Strain Pattern in Supercooled Liquids
Illing, Bernd; Fritschi, Sebastian; Hajnal, David; Klix, Christian; Keim, Peter; Fuchs, Matthias
2016-11-01
Investigations of strain correlations at the glass transition reveal unexpected phenomena. The shear strain fluctuations show an Eshelby-strain pattern [˜cos (4 θ ) /r2 ], characteristic of elastic response, even in liquids, at long times. We address this using a mode-coupling theory for the strain fluctuations in supercooled liquids and data from both video microscopy of a two-dimensional colloidal glass former and simulations of Brownian hard disks. We show that the long-ranged and long-lived strain signatures follow a scaling law valid close to the glass transition. For large enough viscosities, the Eshelby-strain pattern is visible even on time scales longer than the structural relaxation time τ and after the shear modulus has relaxed to zero.
Polarized View of Supercooled Liquid Water Clouds
Alexandrov, Mikhail D.; Cairns, Brian; Van Diedenhoven, Bastiaan; Ackerman, Andrew S.; Wasilewski, Andrzej P.; McGill, Matthew J.; Yorks, John E.; Hlavka, Dennis L.; Platnick, Steven E.; Arnold, G. Thomas
2016-01-01
Supercooled liquid water (SLW) clouds, where liquid droplets exist at temperatures below 0 C present a well known aviation hazard through aircraft icing, in which SLW accretes on the airframe. SLW clouds are common over the Southern Ocean, and climate-induced changes in their occurrence is thought to constitute a strong cloud feedback on global climate. The two recent NASA field campaigns POlarimeter Definition EXperiment (PODEX, based in Palmdale, California, January-February 2013) and Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS, based in Houston, Texas in August- September 2013) provided a unique opportunity to observe SLW clouds from the high-altitude airborne platform of NASA's ER-2 aircraft. We present an analysis of measurements made by the Research Scanning Polarimeter (RSP) during these experiments accompanied by correlative retrievals from other sensors. The RSP measures both polarized and total reflectance in 9 spectral channels with wavelengths ranging from 410 to 2250 nm. It is a scanning sensor taking samples at 0.8deg intervals within 60deg from nadir in both forward and backward directions. This unique angular resolution allows for characterization of liquid water droplet size using the rainbow structure observed in the polarized reflectances in the scattering angle range between 135deg and 165deg. Simple parametric fitting algorithms applied to the polarized reflectance provide retrievals of the droplet effective radius and variance assuming a prescribed size distribution shape (gamma distribution). In addition to this, we use a non-parametric method, Rainbow Fourier Transform (RFT),which allows retrieval of the droplet size distribution without assuming a size distribution shape. We present an overview of the RSP campaign datasets available from the NASA GISS website, as well as two detailed examples of the retrievals. In these case studies we focus on cloud fields with spatial features
Structure, thermodynamics, and dynamical properties of supercooled liquids
International Nuclear Information System (INIS)
Kambayashi, Shaw
1992-12-01
The equilibrium properties of supercooled liquids with repulsive soft-sphere potentials, u(r) = ε(σ/r) n , have been obtained by solving the integral equation of the theory of liquids and by performing constant-temperature molecular dynamics (MD) simulations. A thermodynamically consistent approximation, proposed recently by Rogers and Young (RY), has been examined for the supercooled soft-sphere fluids. Then, a new approximation for the integral equation, called MHNCS (modified hypernetted-chain integral equation for highly supercooled soft-sphere fluids) approximation, is proposed. The solution of the MHNCS integral equation for highly supercooled liquid states agrees well with the results of computer simulations. The MHNCS integral equation has also been applied for binary soft-sphere mixtures. Dynamical properties of soft-sphere fluids have been investigated by molecular dynamics (MD) simulations. The reduced diffusion constant is found to be insensitive to the choice of the softness of the potential. On the other hand, the spectrum of the velocity autocorrelation function shows a pronounced dependence on the softness of the potential. These significant dynamical properties dependent on the softness parameter (n) are consistent to dynamical behavior observed in liquid alkali metals and liquefied inert gases. The self-part of the density-density autocorrelation function obtained shows a clear nonexponential decay in intermediate time, as the liquid-glass transition is approached. (J.P.N.) 105 refs
Supercooled liquid dynamics for the charged hard-sphere model
International Nuclear Information System (INIS)
Lai, S.K.; Chang, S.Y.
1994-08-01
We study the dynamics of supercooled liquid and the liquid-glass transition by applying the mode coupling theory to the charged hard-sphere model. By exploiting the two independent parameters inherent in the charged hard-sphere system we examine structurally the subtle and competitive role played by the short-range hard-core correlation and the long-range Coulomb tail. It is found in this work that the long-range Coulombic charge factor effect is generally a less effective contribution to structure when the plasma parameter is less than 500 and becomes dominant when it is greater thereof. To extend our understanding of the supercooled liquid and the liquid-glass transition, an attempt is made to calculate and to give physical relevance to the mode-coupling parameters which are frequently used as mere fitting parameters in analysis of experiments on supercooled liquid systems. This latter information enables us to discuss the possible application of the model to a realistic system. (author). 22 refs, 4 figs
Liquid phase and supercooled liquid phase welding of bulk metallic glasses
International Nuclear Information System (INIS)
Kawamura, Y.
2004-01-01
Recent progress on welding in bulk metallic glasses (BMGs) has been reviewed. BMGs have been successfully welded to BMGs or crystalline metals by liquid phase welding using explosion, pulse-current and electron-beam methods, and by supercooled liquid phase welding using friction method. Successful welding of the liquid phase methods was due to the high glass-forming ability of the BMGs and the high concentration of welding energy in these methods. In contrast, the supercooled liquid phase welding was successful due to the thermally stable supercooled liquid state of the BMGs and the superplasticity and viscous flow of the supercooled liquid. The successful welding of BMGs to BMGs and crystalline materials is promising for the future development of BMGs as engineering materials
Mixing effects in the crystallization of supercooled quantum binary liquids
International Nuclear Information System (INIS)
Kühnel, M.; Kalinin, A.; Fernández, J. M.; Tejeda, G.; Moreno, E.; Montero, S.; Tramonto, F.; Galli, D. E.; Nava, M.; Grisenti, R. E.
2015-01-01
By means of Raman spectroscopy of liquid microjets, we have investigated the crystallization process of supercooled quantum liquid mixtures composed of parahydrogen (pH 2 ) or orthodeuterium (oD 2 ) diluted with small amounts of neon. We show that the introduction of the Ne impurities affects the crystallization kinetics in terms of a significant reduction of the measured pH 2 and oD 2 crystal growth rates, similarly to what found in our previous work on supercooled pH 2 -oD 2 liquid mixtures [Kühnel et al., Phys. Rev. B 89, 180201(R) (2014)]. Our experimental results, in combination with path-integral simulations of the supercooled liquid mixtures, suggest in particular a correlation between the measured growth rates and the ratio of the effective particle sizes originating from quantum delocalization effects. We further show that the crystalline structure of the mixtures is also affected to a large extent by the presence of the Ne impurities, which likely initiate the freezing process through the formation of Ne-rich crystallites
Mixing effects in the crystallization of supercooled quantum binary liquids
Energy Technology Data Exchange (ETDEWEB)
Kühnel, M.; Kalinin, A. [Institut für Kernphysik, J. W. Goethe-Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany); Fernández, J. M.; Tejeda, G.; Moreno, E.; Montero, S. [Laboratory of Molecular Fluid Dynamics, Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid (Spain); Tramonto, F.; Galli, D. E. [Laboratorio di Calcolo Parallelo e di Simulazioni di Materia Condensata, Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano (Italy); Nava, M. [Laboratorio di Calcolo Parallelo e di Simulazioni di Materia Condensata, Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, 20133 Milano (Italy); Computational Science, Department of Chemistry and Applied Biosciences, ETH Zurich, USI Campus, Via Giuseppe Buffi 13, CH-6900 Lugano (Switzerland); Grisenti, R. E. [Institut für Kernphysik, J. W. Goethe-Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany); GSI - Helmholtzzentrum für Schwerionenforschung, Planckstr. 1, 64291 Darmstadt (Germany)
2015-08-14
By means of Raman spectroscopy of liquid microjets, we have investigated the crystallization process of supercooled quantum liquid mixtures composed of parahydrogen (pH{sub 2}) or orthodeuterium (oD{sub 2}) diluted with small amounts of neon. We show that the introduction of the Ne impurities affects the crystallization kinetics in terms of a significant reduction of the measured pH{sub 2} and oD{sub 2} crystal growth rates, similarly to what found in our previous work on supercooled pH{sub 2}-oD{sub 2} liquid mixtures [Kühnel et al., Phys. Rev. B 89, 180201(R) (2014)]. Our experimental results, in combination with path-integral simulations of the supercooled liquid mixtures, suggest in particular a correlation between the measured growth rates and the ratio of the effective particle sizes originating from quantum delocalization effects. We further show that the crystalline structure of the mixtures is also affected to a large extent by the presence of the Ne impurities, which likely initiate the freezing process through the formation of Ne-rich crystallites.
Evidence for compact cooperatively rearranging regions in a supercooled liquid
International Nuclear Information System (INIS)
Elenius, M; Dzugutov, M
2009-01-01
We examine structural relaxation in a supercooled glass-forming liquid simulated by constant-energy constant-volume (NVE) molecular dynamics. Time correlations of the total kinetic energy fluctuations are used as a comprehensive measure of the system's approach to the ergodic equilibrium. We find that, under cooling, the total structural relaxation becomes delayed as compared with the decay of the component of the intermediate scattering function corresponding to the main peak of the structure factor. This observation can be explained by collective movements of particles preserving many-body structural correlations within compact three-dimensional (3D) cooperatively rearranging regions.
Tensorial analysis of Eshelby stresses in 3D supercooled liquids
Lemaître, Anaël
2015-10-01
It was recently proposed that the local rearrangements governing relaxation in supercooled liquids impress on the liquid medium long-ranged (Eshelby) stress fluctuations that accumulate over time. From this viewpoint, events must be characterized by elastic dipoles, which are second order tensors, and Eshelby fields are expected to show up in stress and stress increment correlations, which are fourth order tensor fields. We construct here an analytical framework that permits analyzing such tensorial correlations in isotropic media in view of accessing Eshelby fields. Two spherical bases are introduced, which correspond to Cartesian and spherical coordinates for tensors. We show how they can be used to decompose stress correlations and thus test such properties as isotropy and power-law scalings. Eshelby fields and the predicted stress correlations in an infinite medium are shown to belong to an algebra that can conveniently be described using the spherical tensor bases. Using this formalism, we demonstrate that the inherent stress field of 3D supercooled liquids is power law correlated and carries the signature of Eshelby fields, thus supporting the idea that relaxation events give rise to Eshelby stresses that accumulate over time.
Linking density functional and mode coupling models for supercooled liquids
Energy Technology Data Exchange (ETDEWEB)
Premkumar, Leishangthem; Bidhoodi, Neeta; Das, Shankar P. [School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067 (India)
2016-03-28
We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.
Linking density functional and mode coupling models for supercooled liquids.
Premkumar, Leishangthem; Bidhoodi, Neeta; Das, Shankar P
2016-03-28
We compare predictions from two familiar models of the metastable supercooled liquid, respectively, constructed with thermodynamic and dynamic approaches. In the so called density functional theory the free energy F[ρ] of the liquid is a functional of the inhomogeneous density ρ(r). The metastable state is identified as a local minimum of F[ρ]. The sharp density profile characterizing ρ(r) is identified as a single particle oscillator, whose frequency is obtained from the parameters of the optimum density function. On the other hand, a dynamic approach to supercooled liquids is taken in the mode coupling theory (MCT) which predict a sharp ergodicity-non-ergodicity transition at a critical density. The single particle dynamics in the non-ergodic state, treated approximately, represents a propagating mode whose characteristic frequency is computed from the corresponding memory function of the MCT. The mass localization parameters in the above two models (treated in their simplest forms) are obtained, respectively, in terms of the corresponding natural frequencies depicted and are shown to have comparable magnitudes.
Mechanical annealing in the flow of supercooled metallic liquid
International Nuclear Information System (INIS)
Zhang, Meng; Dai, Lan Hong; Liu, Lin
2014-01-01
Flow induced structural evolution in a supercooled metallic liquid Vit106a (Zr 58.5 Cu 15.6 Al 10.3 Ni 12.8 Nb 2.8 , at. %) was investigated via uni-axial compression combined with differential scanning calorimeter (DSC). Compression tests at strain rates covering the transition from Newtonian flow to non-Newtonian flow and at the same strain rate 2 × 10 −1 s −1 to different strains were performed at the end of glass transition (T g-end = 703 K). The relaxation enthalpies measured by DSC indicate that the samples underwent non-Newtonian flow contain more free volume than the thermally annealed sample (703 K, 4 min), while the samples underwent Newtonian flow contain less, namely, the free volume of supercooled metallic liquids increases in non-Newtonian flow, while decreases in Newtonian flow. The oscillated variation of the relaxation enthalpies of the samples deformed at the same strain rate 2 × 10 −1 s −1 to different strains confirms that the decrease of free volume was caused by flow stress, i.e., “mechanical annealing.” Micro-hardness tests were also performed to show a similar structural evolution tendency. Based on the obtained results, the stress-temperature scaling in the glass transition of metallic glasses are supported experimentally, as stress plays a role similar to temperature in the creation and annihilation of free volume. In addition, a widening perspective angle on the glass transition of metallic glasses by exploring the 3-dimensional stress-temperature-enthalpy phase diagram is presented. The implications of the observed mechanical annealing effect on the amorphous structure and the work-hardening mechanism of metallic glasses are elucidated based on atomic level stress model
MARKOV CHAIN PORTFOLIO LIQUIDITY OPTIMIZATION MODEL
Directory of Open Access Journals (Sweden)
Eder Oliveira Abensur
2014-05-01
Full Text Available The international financial crisis of September 2008 and May 2010 showed the importance of liquidity as an attribute to be considered in portfolio decisions. This study proposes an optimization model based on available public data, using Markov chain and Genetic Algorithms concepts as it considers the classic duality of risk versus return and incorporating liquidity costs. The work intends to propose a multi-criterion non-linear optimization model using liquidity based on a Markov chain. The non-linear model was tested using Genetic Algorithms with twenty five Brazilian stocks from 2007 to 2009. The results suggest that this is an innovative development methodology and useful for developing an efficient and realistic financial portfolio, as it considers many attributes such as risk, return and liquidity.
Liquid structure and temperature invariance of sound velocity in supercooled Bi melt
International Nuclear Information System (INIS)
Emuna, M.; Mayo, M.; Makov, G.; Greenberg, Y.; Caspi, E. N.; Yahel, E.; Beuneu, B.
