature of the locally confined particle system is that the speed of converging to the steady state is polynomial, if the geometry allows particles hiding from particles in their adjacent cells. This is because if a cell has low total kinetic energy, then those slow particles have to move to the gate area by themselves to have another energy exchange. Stochastic model of heat conduction In the third part, we propose a stochastic energy exchange model [21](2018). As mentioned earlier, the model of hard disk gas captures certain properties of an ideal gas but does not have perfect Fourier’s law. In addition, it is widely acknowledged that conducting a comprehensive theoretical analysis of the multi-body hard disk system is very challenging. To address these limitations, we introduce a stochastic energy exchange model that is more mathematically tractable. The stochastic localized energy exchange model serves as an alternative approach to investigate the dynamics and properties of the gas system in the tube. The deterministic hard disk model exhibits strong chaotic behavior, which heuristically suggests a rapid decay of correlation [6] (2006), Our focus is on finding a Markov process that describes the time evolution of the total energy stored in each cell. We provide both numerical and mathematical justifications for the reduction from the deterministic hard disk model to a stochastic energy exchange model. However, it is viii important to note that this part does not aim to present a fully rigorous mathematical analysis. We study the model with two cells, each of which contains M particles that undergo free motion and elastic collisions. To study the distribution of collision times and the energy transferred during each collision, we utilize Monte Carlo simulation techniques. The configuration of cells is specifically designed to ensure that all cell boundaries are either flat or convex inwards. This geometric arrangement is chosen deliberately to induce chaotic motion for the hard disk system within the cells. First of all, we numerically investigate when and how an energy exchange between two adjacent cells between two adjacent cells should happen. The energy exchange corresponds to a collision between two particles from each cell. Given a fixed energy configuration, we show that the collision times follow an inhomogeneous Poisson process due to the quick correlation decay. The rate of the Poisson process is proportional to the square root of the minimum of energy contained in two adjacent cells. Additional numerical simulation also reveals the rule of an energy exchange. Each cell contributes a proportion of its total energy that satisfies a Beta distribution with parameters 1 and M −1. The contributed energy from adjacent cells are pooled together and randomly distributed back. Applying the novel method proposed in [24](2017), we numerically demonstrate the stochastic energy exchange model preserves the long term dynamics of the hard disk model. More precisely, the rate of correlation decay for both stochastic energy exchange model and the hard disk model is ∼ t −2M. Lastly, we compute the thermal conductivity of the stochastic energy exchange model. We use Monte Carlo simulations to verify that the stochastic energy exchange model has the “normal” thermal conductivity, regardless whether the energy exchange rate gives an exponential or power law rate of correlation decay

Exvivo Experiments of Human Ovarian Cancer Ascites-Derived Exosomes Presented by Dendritic Cells Derived from Umbilical Cord Blood for Immunotherapy Treatment

Objectives Exosomes, a type of membrane vesicles, released from tumor cells have been shown to be capable of transferring tumor antigens to dendritic cells and activating specific cytotoxic T-lymphocytes. Recent work has demonstrated the presence of high numbers of exosomes in malignant effusions. Umbilical cord blood (UCB) is a rich source of hematopoietic stem cells and from which a significant number of dendritic cells can be produced. We hypothesized that the exosomes released from metastatic ovarian carcinoma were able to present tumor specific antigen to dendritic cells derived from unrelated umbilical cord blood, then could stimulate resting T cells to differentiate and induce effective cytotoxicity. Study Design Exosomes were isolated by ultracentrifugation of malignant ascites from ovarian cancer patients (n = 10). Purified exosomes were further characterized by Western blot analyses and immunoelectronic microscopy. Dendritic cells were collected from unrelated umbilical cord blood and cultured in the presence of GM-CSF, IL-4 and TNF-α. Resting T cells were mixed with dentritic cells previously primed with exosomes and the cytotoxicity were measured by MTT method. T cells were activated by DCs presented with exosomes. Results 1) the exosomes isolated from the ascites were membrane vesicles of about 30-90nm in diameter; 2) the exosomes expressed MHC class I molecules, HSP70, HSP90, Her2/Neu, and Mart1; and 3)umbilical cord blood-derived DCs previously exosome-primed stimulated resting T cells to differentiate and produce effective cytotoxicity. Conclusions These results suggested that tumor-specific antigens present on exosomes can be presented by DCs derived from unrelated umbilical cord blood to induce tumor specific cytotoxicity and this may represent as a novel immunotherapy for ovarian cancer