2014-01-01
Structural rearrangement of liquid Bi in the vicinity of the melting point has been proposed due to the unique temperature invariant sound velocity observed above the melting temperature, the low symmetry of Bi in the solid phase and the necessity of overheating to achieve supercooling. The existence of this structural rearrangement is examined by measurements on supercooled Bi. The sound velocity of liquid Bi was measured into the supercooled region to high accuracy and it was found to be invariant over a temperature range of ∼60°, from 35° above the melting point to ∼25° into the supercooled region. The structural origin of this phenomenon was explored by neutron diffraction structural measurements in the supercooled temperature range. These measurements indicate a continuous modification of the short range order in the melt. The structure of the liquid is analyzed within a quasi-crystalline model and is found to evolve continuously, similar to other known liquid pnictide systems. The results are discussed in the context of two competing hypotheses proposed to explain properties of liquid Bi near the melting: (i) liquid bismuth undergoes a structural rearrangement slightly above melting and (ii) liquid Bi exhibits a broad maximum in the sound velocity located incidentally at the melting temperature
Behavior of supercooled aqueous solutions stemming from hidden liquid-liquid transition in water.
Biddle, John W; Holten, Vincent; Anisimov, Mikhail A
2014-08-21
A popular hypothesis that explains the anomalies of supercooled water is the existence of a metastable liquid-liquid transition hidden below the line of homogeneous nucleation. If this transition exists and if it is terminated by a critical point, the addition of a solute should generate a line of liquid-liquid critical points emanating from the critical point of pure metastable water. We have analyzed thermodynamic consequences of this scenario. In particular, we consider the behavior of two systems, H2O-NaCl and H2O-glycerol. We find the behavior of the heat capacity in supercooled aqueous solutions of NaCl, as reported by Archer and Carter [J. Phys. Chem. B 104, 8563 (2000)], to be consistent with the presence of the metastable liquid-liquid transition. We elucidate the non-conserved nature of the order parameter (extent of "reaction" between two alternative structures of water) and the consequences of its coupling with conserved properties (density and concentration). We also show how the shape of the critical line in a solution controls the difference in concentration of the coexisting liquid phases.
Microscopic Theory for the Role of Attractive Forces in the Dynamics of Supercooled Liquids.
Dell, Zachary E; Schweizer, Kenneth S
2015-11-13
We formulate a microscopic, no adjustable parameter, theory of activated relaxation in supercooled liquids directly in terms of the repulsive and attractive forces within the framework of pair correlations. Under isochoric conditions, attractive forces can nonperturbatively modify slow dynamics, but at high enough density their influence vanishes. Under isobaric conditions, attractive forces play a minor role. High temperature apparent Arrhenius behavior and density-temperature scaling are predicted. Our results are consistent with recent isochoric simulations and isobaric experiments on a deeply supercooled molecular liquid. The approach can be generalized to treat colloidal gelation and glass melting, and other soft matter slow dynamics problems.
International Nuclear Information System (INIS)
Saida, Junji; Imafuku, Muneyuki; Sato, Shigeo; Sanada, Takashi; Matsubara, Eiichiro; Inoue, Akihisa
2007-01-01
The correlation between the local structure and stability of supercooled liquid state is investigated in the Zr 70 (Ni, Cu) 30 binary and Zr 70 Al 10 (Ni, Cu) 20 (numbers indicate at.%) ternary metallic glasses. The Zr 70 Ni 30 binary amorphous alloy with a low stability of supercooled liquid state has a tetragonal Zr 2 Ni-like local structure around Ni atom. Meanwhile, the Zr 70 Cu 30 binary metallic glass has a different local structure of tetragonal Zr 2 Cu, where we suggest the icosahedral local structure by the quasicrystallization behavior in addition of a very small amount of noble metals. The effect of Al addition on the local structure in the Zr-Ni alloy is also examined. We have investigated that the dominant local structure changes in the icosahedral-like structure from the tetragonal Zr 2 Ni-like local structure by the Al substitution with Ni accompanying with the significant stabilization of supercooled liquid state. It is concluded that the formation of icosahedral local structure contributes to the enhancement of stability of supercooled liquid state in the Zr-based alloys
A liquid-liquid transition in supercooled aqueous solution related to the HDA-LDA transition
Woutersen, Sander; Ensing, Bernd; Hilbers, Michiel; Zhao, Zuofeng; Angell, C. Austen
2018-03-01
Simulations and theory suggest that the thermodynamic anomalies of water may be related to a phase transition between two supercooled liquid states, but so far this phase transition has not been observed experimentally because of preemptive ice crystallization. We used calorimetry, infrared spectroscopy, and molecular dynamics simulations to investigate a water-rich hydrazinium trifluoroacetate solution in which the local hydrogen bond structure surrounding a water molecule resembles that in neat water at elevated pressure, but which does not crystallize upon cooling. Instead, this solution underwent a sharp, reversible phase transition between two homogeneous liquid states. The hydrogen-bond structures of these two states are similar to those established for high- and low-density amorphous (HDA and LDA) water. Such structural similarity supports theories that predict a similar sharp transition in pure water under pressure if ice crystallization could be suppressed.
Smith, R Scott; Kay, Bruce D
2012-03-15
Experimental measurements of the properties of supercooled liquids at temperatures near their glass transition temperatures, Tg, are requisite for understanding the behavior of glasses and amorphous solids. Unfortunately, many supercooled molecular liquids rapidly crystallize at temperatures far above their Tg, making such measurements difficult to nearly impossible. In this Perspective, we discuss some recent alternative approaches to obtain experimental data in the temperature regime near Tg. These new approaches may yield the additional experimental data necessary to test current theoretical models of the dynamical slowdown that occurs in supercooled liquids approaching the glass transition.
Directory of Open Access Journals (Sweden)
Bo Jakobsen
2016-05-01
Full Text Available We present a simple method for fast and cheap thermal analysis on supercooled glass-forming liquids. This “Thermalization Calorimetry” technique is based on monitoring the temperature and its rate of change during heating or cooling of a sample for which the thermal power input comes from heat conduction through an insulating material, i.e., is proportional to the temperature difference between sample and surroundings. The monitored signal reflects the sample’s specific heat and is sensitive to exo- and endothermic processes. The technique is useful for studying supercooled liquids and their crystallization, e.g., for locating the glass transition and melting point(s, as well as for investigating the stability against crystallization and estimating the relative change in specific heat between the solid and liquid phases at the glass transition.
Energy Technology Data Exchange (ETDEWEB)
Lan, S.; Ma, J. L.; Fan, J. [Department of Physics and Material Science, City University of Hong Kong 83 Tat Chee Ave., Kowloon (Hong Kong); Blodgett, M.; Kelton, K. F. [Department of Physics and Institute of Materials Science and Engineering, Washington University One Brookings Drive, St. Louis, Missouri 63130-4899 (United States); Wang, X.-L., E-mail: xlwang@cityu.edu.hk [Department of Physics and Material Science, City University of Hong Kong 83 Tat Chee Ave., Kowloon (Hong Kong); City University of Hong Kong Shenzhen Research Institute, Shenzhen 518057 (China)
2016-05-23
Time-resolved synchrotron measurements were carried out to capture the structure evolution of an electrostatically levitated metallic-glass-forming liquid during free cooling. The experimental data shows a crossover in the liquid structure at ∼1000 K, about 115 K below the melting temperature and 150 K above the crystallization temperature. The structure change is characterized by a dramatic growth in the extended-range order below the crossover temperature. Molecular dynamics simulations have identified that the growth of the extended-range order was due to an increased correlation between solute atoms. These results provide structural evidence for a liquid-to-liquid-phase-transition in the supercooled metallic liquid.
DEFF Research Database (Denmark)
Jakobsen, Bo; Sanz, Alejandro; Niss, Kristine
2016-01-01
and their crystallization, e.g., for locating the glass transition and melting point(s), as well as for investigating the stability against crystallization and estimating the relative change in specific heat between the solid and liquid phases at the glass transition......We present a simple method for fast and cheap thermal analysis on supercooled glass-forming liquids. This “Thermalization Calorimetry” technique is based on monitoring the temperature and its rate of change during heating or cooling of a sample for which the thermal power input comes from heat...
Predicting How Nanoconfinement Changes the Relaxation Time of a Supercooled Liquid
DEFF Research Database (Denmark)
Ingebrigtsen, Trond; Errington, Jeff; Truskett, Tom
2013-01-01
The properties of nanoconfined fluids can be strikingly different from those of bulk liquids. A basic unanswered question is whether the equilibrium and dynamic consequences of confinement are related to each other in a simple way. We study this question by simulation of a liquid comprising...... asymmetric dumbbell-shaped molecules, which can be deeply supercooled without crystallizing. We find that the dimensionless structural relaxation times—spanning six decades as a function of temperature, density, and degree of confinement—collapse when plotted versus excess entropy. The data also collapse...
Predicting how nanoconfinement changes the relaxation time of a supercooled liquid.
Ingebrigtsen, Trond S; Errington, Jeffrey R; Truskett, Thomas M; Dyre, Jeppe C
2013-12-06
The properties of nanoconfined fluids can be strikingly different from those of bulk liquids. A basic unanswered question is whether the equilibrium and dynamic consequences of confinement are related to each other in a simple way. We study this question by simulation of a liquid comprising asymmetric dumbbell-shaped molecules, which can be deeply supercooled without crystallizing. We find that the dimensionless structural relaxation times-spanning six decades as a function of temperature, density, and degree of confinement-collapse when plotted versus excess entropy. The data also collapse when plotted versus excess isochoric heat capacity, a behavior consistent with the existence of isomorphs in the bulk and confined states.
Density of states of colloidal glasses and supercooled liquids
Ghosh, A.; Mari, R.; Chikkadi, V.; Schall, P.; Kurchan, J.; Bonn, D.
2010-01-01
The glass transition is perhaps the greatest unsolved problem in condensed matter physics: the main question is how to reconcile the liquid-like structure with solid-like mechanical properties. In solids, structure and mechanics are related directly through the vibrational density of states of the
Energy Technology Data Exchange (ETDEWEB)
Zhang, Pei; He, Li [Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI 53706 (United States); Besser, Matthew F. [Materials Science and Engineering, Ames Laboratory, Iowa State University, Ames, IA 50011 (United States); Liu, Ze; Schroers, Jan [Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT 06511 (United States); Kramer, Matthew J. [Materials Science and Engineering, Ames Laboratory, Iowa State University, Ames, IA 50011 (United States); Voyles, Paul M., E-mail: paul.voyles@wisc.edu [Department of Materials Science and Engineering, University of Wisconsin-Madison, Madison, WI 53706 (United States)
2017-07-15
Electron correlation microscopy (ECM) is a way to measure structural relaxation times, τ, of liquids with nanometer-scale spatial resolution using coherent electron scattering equivalent of photon correlation spectroscopy. We have applied ECM with a 3.5 nm diameter probe to Pt{sub 57.5}Cu{sub 14.7}Ni{sub 5.3}P{sub 22.5} amorphous nanorods and Pd{sub 40}Ni{sub 40}P{sub 20} bulk metallic glass (BMG) heated inside the STEM into the supercooled liquid region. These data demonstrate that the ECM technique is limited by the characteristics of the time series, which must be at least 40τ to obtain a well-converged correlation function g{sub 2}(t), and the time per frame, which must be less than 0.1τ to obtain sufficient sampling. A high-speed direct electron camera enables fast acquisition and affords reliable g{sub 2}(t) data even with low signal per frame. - Highlights: • Electron Correlation Microscopy (ECM) technique was applied to measure structural relaxation times of supercooled liquids in metallic glass. • In Pt{sub 57.5}Cu{sub 14.7}Ni{sub 5.3}P{sub 22.5} nanowire, τ and β decreases over the measured supercooled liquid regime. • In Pd{sub 40}Ni{sub 40}P{sub 20} bulk alloy, τ decreases from T{sub g}+28 °C to T{sub g}+48 °C, then increases as the temperature approaches T{sub x}. • ECM experiment requires a length of time series at least 40 times the characteristic relaxation time and a time per diffraction pattern at most 0.1 times the relaxation time.
Behavior of supercooled aqueous solutions stemming from hidden liquid–liquid transition in water
Energy Technology Data Exchange (ETDEWEB)
Biddle, John W.; Holten, Vincent; Anisimov, Mikhail A., E-mail: anisimov@umd.edu [Institute for Physical Science and Technology and Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742 (United States)
2014-08-21
A popular hypothesis that explains the anomalies of supercooled water is the existence of a metastable liquid–liquid transition hidden below the line of homogeneous nucleation. If this transition exists and if it is terminated by a critical point, the addition of a solute should generate a line of liquid–liquid critical points emanating from the critical point of pure metastable water. We have analyzed thermodynamic consequences of this scenario. In particular, we consider the behavior of two systems, H{sub 2}O-NaCl and H{sub 2}O-glycerol. We find the behavior of the heat capacity in supercooled aqueous solutions of NaCl, as reported by Archer and Carter [J. Phys. Chem. B 104, 8563 (2000)], to be consistent with the presence of the metastable liquid–liquid transition. We elucidate the non-conserved nature of the order parameter (extent of “reaction” between two alternative structures of water) and the consequences of its coupling with conserved properties (density and concentration). We also show how the shape of the critical line in a solution controls the difference in concentration of the coexisting liquid phases.
Behavior of supercooled aqueous solutions stemming from hidden liquid–liquid transition in water
International Nuclear Information System (INIS)
Biddle, John W.; Holten, Vincent; Anisimov, Mikhail A.
2014-01-01
A popular hypothesis that explains the anomalies of supercooled water is the existence of a metastable liquid–liquid transition hidden below the line of homogeneous nucleation. If this transition exists and if it is terminated by a critical point, the addition of a solute should generate a line of liquid–liquid critical points emanating from the critical point of pure metastable water. We have analyzed thermodynamic consequences of this scenario. In particular, we consider the behavior of two systems, H 2 O-NaCl and H 2 O-glycerol. We find the behavior of the heat capacity in supercooled aqueous solutions of NaCl, as reported by Archer and Carter [J. Phys. Chem. B 104, 8563 (2000)], to be consistent with the presence of the metastable liquid–liquid transition. We elucidate the non-conserved nature of the order parameter (extent of “reaction” between two alternative structures of water) and the consequences of its coupling with conserved properties (density and concentration). We also show how the shape of the critical line in a solution controls the difference in concentration of the coexisting liquid phases
Orientational ordering as a possible mechanism for viscosity-enhancement of supercooled liquids
International Nuclear Information System (INIS)
Dattagupta, S.
1990-07-01
A supercooled liquid is viewed to have regions of local orientational order which can be picturized in terms of cages that restrict single particle diffusion. The mismatch in the orientation of two locally ordered neighbouring regions causes an internal stress which is added to the stress that appears in the Maxwell model of viscoelasticity. This leads to a ''renormalized'' Maxwell time which is related to the susceptibility associated with the orientational order. Hence, when the latter becomes very large, one obtains a large enhancement of the viscosity. (author). 7 refs
Using Peltier cells to study solid-liquid-vapour transitions and supercooling
International Nuclear Information System (INIS)
Torzo, Giacomo; Soletta, Isabella; Branca, Mario
2007-01-01
We propose an apparatus for teaching experimental thermodynamics in undergraduate introductory courses, using thermoelectric modules and a real-time data acquisition system. The device may be made at low cost, still providing an easy approach to the investigation of liquid-solid and liquid-vapour phase transitions and of metastable states (supercooling). The thermoelectric module (a technological evolution of the thermocouple) is by itself an interesting subject that offers a clear example of both thermo-electric (Seebeck effect) and electro-thermal (Peltier effect) energy transformation. We report here some cooling/heating measurements for several liquids and mixtures, including water, salt/water, ethanol/water and sodium acetate, showing how to evaluate the phenomena of freezing point depression and elevation, and how to evaluate the water latent heat
Correlation between supercooled liquid relaxation and glass poisson’s ratio
DEFF Research Database (Denmark)
Sun, Q.J.; Hu, L.N.; Zhou, C.
2015-01-01
in the ratio r and this relation can be described by the empirical function v = 0.5 − A ∗ exp(−B ∗ r), where A and B are constants. This correlation might imply that glass plasticity is associated with the competition between the α and the slow β relaxations in SLs. The underlying physics of this correlation......We report on a correlation between the supercooled liquid (SL) relaxation and glass Poisson’s ratio (v) by comparing the activation energy ratio (r) of the α and the slow β relaxations and the v values for both metallic and nonmetallic glasses. Poisson’s ratio v generally increases with an increase...... lies in the heredity of the structural heterogeneity from liquid to glass. This work gives insights into both the microscopic mechanism of glass deformation through the SL dynamics and the complex structural evolution during liquid-glass transition....
Elastic properties of Pd40Cu30Ni10P20 bulk glass in supercooled liquid region
DEFF Research Database (Denmark)
Nishiyama, N.; Inoue, A.; Jiang, Jianzhong
2001-01-01
In situ ultrasonic measurements for the Pd40Cu30Ni10P20 bulk glass in three states: Glassy solid, supercooled liquid, and crystalline, have been performed. It is found that velocities of both longitudinal and transverse waves and elastic moduli (shear modulus, bulk modulus, Young's modulus......, and Lame parameter), together with Debye temperature, gradually decrease with increasing temperature through the glass transition temperature as the Poisson's ratio increases. The behavior of the velocity of transverse wave vs. temperature in the supercooled liquid region could be explained by viscosity...
Ding, Jun
Metallic glasses (MGs), discovered five decades ago as a newcomer in the family of glasses, are of current interest because of their unique structures and properties. There are also many fundamental materials science issues that remain unresolved for metallic glasses, as well as their predecessor above glass transition temperature, the supercooled liquids. In particular, it is a major challenge to characterize the local structure and unveil the structure-property relationship for these amorphous materials. This thesis presents a systematic study of the local structure of metallic glasses as well as supercooled liquids via classical and ab initio molecular dynamics simulations. Three typical MG models are chosen as representative candidate, Cu64 Zr36, Pd82Si18 and Mg65Cu 25Y10 systems, while the former is dominant with full icosahedra short-range order and the prism-type short-range order dominate for latter two. Furthermore, we move to unravel the underlying structural signature among several properties in metallic glasses. Firstly, the temperature dependence of specific heat and liquid fragility between Cu-Zr and Mg-Cu-Y (also Pd-Si) in supercooled liquids are quite distinct: gradual versus fast evolution of specific heat and viscosity/relaxation time with undercooling. Their local structural ordering are found to relate with the temperature dependence of specific heat and relaxation time. Then elastic heterogeneity has been studied to correlate with local structure in Cu-Zr MGs. Specifically, this part covers how the degree of elastic deformation correlates with the internal structure at the atomic level, how to quantitatively evaluate the local solidity/liquidity in MGs and how the network of interpenetrating connection of icosahedra determine the corresponding shear modulus. Finally, we have illustrated the structure signature of quasi-localized low-frequency vibrational normal modes, which resides the intriguing vibrational properties in MGs. Specifically, the
International Nuclear Information System (INIS)
Wang Li; Liu Xiangfa; Zhang Yanning; Yang Hua; Chen Ying; Bian Xiufang
2003-01-01
Much more attention has been paid to the microstructure of liquid metal under non-ordinary condition recently. In this Letter, the pair correlation function (PCF), together with internal energy of sheared super-cooled liquid Co as a function of temperature has been calculated by molecular dynamics simulation based upon the embedded atom method (EAM) and analyzed compared to that under normal condition. The finding indicates that there exist three obvious peaks of PCF for liquid Co; while as the shear stress is applied to the liquid, the first and second peaks of PCF become lower, the third peak disappeared. The concentric shell structure representing short-range order of liquid still exists, however, it is weakened by the addition of shear stress, leading to the increases of disordering degree of liquid metal. The curves of energy versus temperature suggest the higher crystalline temperature compared to that under normal condition at the same cooling rate. In addition, the viscosity of super-liquid Co is calculated by non-equilibrium molecular dynamics (NEMD)
Supercooled and glassy water: Metastable liquid(s), amorphous solid(s), and a no-man's land
Handle, Philip H.; Loerting, Thomas; Sciortino, Francesco
2017-12-01
We review the recent research on supercooled and glassy water, focusing on the possible origins of its complex behavior. We stress the central role played by the strong directionality of the water-water interaction and by the competition between local energy, local entropy, and local density. In this context we discuss the phenomenon of polyamorphism (i.e., the existence of more than one disordered solid state), emphasizing both the role of the preparation protocols and the transformation between the different disordered ices. Finally, we present the ongoing debate on the possibility of linking polyamorphism with a liquid-liquid transition that could take place in the no-man's land, the temperature-pressure window in which homogeneous nucleation prevents the investigation of water in its metastable liquid form.
Kinetic details of crystallization in supercooled liquid Pb during the isothermal relaxation
International Nuclear Information System (INIS)
Zhou Lili; Liu Rangsu; Tian Zean; Liu Hairong; Hou Zhaoyang; Peng Ping; Zhu Xuanmin; Liu Quanhui
2012-01-01
The kinetic details of crystallization in supercooled liquid Pb during the isothermal relaxation process have been investigated by molecular dynamics simulations, and the microstructure evolution analyzed by the cluster-type index method (CTIM) and the tracing method. It has been found that, the dynamic features are consistently correlated with the microstructure evolution and the crystallization characteristics in the mean square displacement (MSD) and the non-Gaussian parameter (NGP): the β relaxation regime corresponds to the minor structural rearrangement because of the “cage effect”, and the atoms attempt to escape from the “cages”; the α relaxation regime is related to a more diffusive movement of atoms, and the appearance of the second plateau in MSD and the non-zero plateau in NGP corresponds to the completion of crystallization. In addition, three distinct stages of nucleation, growth of nuclei and coarsening of crystallites in the crystallization process have been clearly revealed.
Vibrating-Wire, Supercooled Liquid Water Content Sensor Calibration and Characterization Progress
King, Michael C.; Bognar, John A.; Guest, Daniel; Bunt, Fred
2016-01-01
NASA conducted a winter 2015 field campaign using weather balloons at the NASA Glenn Research Center to generate a validation database for the NASA Icing Remote Sensing System. The weather balloons carried a specialized, disposable, vibrating-wire sensor to determine supercooled liquid water content aloft. Significant progress has been made to calibrate and characterize these sensors. Calibration testing of the vibrating-wire sensors was carried out in a specially developed, low-speed, icing wind tunnel, and the results were analyzed. The sensor ice accretion behavior was also documented and analyzed. Finally, post-campaign evaluation of the balloon soundings revealed a gradual drift in the sensor data with increasing altitude. This behavior was analyzed and a method to correct for the drift in the data was developed.
Trinh, E. H.
1995-01-01
Non-contact methods have been implemented in conjunction with levitation techniques to carry out the measurement of the macroscopic properties of liquids significantly cooled below their nominal melting point. Free suspension of the sample and remote methods allow the deep excursion into the metastable liquid state and the determination of its thermophysical properties. We used this approach to investigate common substances such as water, o-terphenyl, succinonitrile, as well as higher temperature melts such as molten indium, aluminum and other metals. Although these techniques have thus far involved ultrasonic, electromagnetic, and more recently electrostatic levitation, we restrict our attention to ultrasonic methods in this paper. The resulting magnitude of maximum thermal supercooling achieved have ranged between 10 and 15% of the absolute temperature of the melting point for the materials mentioned above. The physical properties measurement methods have been mostly novel approaches, and the typical accuracy achieved have not yet matched their standard equivalent techniques involving contained samples and invasive probing. They are currently being refined, however, as the levitation techniques become more widespread, and as we gain a better understanding of the physics of levitated liquid samples.
The nucleation process and the roles of structure and density fluctuations in supercooled liquid Fe
International Nuclear Information System (INIS)
Li, Rong; Wu, Yongquan; Xiao, Junjiang
2014-01-01
We observed homogeneous nucleation process of supercooled liquid Fe by molecular dynamics simulations. Using bond-orientational order parameters together with Voronoi polyhedron method, we characterized local structure, calculated the volume of Voronoi polyhedra of atoms and identified the structure and density fluctuations. We monitored the formation of nucleus and analyzed its inner structure. The birth and growth of the pre-nucleus and nucleus are accompanied with aggregating and disaggregating processes in the time scale of femtosecond. Only the initial solid-like clusters (ISLC), ranging from 1 to 7 atoms, pop up directly from liquid. The relation between the logarithm of number of clusters and the cluster size was found to be linear for ISLCs and was observed to be parabolic for all solid-like clusters (SLC) due to aggregating and disaggregating effects. The nucleus and pre-nuclei mainly consist of body centered cubic (BCC) and hexagonal close packed atoms, while the BCC atoms tend to be located at the surface. Medium-range structure fluctuations induce the birth of ISLCs, benefit the aggregation of embryos and remarkably promote the nucleation. But density fluctuations contribute little to nucleation. The lifetime of most icosahedral-like atoms (ICO) is shorter than 0.7 ps. No obvious relationship was found between structure/density fluctuations and the appearance of ICO atoms
Smith, R. Scott; Matthiesen, Jesper; Kay, Bruce D.
2010-03-01
Molecular beam techniques, temperature-programmed desorption (TPD), and reflection absorption infrared spectroscopy (RAIRS) are used to explore the relationship between krypton permeation through and the self-diffusivity of supercooled liquid methanol at temperatures (100-115 K) near the glass transition temperature, Tg (103 K). Layered films, consisting of CH3OH and CD3OH, are deposited on top of a monolayer of Kr on a graphene covered Pt(111) substrate at 25 K. Concurrent Kr TPD and RAIRS spectra are acquired during the heating of the composite film to temperatures above Tg. The CO vibrational stretch is sensitive to the local molecular environment and is used to determine the supercooled liquid diffusivity from the intermixing of the isotopic layers. We find that the Kr permeation and the diffusivity of the supercooled liquid are directly and quantitatively correlated. These results validate the rare-gas permeation technique as a tool for probing the diffusivity of supercooled liquids.
Structural stability of Pd40Cu30Ni10P20 metallic glass in supercooled liquid region
International Nuclear Information System (INIS)
Jiang, J.Z.; Saksl, K.
2004-01-01
Phase separation of bulk and ribbon Pd 40 Cu 30 Ni 10 P 20 glasses, annealed in the supercooled liquid region at ambient pressure and high pressures, has been studied by means of differential scanning calorimetry (DSC) and X-ray diffraction techniques. DSC measurements show only one glass transition event in all annealed samples, indicating that no phase separation occurs in the alloy annealed in the supercooled liquid region. Phase analyses reveal at least six crystalline phases in the crystallized sample: monoclinic, tetragonal Cu 3 Pd-like, rhombohedral, fcc-Ni 2 Pd 2 P, fcc-(Ni, Pd) solid solution, and body-centered tetragonal (bct) Ni 3 P-like phases. Annealing treatments under external pressures in the vicinity of the glass transition temperature neither induce phase separation nor alter the glass transition temperature of the Pd 40 Cu 30 Ni 10 P 20 bulk glass
May, R Alan; Smith, R Scott; Kay, Bruce D
2013-11-21
We investigate the mobility of supercooled liquid toluene, ethylbenzene, and benzene near their respective glass transition temperatures (Tg). The permeation rate of Ar, Kr, and Xe through the supercooled liquid created when initially amorphous overlayers are heated above their glass transition temperature is used to determine the diffusivity. Amorphous benzene crystallizes at temperatures well below its Tg, and as a result, the inert gas underlayer remains trapped until the onset of benzene desorption. In contrast, for toluene and ethylbenzene the onset of inert gas permeation is observed at temperatues near Tg. The inert gas desorption peak temperature as a function of the heating rate and overlayer thickness is used to quantify the diffusivity of supercooled liquid toluene and ethylbenzene from 115 to 135 K. In this temperature range, diffusivities are found to vary across 5 orders of magnitude (∼10(-14) to 10(-9) cm(2)/s). The diffusivity data are compared to viscosity measurements and reveal a breakdown in the Stokes-Einstein relationship at low temperatures. However, the data are well fit by the fractional Stokes-Einstein equation with an exponent of 0.66. Efforts to determine the diffusivity of a mixture of benzene and ethylbenzene are detailed, and the effect of mixing these materials on benzene crystallization is explored using infrared spectroscopy.
Van Hoang, Vo; Teboul, Victor; Odagaki, Takashi
2015-12-24
Via analysis of spatiotemporal arrangements of atoms based on their dynamics in supercooled liquid and glassy states of a 2D monatomic system with a double-well Lennard-Jones-Gauss (LJG) interaction potential, we find a new scenario of dynamical heterogeneity. Atoms with the same or very close mobility have a tendency to aggregate into clusters. The number of atoms with high mobility (and size of their clusters) increases with decreasing temperature passing over a maximum before decreasing down to zero. Position of the peak moves toward a lower temperature if mobility of atoms in clusters is lower together with an enhancement of height of the peak. In contrast, the number of atoms with very low mobility or solidlike atoms (and size of their clusters) has a tendency to increase with decreasing temperature and then it suddenly increases in the vicinity of the glass transition temperature leading to the formation of a glassy state. A sudden increase in the number of strongly correlated solidlike atoms in the vicinity of a glass transition temperature (Tg) may be an origin of a drastical increase in viscosity of the glass-forming systems approaching the glass transition. In fact, we find that the diffusion coefficient decays exponentially with a fraction of solidlike atoms exhibiting a sudden decrease in the vicinity of the glass transition region.