4,4′-Bipyridine–2,2′-(1,2-phenylene­dioxy)diacetic acid–water (1/1/1)

In the title 1:1:1 adduct, C10H8N2·C10H10O6·H2O, the dihedral angle between the rings of the 4,4-bipyridine molecule is 10.981 (8)°. In the crystal, O—H⋯O and O—H⋯N hydrogen bonds link the mol­ecules into a zigzag chain structure

Immunization with a Mixture of HIV Env DNA and VLP Vaccines Augments Induction of CD8 T Cell Responses

The immune response induced by immunization with HIV Env DNA and virus-like particle (VLP) vaccines was investigated. Immunization with the HIV Env DNA vaccine induced a strong CD8 T cell response but relatively weak antibody response against the HIV Env whereas immunization with VLPs induced higher levels of antibody responses but little CD8 T cell response. Interestingly, immunization with a mixture the HIV Env DNA and VLP vaccines induced enhanced CD8 T cell and antibody responses. Further, it was observed that the mixing of DNA and VLP vaccines during immunization is necessary for augmenting induction of CD8 T cell responses and such augmentation of CD8 T cell responses was also observed by mixing the HIV Env DNA vaccine with control VLPs. These results show that immunization with a mixture of DNA and VLP vaccines combines advantages of both vaccine platforms for eliciting high levels of both antibody and CD8 T cell responses

Ebola virus-like particles produced in insect cells exhibit dendritic cell stimulating activity and induce neutralizing antibodies

AbstractRecombinant baculoviruses (rBV) expressing Ebola virus VP40 (rBV-VP40) or GP (rBV-GP) proteins were generated. Infection of Sf9 insect cells by rBV-VP40 led to assembly and budding of filamentous particles from the cell surface as shown by electron microscopy. Ebola virus-like particles (VLPs) were produced by coinfection of Sf9 cells with rBV-VP40 and rBV-GP, and incorporation of Ebola GP into VLPs was demonstrated by SDS-PAGE and Western blot analysis. Recombinant baculovirus infection of insect cells yielded high levels of VLPs, which were shown to stimulate cytokine secretion from human dendritic cells similar to VLPs produced in mammalian cells. The immunogenicity of Ebola VLPs produced in insect cells was evaluated by immunization of mice. Analysis of antibody responses showed that most of the GP-specific antibodies were of the IgG2a subtype, while no significant level of IgG1 subtype antibodies specific for GP was induced, indicating the induction of a Th1-biased immune response. Furthermore, sera from Ebola VLP immunized mice were able to block infection by Ebola GP pseudotyped HIV virus in a single round infection assay, indicating that a neutralizing antibody against the Ebola GP protein was induced. These results show that production of Ebola VLPs in insect cells using recombinant baculoviruses represents a promising approach for vaccine development against Ebola virus infection

HMM-Based Emotional Speech Synthesis Using Average Emotion Model

Abstract. This paper presents a technique for synthesizing emotional speech based on an emotion-independent model which is called “average emotion” model. The average emotion model is trained using a multi-emotion speech da-tabase. Applying a MLLR-based model adaptation method, we can transform the average emotion model to present the target emotion which is not included in the training data. A multi-emotion speech database including four emotions, “neutral”, “happiness”, “sadness”, and “anger”, is used in our experiment. The results of subjective tests show that the average emotion model can effectively synthesize neutral speech and can be adapted to the target emotion model using very limited training data