International Nuclear Information System (INIS)
Tanaka, Hajime
2010-01-01
It is widely believed that a liquid state can be characterized by a single order parameter, density, and that a transition from a liquid to solid can be described by density ordering (translational ordering). For example, this type of theory has had great success in describing the phase behaviour of hard spheres. However, there are some features that cannot be captured by such theories. For example, hard spheres crystallize into either hcp or fcc structures, without a tendency of bcc ordering which is expected by the Alexander–McTague theory based on the Landau-type free energy of the density order parameter. We also found hcp-like bond orientational ordering in a metastable supercooled liquid, which promotes nucleation of hcp crystals. Furthermore, theories based on the single order parameter cannot explain water-like thermodynamic and kinetic anomalies of a liquid and liquid–liquid transition in a single-component liquid. Based on these facts, we argue that we need an additional order parameter to describe a liquid state. It is bond orientational order, which is induced by dense packing in hard spheres or by directional bonding in molecular and atomic liquids. Bond orientational order is intrinsically of local nature, unlike translational order which is of global nature. This feature plays a unique role in crystallization and quasicrystal formation. We also reveal that bond orientational ordering is a cause of dynamic heterogeneity near a glass transition and is linked to slow dynamics. In relation to this, we note that, for describing the structuring of a highly disordered liquid, we need a structural signature of low configurational entropy, which is more general than bond orientational order. Finally, the water-like anomaly and liquid–liquid transition can be explained by bond orientational ordering due to hydrogen or covalent bonding and its cooperativity, respectively. So we argue that bond orientational ordering is a key to the physical understanding
Tanaka, Hajime
1997-01-01
Because of the isotropic and disordered nature of liquids, the anisotropy hidden in intermolecular interactions are often neglected. Accordingly, the order parameter describing a simple liquid has so far been believed to be only density. In contrast to this common sense, we propose that two order parameters, namely, density and bond order parameters, are required to describe the phase behavior of liquids since they intrinsically tend to form local bonds. This model gives us clear physical exp...
Heterogeneous nucleation from a supercooled ionic liquid on a carbon surface.
He, Xiaoxia; Shen, Yan; Hung, Francisco R; Santiso, Erik E
2016-12-07
Classical molecular dynamics simulations were used to study the nucleation of the crystal phase of the ionic liquid [dmim + ][Cl - ] from its supercooled liquid phase, both in the bulk and in contact with a graphitic surface of D = 3 nm. By combining the string method in collective variables [Maragliano et al., J. Chem. Phys. 125, 024106 (2006)], with Markovian milestoning with Voronoi tessellations [Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] and order parameters for molecular crystals [Santiso and Trout, J. Chem. Phys. 134, 064109 (2011)], we computed minimum free energy paths, the approximate size of the critical nucleus, the free energy barrier, and the rates involved in these nucleation processes. For homogeneous nucleation, the subcooled liquid phase has to overcome a free energy barrier of ∼85 kcal/mol to form a critical nucleus of size ∼3.6 nm, which then grows into the monoclinic crystal phase. This free energy barrier becomes about 42% smaller (∼49 kcal/mol) when the subcooled liquid phase is in contact with a graphitic disk, and the critical nucleus formed is about 17% smaller (∼3.0 nm) than the one observed for homogeneous nucleation. The crystal formed in the heterogeneous nucleation scenario has a structure that is similar to that of the bulk crystal, with the exception of the layers of ions next to the graphene surface, which have larger local density and the cations lie with their imidazolium rings parallel to the graphitic surface. The critical nucleus forms near the graphene surface separated only by these layers of ions. The heterogeneous nucleation rate (∼4.8 × 10 11 cm -3 s -1 ) is about one order of magnitude faster than the homogeneous rate (∼6.6 × 10 10 cm -3 s -1 ). The computed free energy barriers and nucleation rates are in reasonable agreement with experimental and simulation values obtained for the homogeneous and heterogeneous nucleation of other systems (ice, urea, Lennard-Jones spheres, and oxide
Nature of the anomalies in the supercooled liquid state of the mW model of water
Holten, Vincent; Limmer, David T.; Molinero, Valeria; Anisimov, Mikhail A.
2013-05-01
The thermodynamic properties of the supercooled liquid state of the mW model of water show anomalous behavior. Like in real water, the heat capacity and compressibility sharply increase upon supercooling. One of the possible explanations of these anomalies, the existence of a second (liquid-liquid) critical point, is not supported by simulations for this model. In this work, we reproduce the anomalies of the mW model with two thermodynamic scenarios: one based on a non-ideal "mixture" with two different types of local order of the water molecules, and one based on weak crystallization theory. We show that both descriptions accurately reproduce the model's basic thermodynamic properties. However, the coupling constant required for the power laws implied by weak crystallization theory is too large relative to the regular backgrounds, contradicting assumptions of weak crystallization theory. Fluctuation corrections outside the scope of this work would be necessary to fit the forms predicted by weak crystallization theory. For the two-state approach, the direct computation of the low-density fraction of molecules in the mW model is in agreement with the prediction of the phenomenological equation of state. The non-ideality of the "mixture" of the two states never becomes strong enough to cause liquid-liquid phase separation, also in agreement with simulation results.
Nature of the anomalies in the supercooled liquid state of the mW model of water.
Holten, Vincent; Limmer, David T; Molinero, Valeria; Anisimov, Mikhail A
2013-05-07
The thermodynamic properties of the supercooled liquid state of the mW model of water show anomalous behavior. Like in real water, the heat capacity and compressibility sharply increase upon supercooling. One of the possible explanations of these anomalies, the existence of a second (liquid-liquid) critical point, is not supported by simulations for this model. In this work, we reproduce the anomalies of the mW model with two thermodynamic scenarios: one based on a non-ideal "mixture" with two different types of local order of the water molecules, and one based on weak crystallization theory. We show that both descriptions accurately reproduce the model's basic thermodynamic properties. However, the coupling constant required for the power laws implied by weak crystallization theory is too large relative to the regular backgrounds, contradicting assumptions of weak crystallization theory. Fluctuation corrections outside the scope of this work would be necessary to fit the forms predicted by weak crystallization theory. For the two-state approach, the direct computation of the low-density fraction of molecules in the mW model is in agreement with the prediction of the phenomenological equation of state. The non-ideality of the "mixture" of the two states never becomes strong enough to cause liquid-liquid phase separation, also in agreement with simulation results.
Fe-based bulk metallic glasses with a larger supercooled liquid region and high ductility
Energy Technology Data Exchange (ETDEWEB)
Qiu, K.Q. [School of Materials Science and Engineering, Shenyang University of Technology, Shenyang 110178 (China)], E-mail: kqqiu@yahoo.com.cn; Pang, J.; Ren, Y.L.; Zhang, H.B. [School of Materials Science and Engineering, Shenyang University of Technology, Shenyang 110178 (China); Ma, C.L.; Zhang, T. [School of Materials Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083 (China)
2008-12-20
Bulk metallic glasses (BMGs) with compositions of Fe{sub 61.5-x}Co{sub 3}Mo{sub 14}C{sub 15}B{sub 6}Er{sub 0.5}M{sub x} (x = 2, 3; M = Ni, Nb) were fabricated by copper mold casting using raw industrial materials. The X-ray diffraction (XRD), differential scanning calorimetry (DSC), mechanical tester and scanning electron microscope (SEM) were employed to check the phase constituent, the thermal stability, the mechanical properties and the fracture surfaces of as-cast samples. The results indicate that the BMGs with diameters of 1.5-3 mm were fabricated for the alloys investigated. The largest supercooled liquid region (SLR) up to 76 K was found for Fe{sub 58.5}Co{sub 3}Mo{sub 14}C{sub 15}B{sub 6}Er{sub 0.5}Ni{sub 3} BMG. The BMGs with Ni addition exhibit not only high fracture strengths reaching 3770 MPa for x = 2 and 3980 MPa for x = 3 alloys, respectively, but also apparently plastic strains up to 0.67% and 0.93%, respectively. The fracture surfaces of the Fe{sub 61.5-x}Co{sub 3}Mo{sub 14}C{sub 15}B{sub 6}Er{sub 0.5}Ni{sub x} (x = 2, 3) alloys with plasticity show narrow ridges characteristic of venous patterns combining with tearing flow between the ridges. While the Nb containing alloys show not only a lower SLR below 60 K but also a lower stress below 2400 MPa, as well as almost no plastic strain before fracture.
Energy Technology Data Exchange (ETDEWEB)
Cao, Qi-Long; Huang, Duo-Hui; Yang, Jun-Sheng; Wan, Min-Jie; Wang, Fan-Hou, E-mail: eatonch@gmail.com
2014-10-01
Molecular dynamics simulations were applied to study the dynamic and structural properties of supercooled liquid and glassy iron in the rapid-cooling processes. The mean-square displacement and the non-Gaussian parameter were used to describe the dynamic properties. The evolution of structural properties was investigated using the pair distribution functions and bond-angle distribution functions. Results for dynamic and structural relaxations indicate that the dynamic features are consistently correlated with the structure evolution, and there are three temperature regions as the temperature decreases: (1) at higher temperatures (1500 K, 1300 K, and 1100 K), the system remains in the liquid characteristics during the overall relaxation process. (2) At medial temperatures (1050 K, 900 K, and 700 K), a fast β-relaxation is followed by a much slower α-relaxation. There is a little change in the structural properties in the β-relaxation region, while major configuration rearrangements occurred in the α-relaxation range and the crystallization process was completed at the end of α-relaxation region. (3) At lower temperature (500 K), the system shows glassy characteristics during the overall relaxation process. In addition, the melting temperature, glass transition temperature and diffusion coefficients of supercooled liquid iron are also computed.
Directory of Open Access Journals (Sweden)
Hua Tong
2018-03-01
Full Text Available The dynamics of a supercooled liquid near the glass transition is characterized by two-step relaxation, fast β and slow α relaxations. Because of the apparently disordered nature of glassy structures, there have been long debates over whether the origin of drastic slowing-down of the α relaxation accompanied by heterogeneous dynamics is thermodynamic or dynamic. Furthermore, it has been elusive whether there is any deep connection between fast β and slow α modes. To settle these issues, here we introduce a set of new structural order parameters characterizing sterically favored structures with high local packing capability, and then access structure-dynamics correlation by a novel nonlocal approach. We find that the particle mobility is under control of the static order parameter field. The fast β process is controlled by the instantaneous order parameter field locally, resulting in short-time particle-scale dynamics. Then the mobility field progressively develops with time t, following the initial order parameter field from disorder to more ordered regions. As is well known, the heterogeneity in the mobility field (dynamic heterogeneity is maximized with a characteristic length ξ_{4}, when t reaches the relaxation time τ_{α}. We discover that this mobility pattern can be predicted solely by a spatial coarse graining of the initial order parameter field at t=0 over a length ξ without any dynamical information. Furthermore, we find a relation ξ∼ξ_{4}, indicating that the static length ξ grows coherently with the dynamic one ξ_{4} upon cooling. This further suggests an intrinsic link between τ_{α} and ξ: the growth of the static length ξ is the origin of dynamical slowing-down. These we confirm for the first time in binary glass formers both in two and three spatial dimensions. Thus, a static structure has two intrinsic characteristic lengths, particle size and ξ, which control dynamics in local and nonlocal manners, resulting
Tong, Hua; Tanaka, Hajime
2018-01-01
The dynamics of a supercooled liquid near the glass transition is characterized by two-step relaxation, fast β and slow α relaxations. Because of the apparently disordered nature of glassy structures, there have been long debates over whether the origin of drastic slowing-down of the α relaxation accompanied by heterogeneous dynamics is thermodynamic or dynamic. Furthermore, it has been elusive whether there is any deep connection between fast β and slow α modes. To settle these issues, here we introduce a set of new structural order parameters characterizing sterically favored structures with high local packing capability, and then access structure-dynamics correlation by a novel nonlocal approach. We find that the particle mobility is under control of the static order parameter field. The fast β process is controlled by the instantaneous order parameter field locally, resulting in short-time particle-scale dynamics. Then the mobility field progressively develops with time t , following the initial order parameter field from disorder to more ordered regions. As is well known, the heterogeneity in the mobility field (dynamic heterogeneity) is maximized with a characteristic length ξ4, when t reaches the relaxation time τα. We discover that this mobility pattern can be predicted solely by a spatial coarse graining of the initial order parameter field at t =0 over a length ξ without any dynamical information. Furthermore, we find a relation ξ ˜ξ4, indicating that the static length ξ grows coherently with the dynamic one ξ4 upon cooling. This further suggests an intrinsic link between τα and ξ : the growth of the static length ξ is the origin of dynamical slowing-down. These we confirm for the first time in binary glass formers both in two and three spatial dimensions. Thus, a static structure has two intrinsic characteristic lengths, particle size and ξ , which control dynamics in local and nonlocal manners, resulting in the emergence of the two
Vinš, Václav; Hošek, Jan; Hykl, Jiří; Hrubý, Jan
2015-05-01
New experimental apparatus for measurement of the surface tension of liquids under the metastable supercooled state has been designed and assembled in the study. The measuring technique is similar to the method employed by P.T. Hacker [NACA TN 2510] in 1951. A short liquid thread of the liquid sample was sucked inside a horizontal capillary tube partly placed in a temperature-controlled glass chamber. One end of the capillary tube was connected to a setup with inert gas which allowed for precise tuning of the gas overpressure in order of hundreds of Pa. The open end of the capillary tube was precisely grinded and polished before the measurement in order to assure planarity and perpendicularity of the outer surface. The liquid meniscus at the open end was illuminated by a laser beam and observed by a digital camera. Application of an increasing overpressure of the inert gas at the inner meniscus of the liquid thread caused variation of the outer meniscus such that it gradually changed from concave to flat and subsequently convex shape. The surface tension at the temperature of the inner meniscus could be evaluated from the overpressure corresponding to exactly planar outer meniscus. Detailed description of the new setup together with results of the preliminary tests is provided in the study.
Supercooled smectic nanoparticles
DEFF Research Database (Denmark)
Kuntsche, Judith; Westesen, K; Drechsler, M
2004-01-01
The possibility of preparing nanoparticles in the supercooled thermotropic liquid crystalline state from cholesterol esters with saturated acyl chains as well as the incorporation of model drugs into the dispersions was investigated using cholesteryl myristate (CM) as a model cholesterol ester....
Zhang, Meng; Liu, Lin
2018-06-01
To unravel the true nature of glass transition, broader insights into glass forming have been gained by examining the stress-driven glassy systems, where strong shear thinning, i.e. a reduced viscosity under increasing shear rate, is encountered. It is argued that arbitrarily small stress-driven shear rates would ‘melt’ the glass and erase any memory of its thermal history. In this work, we report a glass transition memorized by the enthalpy-entropy compensation in strongly shear-thinned supercooled metallic liquids, which coincides with the thermal glass transition in both the transition temperature and the activation Gibbs free energy. Our findings provide distinctive insights into both glass forming and shear thinning, and enrich current knowledge on the ubiquitous enthalpy-entropy compensation empirical law in condensed matter physics.
Energy Technology Data Exchange (ETDEWEB)
Singh, Rakesh S.; Debenedetti, Pablo G. [Department of Chemical & Biological Engineering, Princeton University, Princeton, New Jersey 08544 (United States); Biddle, John W.; Anisimov, Mikhail A., E-mail: anisimov@umd.edu [Institute of Physical Science and Technology and Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742 (United States)
2016-04-14
Water shows intriguing thermodynamic and dynamic anomalies in the supercooled liquid state. One possible explanation of the origin of these anomalies lies in the existence of a metastable liquid-liquid phase transition (LLPT) between two (high and low density) forms of water. While the anomalies are observed in experiments on bulk and confined water and by computer simulation studies of different water-like models, the existence of a LLPT in water is still debated. Unambiguous experimental proof of the existence of a LLPT in bulk supercooled water is hampered by fast ice nucleation which is a precursor of the hypothesized LLPT. Moreover, the hypothesized LLPT, being metastable, in principle cannot exist in the thermodynamic limit (infinite size, infinite time). Therefore, computer simulations of water models are crucial for exploring the possibility of the metastable LLPT and the nature of the anomalies. In this work, we present new simulation results in the NVT ensemble for one of the most accurate classical molecular models of water, TIP4P/2005. To describe the computed properties and explore the possibility of a LLPT, we have applied two-structure thermodynamics, viewing water as a non-ideal mixture of two interconvertible local structures (“states”). The results suggest the presence of a liquid-liquid critical point and are consistent with the existence of a LLPT in this model for the simulated length and time scales. We have compared the behavior of TIP4P/2005 with other popular water-like models, namely, mW and ST2, and with real water, all of which are well described by two-state thermodynamics. In view of the current debate involving different studies of TIP4P/2005, we discuss consequences of metastability and finite size in observing the liquid-liquid separation. We also address the relationship between the phenomenological order parameter of two-structure thermodynamics and the microscopic nature of the low-density structure.
International Nuclear Information System (INIS)
Singh, Rakesh S.; Debenedetti, Pablo G.; Biddle, John W.; Anisimov, Mikhail A.
2016-01-01
Water shows intriguing thermodynamic and dynamic anomalies in the supercooled liquid state. One possible explanation of the origin of these anomalies lies in the existence of a metastable liquid-liquid phase transition (LLPT) between two (high and low density) forms of water. While the anomalies are observed in experiments on bulk and confined water and by computer simulation studies of different water-like models, the existence of a LLPT in water is still debated. Unambiguous experimental proof of the existence of a LLPT in bulk supercooled water is hampered by fast ice nucleation which is a precursor of the hypothesized LLPT. Moreover, the hypothesized LLPT, being metastable, in principle cannot exist in the thermodynamic limit (infinite size, infinite time). Therefore, computer simulations of water models are crucial for exploring the possibility of the metastable LLPT and the nature of the anomalies. In this work, we present new simulation results in the NVT ensemble for one of the most accurate classical molecular models of water, TIP4P/2005. To describe the computed properties and explore the possibility of a LLPT, we have applied two-structure thermodynamics, viewing water as a non-ideal mixture of two interconvertible local structures (“states”). The results suggest the presence of a liquid-liquid critical point and are consistent with the existence of a LLPT in this model for the simulated length and time scales. We have compared the behavior of TIP4P/2005 with other popular water-like models, namely, mW and ST2, and with real water, all of which are well described by two-state thermodynamics. In view of the current debate involving different studies of TIP4P/2005, we discuss consequences of metastability and finite size in observing the liquid-liquid separation. We also address the relationship between the phenomenological order parameter of two-structure thermodynamics and the microscopic nature of the low-density structure.
More accurate X-ray scattering data of deeply supercooled bulk liquid water
Energy Technology Data Exchange (ETDEWEB)
Neuefeind, Joerg C [ORNL; Benmore, Chris J [Argonne National Laboratory (ANL); Weber, Richard [Argonne National Laboratory (ANL); Paschek, Dietmar [Rostock University, Rostock, Germany
2011-01-01
Deeply supercooled water droplets held container-less in an acoustic levitator are investigated with high energy X-ray scattering. The temperature dependence X-ray structure function is found to be non-linear. Comparison with two popular computer models reveals that structural changes are predicted too abrupt by the TIP5P model, while the rate of change predicted by TIP4P is in much better agreement with experiment. The abrupt structural changes predicted by the TIP5P model to occur in the temperature range between 260-240K as water approaches the homogeneous nucleation limit are unrealistic. Both models underestimate the distance between neighbouring oxygen atoms and overestimate the sharpness of the OO distance distribution, indicating that the strength of the H-bond is overestimated in these models.
International Nuclear Information System (INIS)
Busch, R.; Johnson, W.L.
1998-01-01
Viscosity and enthalpy relaxation from the amorphous state into the supercooled liquid state was investigated in the bulk metallic glass forming Zr 46.75 Ti 8.25 Cu 7.5 Ni 10 Be 27.5 alloy below the calorimetric glass transition. At different temperatures, the viscosities relax into states that obey the same Vogel endash Fulcher endash Tammann relation as the data obtained at higher temperatures in the supercooled liquid. Enthalpy recovery experiments after relaxation in the same temperature range show that the enthalpy of the material reaches values that also corresponds to the supercooled liquid state. The glass relaxes into a metastable supercooled liquid state, if it is observed on a long time scale. Equilibration is possible far below the calorimetric glass transition and very likely even below the isentropic temperature. copyright 1998 American Institute of Physics
DEFF Research Database (Denmark)
Jiang, Jianzhong; Olsen, J. S.; Gerward, Leif
2000-01-01
The effect of pressure on the crystallization behavior of metallic glass Fe72P11C6Al5B4Ga2 alloy with a wide supercooled liquid region has been investigated by in situ high-pressure and high-temperature x-ray diffraction measurements using synchrotron radiation. In the pressure range from 0 to 2...... mobility and changes of the Gibbs free energy of various phases with pressure. ©2000 American Institute of Physics....
Freed, Karl F
2014-10-14
A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, "The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition" [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.
Energy Technology Data Exchange (ETDEWEB)
Freed, Karl F., E-mail: freed@uchicago.edu [James Franck Institute and Department of Chemistry, University of Chicago, 929 East 57 Street, Chicago, Illinois 60637 (United States)
2014-10-14
A general theory of the long time, low temperature dynamics of glass-forming fluids remains elusive despite the almost 20 years since the famous pronouncement by the Nobel Laureate P. W. Anderson, “The deepest and most interesting unsolved problem in solid state theory is probably the theory of the nature of glass and the glass transition” [Science 267, 1615 (1995)]. While recent work indicates that Adam-Gibbs theory (AGT) provides a framework for computing the structural relaxation time of supercooled fluids and for analyzing the properties of the cooperatively rearranging dynamical strings observed in low temperature molecular dynamics simulations, the heuristic nature of AGT has impeded general acceptance due to the lack of a first principles derivation [G. Adam and J. H. Gibbs, J. Chem. Phys. 43, 139 (1965)]. This deficiency is rectified here by a statistical mechanical derivation of AGT that uses transition state theory and the assumption that the transition state is composed of elementary excitations of a string-like form. The strings are assumed to form in equilibrium with the mobile particles in the fluid. Hence, transition state theory requires the strings to be in mutual equilibrium and thus to have the size distribution of a self-assembling system, in accord with the simulations and analyses of Douglas and co-workers. The average relaxation rate is computed as a grand canonical ensemble average over all string sizes, and use of the previously determined relation between configurational entropy and the average cluster size in several model equilibrium self-associating systems produces the AGT expression in a manner enabling further extensions and more fundamental tests of the assumptions.
International Nuclear Information System (INIS)
Dhawan, A.; Sharma, S.K.; Raetzke, K.; Faupel, F.
2003-01-01
The oxidation behaviour of the bulk amorphous alloy Zr 65 Cu 17.5 Ni 10 Al 7.5 was studied in air at various temperatures in the temperature range 591-732 K using a thermogravimetric analyser (TGA). The oxidation kinetics of the alloy obeys the parabolic rate law showing two different linear regions (in the plots of mass gain versus square root of oxidation time) which are attributed to the amorphous and the supercooled liquid states of the alloy. The value of the activation energy Q for the amorphous state as calculated from the temperature dependence of the rate constants is found to be 1.80±0.1 eV and the corresponding value obtained for the supercooled liquid state is 1.20±0.1 eV. It is suggested that the rate controlling process during oxidation of the amorphous state is the back-diffusion of Ni, and possibly Cu also, while the oxidation in the supercooled liquid state is dominated by the inward diffusion of oxygen. (copyright 2003 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
Comparison of the Supercooled Spin Liquid States in the Pyrochlore Magnets Dy2Ti2O7 and Ho2Ti2O7
Eyal, Anna; Eyvazov, Azar B.; Dusad, Ritika; Munsie, Timothy J. S.; Luke, Graeme M.; Davis, J. C. Séamus
Despite a well-ordered crystal structure and strong magnetic interactions between the Dy or Ho ions, no long-range magnetic order has been detected in the pyrochlore titanates Ho2Ti2O7 and Dy2Ti2O7. The low temperature state in these materials is governed by spin-ice rules. These constrain the Ising like spins in the materials, yet does not result in a global broken symmetry state. To explore the actual magnetic phases, we simultaneously measure the time- and frequency-dependent magnetization dynamics of Dy2Ti2O7 and Ho2Ti2O7 using toroidal, boundary-free magnetization transport techniques. We demonstrate a distinctive behavior of the magnetic susceptibility of both compounds, that is indistinguishable in form from the permittivity of supercooled dipolar liquids. Moreover, we show that the microscopic magnetic relaxation times for both materials increase along a super-Arrhenius trajectory also characteristic of supercooled glass-forming liquids. Both materials therefore exhibit characteristics of a supercooled spin liquid. Strongly-correlated dynamics of loops of spins is suggested as a possible mechanism which could account for these findings. Potential connections to many-body spin localization will also be discussed.
Supercooled dynamics of glass-forming liquids and polymers under hydrostatic pressure
Energy Technology Data Exchange (ETDEWEB)
Roland, C M [Naval Research Laboratory, Chemistry Division, Code 6120, Washington, DC 20375-5342 (United States); Hensel-Bielowka, S [Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40-007 Katowice (Poland); Paluch, M [Institute of Physics, Silesian University, ul. Uniwersytecka 4, 40-007 Katowice (Poland); Casalini, R [Naval Research Laboratory, Chemistry Division, Code 6120, Washington, DC 20375-5342 (United States); Chemistry Department, George Mason University, Fairfax, VA 22030 (United States)
2005-06-01
An intriguing problem in condensed matter physics is understanding the glass transition, in particular the dynamics in the equilibrium liquid close to vitrification. Recent advances have been made by using hydrostatic pressure as an experimental variable. These results are reviewed, with an emphasis in the insight provided into the mechanisms underlying the relaxation properties of glass-forming liquids and polymers.
Haftka, J.J.H.; Parsons, J.R.; Govers, H.A.J.
2006-01-01
A gas chromatographic method using Kovats retention indices has been applied to determine the liquid vapour pressure (P-i), enthalpy of vaporization (Delta H-i) and difference in heat capacity between gas and liquid phase (Delta C-i) for a group of polycyclic aromatic hydrocarbons (PAHs). This group
Using Peltier Cells to Study Solid-Liquid-Vapour Transitions and Supercooling
Torzo, Giacomo; Soletta, Isabella; Branca, Mario
2007-01-01
We propose an apparatus for teaching experimental thermodynamics in undergraduate introductory courses, using thermoelectric modules and a real-time data acquisition system. The device may be made at low cost, still providing an easy approach to the investigation of liquid-solid and liquid-vapour phase transitions and of metastable states…
Energy Technology Data Exchange (ETDEWEB)
Yang, Ke; Fan, Xinhui; Li, Bing; Li, Yanhong; Wang, Xin; Xu, Xuanxuan [Xi' an Technological Univ. (China). School of Material and Chemical Engineering
2017-08-15
In this paper, a systematic study of crystallization kinetics and deformation behavior is presented for (Cu{sub 50}Zr{sub 50}){sub 94}Al{sub 6} bulk metallic glass in the supercooled liquid region. Crystallization results showed that the activation energy for (Cu{sub 50}Zr{sub 50}){sub 94}Al{sub 6} was calculated using the Arrhenius equation in isothermal mode and the Kissinger-Akahira-Sunose method in non-isothermal mode. The activation energy was quite high compared with other bulk metallic glasses. Based on isothermal transformation kinetics described by the Johson-Mehl-Avrami model, the average Avrami exponent of about 3.05 implies a mainly diffusion controlled three-dimensional growth with an increasing nucleation rate during the crystallization. For warm deformation, the results showed that deformation behavior, composed of homogeneous and inhomogeneous deformation, is strongly dependent on strain rate and temperature. The homogeneous deformation transformed from non-Newtonian flow to Newtonian flow with a decrease in strain rate and an increase in temperature. It was found that the crystallization during high temperature deformation is induced by heating. The appropriate working temperature/strain rate combination for the alloy forming, without in-situ crystallization, was deduced by constructing an empirical deformation map. The optimum process condition for (Cu{sub 50}Zr{sub 50}){sub 94}Al{sub 6} can be expressed as T∝733 K and ∝ ε 10{sup -3} s{sup -1}.
Equilibrium and out-of-equilibrium thermodynamics in supercooled liquids and glasses
International Nuclear Information System (INIS)
Mossa, S; Nave, E La; Tartaglia, P; Sciortino, F
2003-01-01
We review the inherent structure thermodynamical formalism and the formulation of an equation of state (EOS) for liquids in equilibrium based on the (volume) derivatives of the statistical properties of the potential energy surface. We also show that, under the hypothesis that during ageing the system explores states associated with equilibrium configurations, it is possible to generalize the proposed EOS to out-of-equilibrium (OOE) conditions. The proposed formulation is based on the introduction of one additional parameter which, in the chosen thermodynamic formalism, can be chosen as the local minimum where the slowly relaxing OOE liquid is trapped
Dynamics of supercooled liquids: excess wings, β peaks, and rotation-translation coupling
International Nuclear Information System (INIS)
Cummins, H Z
2005-01-01
Dielectric susceptibility spectra of liquids cooled towards the liquid-glass transition often exhibit secondary structure in the frequency region between the α peak and the susceptibility minimum, in the form of either an 'excess wing' or a secondary peak-the Johari-Goldstein β peak. Recently, Goetze and Sperl (2004 Phys. Rev. Lett. 92 105701) showed that a simple schematic mode coupling theory model, which incorporates rotation-translation (RT) coupling, successfully describes the nearly logarithmic decay observed in optical Kerr effect data. This model also exhibits both excess wing and β peak features, qualitatively resembling experimental dielectric data. It also predicts that the excess wing slope decreases with decreasing temperature and gradually evolves into a β peak with increasing RT coupling. We therefore suggest that these features and their observed evolution with temperature may be consequences of RT coupling
International Nuclear Information System (INIS)
Sidebottom, D.L.; Green, P.F.; Brow, R.K.
1997-01-01
We compare the dielectric response of ionic glasses and dipolar liquids near the glass transition. Our work is divided into two parts. In the first section we examine ionic glasses and the two prominent approaches to analyzing the dielectric response. The conductivity of ion-conducting glasses displays a power law dispersion σ(ω)∝ω n , where n∼0.67, but frequently the dielectric response is analyzed using the electrical modulus M * (ω)=1/var-epsilon * (ω), where var-epsilon * (ω)=var-epsilon(ω)-iσ(ω)/ω is the complex permittivity. We reexamine two specific examples where the shape of M * (ω) changes in response to changes in (a) temperature and (b) ion concentration, to suggest fundamental changes in ion dynamics are occurring. We show, however, that these changes in the shape of M * (ω) occur in the absence of changes in the scaling properties of σ(ω), for which n remains constant. In the second part, we examine the dielectric relaxation found in dipolar liquids, for which var-epsilon * (ω) likewise exhibits changes in shape on approach to the glass transition. Guided by similarities of M * (ω) in ionic glasses and var-epsilon * (ω) in dipolar liquids, we demonstrate that a recent scaling approach proposed by Dixon and co-workers for var-epsilon * (ω) of dipolar relaxation also appears valid for M * (ω) in the ionic case. While this suggests that the Dixon scaling approach is more universal than previously recognized, we demonstrate how the dielectric response can be scaled in a linear manner using an alternative data representation. copyright 1997 The American Physical Society
Molecular dynamics studies of the dynamics of supercooled Lennard-Jones liquids
International Nuclear Information System (INIS)
De Leeuw, S.W.; Brakkee, M.J.D.
1990-01-01
Results are presented of molecular dynamics experiments, in which the Lennard-Jones liquid is cooled isobarically into the metastable temperature region below the freezing temperature. The variation of the density-density and transverse current correlation functions with temperature is studied. We observed a power-law behaviour for the temperature dependence of dynamical properties (viscosity and coefficienty of self-diffusion) with an exponent in good agreement with prediction of mode coupling theories and recent experimental results. (author). 23 refs, 5 figs
Tarnacka, M; Madejczyk, O; Adrjanowicz, K; Pionteck, J; Kaminska, E; Kamiński, K; Paluch, M
2015-06-14
Pressure-Volume-Temperature (PVT) measurements and broadband dielectric spectroscopy were carried out to investigate molecular dynamics and to test the validity of thermodynamic scaling of two homologous compounds of pharmaceutical activity: itraconazole and ketoconazole in the wide range of thermodynamic conditions. The pressure coefficients of the glass transition temperature (dT(g)/dp) for itraconazole and ketoconazole were determined to be equal to 183 and 228 K/GPa, respectively. However, for itraconazole, the additional transition to the nematic phase was observed and characterized by the pressure coefficient dT(n)/dp = 258 K/GPa. From PVT and dielectric data, we obtained that the liquid-nematic phase transition is governed by the relaxation time since it occurred at constant τ(α) = 10(-5) s. Furthermore, we plotted the obtained relaxation times as a function of T(-1)v(-γ), which has revealed that the validity of thermodynamic scaling with the γ exponent equals to 3.69 ± 0.04 and 3.64 ± 0.03 for itraconazole and ketoconazole, respectively. Further analysis of the scaling parameter in itraconazole revealed that it unexpectedly decreases with increasing relaxation time, which resulted in dramatic change of the shape of the thermodynamic scaling master curve. While in the case of ketoconazole, it remained the same within entire range of data (within experimental uncertainty). We suppose that in case of itraconazole, this peculiar behavior is related to the liquid crystals' properties of itraconazole molecule.
Haftka, Joris J H; Parsons, John R; Govers, Harrie A J
2006-11-24
A gas chromatographic method using Kováts retention indices has been applied to determine the liquid vapour pressure (P(i)), enthalpy of vaporization (DeltaH(i)) and difference in heat capacity between gas and liquid phase (DeltaC(i)) for a group of polycyclic aromatic hydrocarbons (PAHs). This group consists of 19 unsubstituted, methylated and sulphur containing PAHs. Differences in log P(i) of -0.04 to +0.99 log units at 298.15K were observed between experimental values and data from effusion and gas saturation studies. These differences in log P(i) have been fitted with multilinear regression resulting in a compound and temperature dependent correction. Over a temperature range from 273.15 to 423.15K, differences in corrected log P(i) of a training set (-0.07 to +0.03 log units) and a validation set (-0.17 to 0.19 log units) were within calculated error ranges. The corrected vapour pressures also showed a good agreement with other GC determined vapour pressures (average -0.09 log units).
Configurational entropy measurements in extremely supercooled liquids that break the glass ceiling
Berthier, Ludovic; Charbonneau, Patrick; Coslovich, Daniele; Ninarello, Andrea; Ozawa, Misaki; Yaida, Sho
2017-10-01
Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, because of the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally relevant timescales. In this work, we not only close the colossal gap between experiments and simulations but manage to create in silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four estimates of their configurational entropy. These measurements consistently confirm that the steep entropy decrease observed in experiments is also found in simulations, even beyond the experimental glass transition. Our numerical results thus extend the observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.
Breaking the glass ceiling: Configurational entropy measurements in extremely supercooled liquids
Berthier, Ludovic
Liquids relax extremely slowly on approaching the glass state. One explanation is that an entropy crisis, due to the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this scenario is challenging, because experiments offer limited resolution, while numerical studies lag more than eight orders of magnitude behind experimentally-relevant timescales. In this work we not only close the colossal gap between experiments and simulations but manage to create in-silico configurations that have no experimental analog yet. Deploying a range of computational tools, we obtain four independent estimates of their configurational entropy. These measurements consistently indicate that the steep entropy decrease observed in experiments is found in simulations even beyond the experimental glass transition. Our numerical results thus open a new observational window into the physics of glasses and reinforce the relevance of an entropy crisis for understanding their formation.
Energy Technology Data Exchange (ETDEWEB)
Tarnacka, M., E-mail: mtarnacka@us.edu.pl; Madejczyk, O.; Kamiński, K.; Paluch, M. [Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice (Poland); Silesian Center of Education and Interdisciplinary Research, University of Silesia, ul. 75 Pulku Piechoty 1A, 41-500 Chorzow (Poland); Adrjanowicz, K. [NanoBioMedical Centre, ul. Umultowska 85, 61-614 Poznan (Poland); Pionteck, J. [Leibniz Institute of Polymer Research Dresden, Hohe Strasse 6, D-01069 Dresden (Germany); Kaminska, E. [Department of Pharmacognosy and Phytochemistry, School of Pharmacy and Division of Laboratory Medicine in Sosnowiec, Medical University of Silesia, ul. Jagiellonska 4, 41-200 Sosnowiec (Poland)
2015-06-14
Pressure-Volume-Temperature (PVT) measurements and broadband dielectric spectroscopy were carried out to investigate molecular dynamics and to test the validity of thermodynamic scaling of two homologous compounds of pharmaceutical activity: itraconazole and ketoconazole in the wide range of thermodynamic conditions. The pressure coefficients of the glass transition temperature (dT{sub g}/dp) for itraconazole and ketoconazole were determined to be equal to 183 and 228 K/GPa, respectively. However, for itraconazole, the additional transition to the nematic phase was observed and characterized by the pressure coefficient dT{sub n}/dp = 258 K/GPa. From PVT and dielectric data, we obtained that the liquid-nematic phase transition is governed by the relaxation time since it occurred at constant τ {sub α} = 10{sup −5} s. Furthermore, we plotted the obtained relaxation times as a function of T{sup −1}v{sup −γ}, which has revealed that the validity of thermodynamic scaling with the γ exponent equals to 3.69 ± 0.04 and 3.64 ± 0.03 for itraconazole and ketoconazole, respectively. Further analysis of the scaling parameter in itraconazole revealed that it unexpectedly decreases with increasing relaxation time, which resulted in dramatic change of the shape of the thermodynamic scaling master curve. While in the case of ketoconazole, it remained the same within entire range of data (within experimental uncertainty). We suppose that in case of itraconazole, this peculiar behavior is related to the liquid crystals’ properties of itraconazole molecule.
Thermal conductivity of supercooled water.
Biddle, John W; Holten, Vincent; Sengers, Jan V; Anisimov, Mikhail A
2013-04-01
The heat capacity of supercooled water, measured down to -37°C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i.e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothesized liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum when temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.
Tournier, Robert F.
2018-01-01
Glass-to-glass and liquid-to-liquid phase transitions are observed in bulk and confined water, with or without applied pressure. They result from the competition of two liquid phases separated by an enthalpy difference depending on temperature. The classical nucleation equation of these phases is completed by this quantity existing at all temperatures, a pressure contribution, and an enthalpy excess. This equation leads to two homogeneous nucleation temperatures in each liquid phase; the first one (Tn- below Tm) being the formation temperature of an "ordered" liquid phase and the second one corresponding to the overheating temperature (Tn+ above Tm). Thermodynamic properties, double glass transition temperatures, sharp enthalpy and volume changes are predicted in agreement with experimental results. The first-order transition line at TLL = 0.833 × Tm between fragile and strong liquids joins two critical points. Glass phase above Tg becomes "ordered" liquid phase disappearing at TLL at low pressure and at Tn+ = 1.302 × Tm at high pressure.
An energy landscape based approach for studying supercooled liquid and glassy thin films
Shah, Pooja; Mittal, Jeetain; Truskett, Thomas M.
2004-03-01
Materials in confined spaces are important in science and technology. Examples include biological fluids in membranes, liquids trapped in porous rocks, and thin-film materials used in high-resolution patterning technologies. However, few reliable rules exist to predict how the properties of materials will be affected by thin-film confinement. We have recently shown that the potential energy landscape formalism can be used to study, by both theory [1] and simulation [2], how the behavior of thin-film materials depends on sample dimensions and film-substrate interactions. Our landscape-based mean-field theory [1] can be used to study both the thermodynamic properties and the ideal glass transition of thin films. It predicts that, in the case of neutral or repulsive walls, the ideal glass transition temperature is lowered by decreasing film thickness. This is in qualitative agreement with experimental trends for the kinetic glass transition in confined fluids. Landscape-based approaches are also valuable for understanding the structural and mechanical properties of thin-film glasses. We demonstrate how the concept of an "equation of state of the energy landscape" [3] can be generalized to thin films [1, 2], where it gives insights into potential molecular mechanisms of tensile strength. [1] T. M. Truskett and V. Ganesan, J. Chem. Phys. 119, 1897-1900(2003); J. Mittal, P. Shah and T. M. Truskett, to be submitted to Langmuir. [2] P. Shah and T. M. Truskett, to be submitted to J. Phys. Chem. B. [3] S. Sastry, P. G. Debenedetti and F. H. Stillinger, Phys. Rev. E 56, 5533 (1997)
King, Michael C.
2016-01-01
The National Aeronautics and Space Administration (NASA) has developed a system for remotely detecting the hazardous conditions leading to aircraft icing in flight, the NASA Icing Remote Sensing System (NIRSS). Newly developed, weather balloon-borne instruments have been used to obtain in-situ measurements of supercooled liquid water during March 2014 to validate the algorithms used in the NIRSS. A mathematical model and a processing method were developed to analyze the data obtained from the weather balloon soundings. The data from soundings obtained in March 2014 were analyzed and compared to the output from the NIRSS and pilot reports.
International Nuclear Information System (INIS)
Kotkata, M.F.; Mahmoud, E.A.; El-Mously, M.K.
1979-07-01
Curves of reaction rate versus temperature for constant heating rates (phi=1-10 0 C/min) constructed by analytical methods have been used to demonstrate the crystallization kinetics of amorphous solid TeSe 20 . The devitrification process takes place with predominance of random nucleation and one-dimensional growth, and is limited by combined switching and splitting of the chemical bonds. The mean value for the activation energy of the amorphous-crystal transformation, average E, is found to be 64 Kcal/mole. While, the quantity E calculated on the basis of d.c. conductivity changes during different isothermal crystallization (120-175 0 C) in supercooled liquid TeSe 20 , amounts to 11.5 Kcal/mole and suggests the existence of mixed chains in the liquid alloys. (author)
Kalampounias, Angelos G.; Papatheodorou, George N.
2018-06-01
Temperature dependent Raman spectra of boric oxide have been measured in a temperature range covering the glassy, supercooled and liquid state. The shift of the isotropic band assigned to boroxol rings relative to the anisotropic component upon heating the glass is measured and attributed to the Raman non-coincidence effect. The measured shift is associated with the competition between attraction and repulsion forces with increasing temperature. The relation of dephasing and orientational relaxation times to the non-coincidence effect of the condensed phases has been examined. We discuss our results in the framework of the current phenomenological status of the field in an attempt to separate the attraction and repulsion contributions corresponding to the observed non-coincidence effect.
Energy Technology Data Exchange (ETDEWEB)
Shi, L.; Skinner, J. L. [Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 (United States)
2015-07-07
OH-stretch inelastic incoherent neutron scattering (IINS) has been measured to determine the vibrational density of states (VDOS) in the OH-stretch region for liquid water, supercooled water, and ice Ih, providing complementary information to IR and Raman spectroscopies about hydrogen bonding in these phases. In this work, we extend the combined electronic-structure/molecular-dynamics (ES/MD) method, originally developed by Skinner and co-workers to simulate OH-stretch IR and Raman spectra, to the calculation of IINS spectra with small k values. The agreement between theory and experiment in the limit k → 0 is reasonable, further validating the reliability of the ES/MD method in simulating OH-stretch spectroscopy in condensed phases. The connections and differences between IINS and IR spectra are analyzed to illustrate the advantages of IINS over IR in estimating the OH-stretch VDOS.
International Nuclear Information System (INIS)
Shi, L.; Skinner, J. L.
2015-01-01
OH-stretch inelastic incoherent neutron scattering (IINS) has been measured to determine the vibrational density of states (VDOS) in the OH-stretch region for liquid water, supercooled water, and ice Ih, providing complementary information to IR and Raman spectroscopies about hydrogen bonding in these phases. In this work, we extend the combined electronic-structure/molecular-dynamics (ES/MD) method, originally developed by Skinner and co-workers to simulate OH-stretch IR and Raman spectra, to the calculation of IINS spectra with small k values. The agreement between theory and experiment in the limit k → 0 is reasonable, further validating the reliability of the ES/MD method in simulating OH-stretch spectroscopy in condensed phases. The connections and differences between IINS and IR spectra are analyzed to illustrate the advantages of IINS over IR in estimating the OH-stretch VDOS
International Nuclear Information System (INIS)
Bhattacharya, Deepanjan; Sadtchenko, Vlad
2015-01-01
Vapor deposition of molecules on a substrate often results in glassy materials of high kinetic stability and low enthalpy. The extraordinary properties of such glasses are attributed to high rates of surface diffusion during sample deposition, which makes it possible for constituents to find a configuration of much lower energy on a typical laboratory time scale. However, the exact nature of the resulting phase and the mechanism of its formation are not completely understood. Using fast scanning calorimetry technique, we show that out-of-equilibrium relaxation kinetics and possibly the enthalpy of vapor-deposited films of toluene and ethylbenzene, archetypical fragile glass formers, are distinct from those of ordinary supercooled phase even when the deposition takes place at temperatures above the ordinary glass softening transition temperatures. These observations along with the absolute enthalpy dependences on deposition temperatures support the conjecture that the vapor-deposition may result in formation of non-crystalline phase of unique structural, thermodynamic, and kinetic properties
Energy Technology Data Exchange (ETDEWEB)
Ni, Yicun; Skinner, J. L. [Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 (United States)
2016-06-07
Supercooled water exhibits many thermodynamic anomalies, and several scenarios have been proposed to interpret them, among which the liquid-liquid critical point (LLCP) hypothesis is the most commonly discussed. We investigated Widom lines and the LLCP of deeply supercooled water, by using molecular dynamics simulation with a newly reparameterized water model that explicitly includes three-body interactions. Seven isobars are studied from ambient pressure to 2.5 kbar, and Widom lines are identified by calculating maxima in the coefficient of thermal expansion and the isothermal compressibility (both with respect to temperature). From these data we estimate that the LLCP of the new water model is at 180 K and 2.1 kbar. The oxygen radial distribution function is calculated along the 2 kbar isobar. It shows a steep change in the height of its second peak between 180 and 185 K, which indicates a transition between the high-density liquid and low-density liquid phases and which is consistent with the ascribed location of the critical point. The good agreement of the height of the second peak of the radial distribution function between simulation and experiment at 1 bar, as a function of temperature, supports the validity of the model. The location of the LLCP within the model is close to the kink in the experimental homogeneous nucleation line. We use existing experimental data to argue that the experimental LLCP is at 168 K and 1.95 kbar and speculate how this LLCP and its Widom line might be responsible for the kink in the homogeneous nucleation line.
International Nuclear Information System (INIS)
Wang Zunyao; Zeng Xiaolan; Zhai Zhicai
2008-01-01
The molecular geometries of 209 polybrominated diphenyl ethers (PBDEs) were optimized at the B3LYP/6-31G* level with Gaussian 98 program. The calculated structural parameters were taken as theoretical descriptors to establish two novel QSPR models for predicting supercooled liquid vapor pressures (P L ) and octanol/air partition coefficients (K OA ) of PBDEs based on the theoretical linear solvation energy relationship (TLSER) model, respectively. The two models achieved in this work both contain three variables: most negative atomic partial charge in molecule (q - ), dipole moment of the molecules (μ) and mean molecular polarizability (α), of which R 2 values are both as high as 0.997, their root-mean-square errors in modeling (RSMEE) are 0.069 and 0.062 respectively. In addition, the F-value of two models are both evidently larger than critical values F 0.05 and the variation inflation factors (VIF) of variables herein are all less than 5.0, suggesting obvious statistic significance of the P L and K OA predicting models. The results of Leave-One-Out (LOO) cross-validation for training set and validation with external test set both show that the two models obtained exhibited optimum stability and good predictive power. We suggest that the QSPRs derived here can be used to predict accurately P L and K OA for non-tested PBDE congeners from Mono-BDEs to Hepta-BDEs and from Mono-BDEs to Hexa-BDEs, respectively
Adrjanowicz, K; Zakowiecki, D; Kaminski, K; Hawelek, L; Grzybowska, K; Tarnacka, M; Paluch, M; Cal, K
2012-06-04
Antibiotics are chemical compounds of extremely important medical role. Their history can be traced back more than one hundred years. Despite the passing time and significant progress made in pharmacy and medicine, treatment of many bacterial infections without antibiotics would be completely impossible. This makes them particularly unique substances and explains the unflagging popularity of antibiotics within the medical community. Herein, using dielectric spectroscopy we have studied the molecular mobility in the supercooled liquid and glassy states of three well-known antibiotic agents: azithromycin, clarithromycin and roxithromycin. Dielectric studies revealed a number of relaxation processes of different molecular origin. Besides the primary α-relaxation, observed above the respective glass transition temperatures of antibiotics, two secondary relaxations in the glassy state were identified. Interestingly, the fragility index as well as activation energies of the secondary processes turned out to be practically the same for all three compounds, indicating probably much the same molecular dynamics. Long-term stability of amorphous antibiotics at room temperature was confirmed by X-ray diffraction technique, and calorimetric studies were performed to evaluate the basic thermodynamic parameters. Finally, we have also checked the experimental solubility advantages given by the amorphous form of the examined antibiotics.
Vikas; Chayawan
2014-01-01
For predicting physico-chemical properties related to environmental fate of molecules, quantitative structure-property relationships (QSPRs) are valuable tools in environmental chemistry. For developing a QSPR, molecular descriptors computed through quantum-mechanical methods are generally employed. The accuracy of a quantum-mechanical method, however, rests on the amount of electron-correlation estimated by the method. In this work, single-descriptor QSPRs for supercooled liquid vapor pressure of chloronaphthalenes and polychlorinated-naphthalenes are developed using molecular descriptors based on the electron-correlation contribution of the quantum-mechanical descriptor. The quantum-mechanical descriptors for which the electron-correlation contribution is analyzed include total-energy, mean polarizability, dipole moment, frontier orbital (HOMO/LUMO) energy, and density-functional theory (DFT) based descriptors, namely, absolute electronegativity, chemical hardness, and electrophilicity index. A total of 40 single-descriptor QSPRs were developed using molecular descriptors computed with advanced semi-empirical (SE) methods, namely, RM1, PM7, and ab intio methods, namely, Hartree-Fock and DFT. The developed QSPRs are validated using state-of-the-art external validation procedures employing an external prediction set. From the comparison of external predictivity of the models, it is observed that the single-descriptor QSPRs developed using total energy and correlation energy are found to be far more robust and predictive than those developed using commonly employed descriptors such as HOMO/LUMO energy and dipole moment. The work proposes that if real external predictivity of a QSPR model is desired to be explored, particularly, in terms of intra-molecular interactions, correlation-energy serves as a more appropriate descriptor than the polarizability. However, for developing QSPRs, computationally inexpensive advanced SE methods such as PM7 can be more reliable than
Levashov, Valentin A.; Morris, James R.; Egami, Takeshi
2012-02-01
Temporal and spatial correlations among the local atomic level shear stresses were studied for a model liquid iron by molecular dynamics simulation [PRL 106,115703]. Integration over time and space of the shear stress correlation function F(r,t) yields viscosity via Green-Kubo relation. The stress correlation function in time and space F(r,t) was Fourier transformed to study the dependence on frequency, E, and wave vector, Q. The results, F(Q,E), showed damped shear stress waves propagating in the liquid for small Q at high and low temperatures. We also observed additional diffuse feature that appears as temperature is reduced below crossover temperature of potential energy landscape at relatively low frequencies at small Q. We suggest that this additional feature might be related to dynamic heterogeneity and boson peaks. We also discuss a relation between the time-scale of the stress-stress correlation function and the alpha-relaxation time of the intermediate self-scattering function S(Q,E).
Meier, G.; Gapinski, J.; Ratajczyk, M.; Lettinga, M. P.; Hirtz, K.; Banachowicz, E.; Patkowski, A.
2018-03-01
The Stokes-Einstein relation allows us to calculate apparent viscosity experienced by tracers in complex media on the basis of measured self-diffusion coefficients. Such defined nano-viscosity values can be obtained through single particle techniques, like fluorescence correlation spectroscopy (FCS) and particle tracking (PT). In order to perform such measurements, as functions of pressure and temperature, a new sample cell was designed and is described in this work. We show that this cell in combination with a long working distance objective of the confocal microscope can be used for successful FCS, PT, and confocal imaging experiments in broad pressure (0.1-100 MPa) and temperature ranges. The temperature and pressure dependent nano-viscosity of a van der Waals liquid obtained from the translational diffusion coefficient measured in this cell by means of FCS obeys the same scaling as the rotational relaxation and macro-viscosity of the system.
Sigurbjörnsson, Omar F; Signorell, Ruth
2008-11-07
Recent evidence for ethane clouds and condensation in Titan's atmosphere raise the question whether liquid ethane condensation nuclei and supercooled liquid ethane droplets exist under the prevalent conditions. We present laboratory studies on the phase behaviour of pure ethane aerosols and ethane aerosols formed in the presence of other ice nuclei under conditions relevant to Titan's atmosphere. Combining bath gas cooling with infrared spectroscopy, we find evidence for the existence of supercooled liquid ethane aerosol droplets. The observed homogeneous freezing rates imply that supercooled ethane could be a long-lived species in ethane-rich regions of Titan's atmosphere similar to supercooled water in the Earth's atmosphere.
The Widom line of supercooled water
International Nuclear Information System (INIS)
Franzese, Giancarlo; Stanley, H Eugene
2007-01-01
Water can be supercooled to temperatures as low as -92 deg. C, the experimental crystal homogeneous nucleation temperature T H at 2 kbar. Within the supercooled liquid phase its response functions show an anomalous increase consistent with the presence of a liquid-liquid critical point located in a region inaccessible to experiments on bulk water. Recent experiments on the dynamics of confined water show that a possible way to understand the properties of water is to investigate the supercooled phase diagram in the vicinity of the Widom line (locus of maximum correlation length) that emanates from the hypothesized liquid-liquid critical point. Here we explore the Widom line for a Hamiltonian model of water using an analytic approach, and discuss the plausibility of the hypothesized liquid-liquid critical point, as well as its possible consequences, on the basis of the assumptions of the model. The present analysis allows us (i) to find an analytic expression for the spinodal line of the high-density liquid phase, with respect to the low-density liquid phase, showing that this line becomes flat in the P-T phase diagram in the physical limit of a large number of available orientations for the hydrogen bonds, as recently seen in simulations and experiments (Xu et al 2005 Proc. Natl Acad. Sci. 102 16558); (ii) to find an estimate of the values for the hypothesized liquid-liquid critical point coordinates that compare very well with Monte Carlo results; and (iii) to show how the Widom line can be located by studying the derivative of the probability of forming hydrogen bonds with local tetrahedral orientation which can be calculated analytically within this approach
Mechanism of supercooled droplet freezing on surfaces.
Jung, Stefan; Tiwari, Manish K; Doan, N Vuong; Poulikakos, Dimos
2012-01-10
Understanding ice formation from supercooled water on surfaces is a problem of fundamental importance and general utility. Superhydrophobic surfaces promise to have remarkable 'icephobicity' and low ice adhesion. Here we show that their icephobicity can be rendered ineffective by simple changes in environmental conditions. Through experiments, nucleation theory and heat transfer physics, we establish that humidity and/or the flow of a surrounding gas can fundamentally switch the ice crystallization mechanism, drastically affecting surface icephobicity. Evaporative cooling of the supercooled liquid can engender ice crystallization by homogeneous nucleation at the droplet-free surface as opposed to the expected heterogeneous nucleation at the substrate. The related interplay between droplet roll-off and rapid crystallization is also studied. Overall, we bring a novel perspective to icing and icephobicity, unveiling the strong influence of environmental conditions in addition to the accepted effects of the surface conditions and hydrophobicity.
Time scales of supercooled water and implications for reversible polyamorphism
Limmer, David T.; Chandler, David
2015-09-01
Deeply supercooled water exhibits complex dynamics with large density fluctuations, ice coarsening and characteristic time scales extending from picoseconds to milliseconds. Here, we discuss implications of these time scales as they pertain to two-phase coexistence and to molecular simulations of supercooled water. Specifically, we argue that it is possible to discount liquid-liquid criticality because the time scales imply that correlation lengths for such behaviour would be bounded by no more than a few nanometres. Similarly, it is possible to discount two-liquid coexistence because the time scales imply a bounded interfacial free energy that cannot grow in proportion to a macroscopic surface area. From time scales alone, therefore, we see that coexisting domains of differing density in supercooled water can be no more than nanoscale transient fluctuations.
Transport properties of supercooled confined water
International Nuclear Information System (INIS)
Mallamace, F.; Baglioni, P.; Corsaro, C.; Spooren, J.; Stanley, H.E.; Chen, S.-H.
2011-01-01
We present an overview of recent experiments performed on water in the deeply supercooled region, a temperature region of fundamental importance in the science of water. We examine data generated by nuclear magnetic resonance, quasi-elastic neutron scattering, Fourier-transform infrared spectroscopy, and Raman spectroscopy, and study water confined in nanometer-scale environments. When contained within small pores, water does not crystallize and can be supercooled well below its homogeneous nucleation temperature T H. On this basis, it is possible to carry out a careful analysis of the well-known thermodynamic anomalies of water. Studying the temperature and pressure dependencies of water dynamics, we show that the liquid-liquid phase transition (LLPT) hypothesis represents a reliable model for describing liquid water. In this model, liquid water is a mixture of two different local structures: a low density liquid (LDL) and a high-density liquid (HDL). The LLPT line terminates at a low-T liquid-liquid critical point. We discuss the following experimental findings: 1.) the crossover from non-Arrhenius behavior at high T to Arrhenius behavior at low T in transport parameters; 2.) the breakdown of the Stokes-Einstein relation; 3.) the existence of a Widom line, which is the locus of points corresponding to a maximum correlation length in the P-T phase diagram and which ends in the liquid-liquid critical point; 4.) the direct observation of the LDL phase; and 5.) the minimum in the density at approximately 70 K below the temperature of the density maximum. In our opinion these results strongly support the LLPT hypothesis. All of the basic science and technology community should be impressed by the fact that, although the few ideas (apparently elementary) developed concerning water approximately 27 centuries ago have changed very little up to now, because of the current expansion in our knowledge in this area, they can begin to change in the near future.
Supercooled smectic nanoparticles
DEFF Research Database (Denmark)
Kuntsche, Judith; Koch, Michel H J; Fahr, Alfred
2009-01-01
Cholesteryl nonanoate (CN), myristate (CM), palmitate (CP) and oleate (CO) alone or in combination were evaluated as matrix lipids for the preparation of supercooled smectic nanoparticles with a high stability against recrystallization during storage. The phase behavior of the cholesterol esters......, laser diffraction combined with polarizing intensity differential scattering, DSC and SAXS. The morphology of selected formulations was studied by freeze-fracture electron microscopy. All smectic nanoparticles with a mixed cholesterol ester matrix were stable against recrystallization when stored...... at room temperature. Nanoparticles with a pure CN and mixed CM/CN matrix with a high fraction of CN (60% of the whole lipid matrix) could even be stored at 4 degrees C for at least 18 months without any recrystallization. As smectic nanoparticles are studied especially with regard to parenteral...
METHANE GAS STABILIZES SUPERCOOLED ETHANE DROPLETS IN TITAN'S CLOUDS
International Nuclear Information System (INIS)
Wang, Chia C.; Lang, E. Kathrin; Signorell, Ruth
2010-01-01
Strong evidence for ethane clouds in various regions of Titan's atmosphere has recently been found. Ethane is usually assumed to exist as ice particles in these clouds, although the possible role of liquid and supercooled liquid ethane droplets has been recognized. Here, we report on infrared spectroscopic measurements of ethane aerosols performed in the laboratory under conditions mimicking Titan's lower atmosphere. The results clearly show that liquid ethane droplets are significantly stabilized by methane gas which is ubiquitous in Titan's nitrogen atmosphere-a phenomenon that does not have a counterpart for water droplets in Earth's atmosphere. Our data imply that supercooled ethane droplets are much more abundant in Titan's clouds than previously anticipated. Possibly, these liquid droplets are even more important for cloud processes and the formation of lakes than ethane ice particles.
Kirkwood, James R
2015-01-01
Review of ProbabilityShort HistoryReview of Basic Probability DefinitionsSome Common Probability DistributionsProperties of a Probability DistributionProperties of the Expected ValueExpected Value of a Random Variable with Common DistributionsGenerating FunctionsMoment Generating FunctionsExercisesDiscrete-Time, Finite-State Markov ChainsIntroductionNotationTransition MatricesDirected Graphs: Examples of Markov ChainsRandom Walk with Reflecting BoundariesGamblerâ€™s RuinEhrenfest ModelCentral Problem of Markov ChainsCondition to Ensure a Unique Equilibrium StateFinding the Equilibrium StateTransient and Recurrent StatesIndicator FunctionsPerron-Frobenius TheoremAbsorbing Markov ChainsMean First Passage TimeMean Recurrence Time and the Equilibrium StateFundamental Matrix for Regular Markov ChainsDividing a Markov Chain into Equivalence ClassesPeriodic Markov ChainsReducible Markov ChainsSummaryExercisesDiscrete-Time, Infinite-State Markov ChainsRenewal ProcessesDelayed Renewal ProcessesEquilibrium State f...
Energy Technology Data Exchange (ETDEWEB)
Stern, J.; Seidl, M. [Institute of Physical Chemistry, University of Innsbruck, 6020 Innsbruck (Austria); Gainaru, C. [Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund (Germany); Fuentes-Landete, V.; Amann-Winkel, K.; Handle, P.H. [Institute of Physical Chemistry, University of Innsbruck, 6020 Innsbruck (Austria); Köster, K.W.; Nelson, H. [Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund (Germany); Böhmer, R., E-mail: roland.bohmer@tu-dortmund.de [Fakultät Physik, Technische Universität Dortmund, 44221 Dortmund (Germany); Loerting, T., E-mail: thomas.loerting@uibk.ac.at [Institute of Physical Chemistry, University of Innsbruck, 6020 Innsbruck (Austria)
2015-10-10
Highlights: • Two samples of amorphous ices quench-recovered from 140 K to 0.07 GPa are compared. • Calorimetry, X-ray diffraction, dielectric spectroscopy and volumetry are employed. • The two samples are distinct and cannot both be termed “pressure-densified glassy water”. • One route of preparation leads to high- (HDA), and the other to low-density amorphous ice (LDA). • Two distinct glass transitions are observed and interpreted to indicate two liquid H{sub 2}O phases. - Abstract: Recently, our earlier data which led us to conclude that deeply supercooled water displays a second glass transition (Amann-Winkel et al., 2013) was reinterpreted (Johari, 2015). In particular, the increase in heat capacity observed for high-density amorphous ice (HDA) samples at 116 K was reinterpreted to indicate sub-T{sub g} features of low-density amorphous ice's (LDA's) glass transition. We reply to the criticism in detail and report an experiment triggered by the comment on our work. This experiment unequivocally confirms our original interpretation of the observations and reinforces the case for water's second glass transition, its polyamorphism, and the observation of two distinct ultraviscous states of water differing by about 25% in density.
Markov Chains and Markov Processes
Ogunbayo, Segun
2016-01-01
Markov chain, which was named after Andrew Markov is a mathematical system that transfers a state to another state. Many real world systems contain uncertainty. This study helps us to understand the basic idea of a Markov chain and how is been useful in our daily lives. For some times there had been suspense on distinct predictions and future existences. Also in different games there had been different expectations or results involved. That is the reason why we need Markov chains to predict o...
Supercooling of natural water, heavy water and of the blends H2O-D2O
International Nuclear Information System (INIS)
Lafargue, C.; Babin, L.; Clausse, D.; Lere-Porte, M.; Broto, F.
1975-01-01
It is shown that the coherency of the results of various measurements on water freezing temperatures proves that freezing temperatures must be dependent on the structure of the supercooled liquid. Recent experiments that confirm this interpretation are described: study of the stability of supercooled water as a function of time at fixed temperature, study of the influence of various thermal treatments on the behavior of supercooled water, study of the supercooling of heavy water and of D 2 O-H 2 O blends [fr
Fragile to strong crossover at the Widom line in supercooled aqueous solutions of NaCl
Energy Technology Data Exchange (ETDEWEB)
Gallo, P. [Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, I-00146 Rome, Italy and INFN, Sezione di Roma Tre, Via della Vasca Navale 84, I-00146 Rome (Italy); Corradini, D.; Rovere, M., E-mail: rovere@fis.uniroma3.it [Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, I-00146 Rome (Italy)
2013-11-28
We study by molecular dynamics simulations the dynamical properties of an aqueous solution of NaCl at a concentration of 0.67 mol/kg upon supercooling. In a previous study of the same ionic solution, we have located the liquid-liquid critical point (LLCP) and determined the Widom line connected to the liquid-liquid transition. We present here the results obtained from the study of the self-intermediate scattering function in a large range of temperatures and densities approaching the LLCP. The structural relaxation is in agreement with the mode coupling theory (MCT) in the region of mild supercooling. In the deeper supercooled region the α-relaxation time as function of temperature deviates from the MCT power law prediction showing a crossover from a fragile to a strong behavior. This crossover is found upon crossing the Widom line. The same trend was found in bulk water upon supercooling and it appears almost unchanged by the interaction with ions apart from a shift in the thermodynamic plane toward lower pressures and higher temperatures. These results show that the phenomenology of supercooled water transfers from bulk to solution where the study of the supercooled region is experimentally less difficult.
Patro, L N; Burghaus, O; Roling, B
2017-04-21
We have measured the third-order permittivity spectra ε 3 3 of a monocationic and of a dicationic liquid close to the glass transition temperature by applying ac electric fields with large amplitudes up to 180 kV/cm. A peak ("hump") in the modulus of ε 3 3 is observed for a mono-cationic liquid after subtraction of the dc contribution from the imaginary part of ε 3 3 . We show that the origin of this experimental "hump" is a peak in the imaginary part of ε 3 3 , with the peak height strongly increasing with decreasing temperature. Overall, the spectral shape of the third-order permittivity of both ionic liquids is similar to the predictions of a symmetric double well potential model, although this model does not predict a "hump" in the modulus. In contrast, an asymmetric double well potential model predicts a "hump," but the spectral shape of both the real and imaginary part of ε 3 3 deviates significantly from the experimental spectra. These results show that not only the modulus of ε 3 3 but also its phase is an important quantity when comparing experimental results with theoretical predictions.
Singularity-free interpretation of the thermodynamics of supercooled water
International Nuclear Information System (INIS)
Sastry, S.; Debenedetti, P.G.; Sciortino, F.; Stanley, H.E.
1996-01-01
The pronounced increases in isothermal compressibility, isobaric heat capacity, and in the magnitude of the thermal expansion coefficient of liquid water upon supercooling have been interpreted either in terms of a continuous, retracing spinodal curve bounding the superheated, stretched, and supercooled states of liquid water, or in terms of a metastable, low-temperature critical point. Common to these two scenarios is the existence of singularities associated with diverging density fluctuations at low temperature. We show that the increase in compressibility upon lowering the temperature of a liquid that expands on cooling, like water, is not contingent on any singular behavior, but rather is a thermodynamic necessity. We perform a thermodynamic analysis for an anomalous liquid (i.e., one that expands when cooled) in the absence of a retracing spinodal and show that one may in general expect a locus of compressibility extrema in the anomalous regime. Our analysis suggests that the simplest interpretation of the behavior of supercooled water consistent with experimental observations is free of singularities. We then develop a waterlike lattice model that exhibits no singular behavior, while capturing qualitative aspects of the thermodynamics of water. copyright 1996 The American Physical Society
Communication: Minimum in the thermal conductivity of supercooled water: A computer simulation study
Energy Technology Data Exchange (ETDEWEB)
Bresme, F., E-mail: f.bresme@imperial.ac.uk [Chemical Physics Section, Department of Chemistry, Imperial College, London SW7 2AZ, United Kingdom and Department of Chemistry, Norwegian University of Science and Technology, Trondheim 7491 (Norway); Biddle, J. W.; Sengers, J. V.; Anisimov, M. A. [Institute for Physical Science and Technology, and Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20742 (United States)
2014-04-28
We report the results of a computer simulation study of the thermodynamic properties and the thermal conductivity of supercooled water as a function of pressure and temperature using the TIP4P-2005 water model. The thermodynamic properties can be represented by a two-structure equation of state consistent with the presence of a liquid-liquid critical point in the supercooled region. Our simulations confirm the presence of a minimum in the thermal conductivity, not only at atmospheric pressure, as previously found for the TIP5P water model, but also at elevated pressures. This anomalous behavior of the thermal conductivity of supercooled water appears to be related to the maximum of the isothermal compressibility or the minimum of the speed of sound. However, the magnitudes of the simulated thermal conductivities are sensitive to the water model adopted and appear to be significantly larger than the experimental thermal conductivities of real water at low temperatures.
Communication: Minimum in the thermal conductivity of supercooled water: A computer simulation study
International Nuclear Information System (INIS)
Bresme, F.; Biddle, J. W.; Sengers, J. V.; Anisimov, M. A.
2014-01-01
We report the results of a computer simulation study of the thermodynamic properties and the thermal conductivity of supercooled water as a function of pressure and temperature using the TIP4P-2005 water model. The thermodynamic properties can be represented by a two-structure equation of state consistent with the presence of a liquid-liquid critical point in the supercooled region. Our simulations confirm the presence of a minimum in the thermal conductivity, not only at atmospheric pressure, as previously found for the TIP5P water model, but also at elevated pressures. This anomalous behavior of the thermal conductivity of supercooled water appears to be related to the maximum of the isothermal compressibility or the minimum of the speed of sound. However, the magnitudes of the simulated thermal conductivities are sensitive to the water model adopted and appear to be significantly larger than the experimental thermal conductivities of real water at low temperatures
Physical limit of stability in supercooled D2O and D2O+H2O mixtures
Kiselev, S. B.; Ely, J. F.
2003-01-01
The fluctuation theory of homogeneous nucleation was applied for calculating the physical boundary of metastable states, the kinetic spinodal, in supercooled D2O and D2O+H2O mixtures. The kinetic spinodal in our approach is completely determined by the surface tension and equation of state of the supercooled liquid. We developed a crossover equation of state for supercooled D2O, which predicts a second critical point of low density water-high density water equilibrium, CP2, and represents all available experimental data in supercooled D2O within experimental accuracy. Using Turnbull's expression for the surface tension we calculated with the crossover equation of state for supercooled D2O the kinetic spinodal, TKS, which lies below the homogeneous nucleation temperature, TH. We show that CP2 always lies inside in the so-called "nonthermodynamic habitat" and physically does not exist. However, the concept of a second "virtual" critical point is physical and very useful. Using this concept we have extended this approach to supercooled D2O+H2O mixtures. As an example, we consider here an equimolar D2O+H2O mixture in normal and supercooled states at atmospheric pressure, P=0.1 MPa.
Correlation between thermodynamic anomalies and pathways of ice nucleation in supercooled water
International Nuclear Information System (INIS)
Singh, Rakesh S.; Bagchi, Biman
2014-01-01
The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) liquid phases in supercooled state. The explanations of thermodynamic and dynamic anomalies of supercooled water often invoke the possible influence of a liquid-liquid transition between two metastable liquid phases. To investigate both the role of thermodynamic anomalies and presence of distinct metastable liquid phases in supercooled water on ice nucleation, we employ density functional theoretical approach to find nucleation free energy barrier in different regions of phase diagram. The theory makes a number of striking predictions, such as a dramatic lowering of nucleation barrier due to presence of a metastable intermediate phase and crossover in the dependence of free energy barrier on temperature near liquid-liquid critical point. These predictions can be tested by computer simulations as well as by controlled experiments
Markov processes and controlled Markov chains
Filar, Jerzy; Chen, Anyue
2002-01-01
The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South Ameri...
Thermodynamics of Supercooled and Glassy Water
Debenedetti, Pablo G.
1998-03-01
The behavior of metastable water at low temperatures is unusual. The isothermal compressibility, the isobaric heat capacity, and the magnitude of the thermal expansion coefficient increase sharply upon supercooling, and structural relaxation becomes extremely sluggish at temperatures far above the glass transition(Angell, C.A., Annu. Rev. Phys. Chem., 34, 593, 1983)(Debenedetti, P.G., Metastable Liquids. Concepts and Principles, Princeton University Press, 1996). Water has two distinct glassy phases, low- and high-density amorphous ice (LDA, HDA). The transition between LDA and HDA is accompanied by sharp volume and enthalpy changes, and appears to be first-order(Mishima, O., L.D.Calvert, and E. Whalley, Nature, 314, 76, 1985)(Mishima, O., J. Chem. Phys., 100, 5910, 1994). The understanding of these observations in terms of an underlying global phase behavior remains incomplete(Speedy, R.J., J. Phys. Chem., 86, 982, 1982)(Poole, P.H., F. Sciortino, U. Essman, and H.E. Stanley, Nature, 360, 324, 1992)(Sastry, S., P.G. Debenedetti, F. Sciortino, and H.E. Stanley, Phys. Rev. E, 53, 6144, 1996)(Tanaka, H., Nature, 380, 328, 1996)(Xie, Y., K.F. Ludwig, G. Morales, D.E. Hare, and C.M. Sorensen, Phys. Rev. Lett., 71, 2050, 1993). Microscopic theories and computer simulations suggest several scenarios that can reproduce some experimental observations. Interesting and novel ideas have resulted from this body of theoretical work, such as the possibility of liquid-liquid immiscibility in a pure substance(Poole, P.H., F.Sciortino, T.Grande, H.E. Stanley, and C.A. Angell, Phys. Rev. Lett., 73, 1632, 1994)(Roberts, C.J., and P.G. Debenedetti, J. Chem. Phys., 105, 658, 1996)(Roberts, C.J., P.G. Debenedetti, and A.Z. Panagiotopoulos, Phys. Rev. Lett., 77, 4386, 1996)(Harrington, S., R. Zhang, P.H. Poole, F. Sciortino, and H.E. Stanley, Phys. Rev. Lett., 78, 2409, 1997). In this talk I will review the experimental facts, discuss their theoretical interpretation, and identify key
Surface Tension of Supercooled Water Determined by Using a Counterpressure Capillary Rise Method
Czech Academy of Sciences Publication Activity Database
Vinš, Václav; Fransen, M. A. L. J.; Hykl, Jiří; Hrubý, Jan
2015-01-01
Roč. 119, č. 17 (2015), s. 5567-5575 ISSN 1520-6106 R&D Projects: GA MŠk LG13056; GA ČR GJ15-07129Y Institutional support: RVO:61388998 Keywords : capillary tube * interfacial tension * metastable liquid * supercooled liquid Subject RIV: BJ - Thermodynamics Impact factor: 3.187, year: 2015 http://pubs.acs.org/doi/abs/10.1021/acs.jpcb.5b00545
Phase diagram of supercooled water confined to hydrophilic nanopores
Limmer, David T.; Chandler, David
2012-07-01
We present a phase diagram for water confined to cylindrical silica nanopores in terms of pressure, temperature, and pore radius. The confining cylindrical wall is hydrophilic and disordered, which has a destabilizing effect on ordered water structure. The phase diagram for this class of systems is derived from general arguments, with parameters taken from experimental observations and computer simulations and with assumptions tested by computer simulation. Phase space divides into three regions: a single liquid, a crystal-like solid, and glass. For large pores, radii exceeding 1 nm, water exhibits liquid and crystal-like behaviors, with abrupt crossovers between these regimes. For small pore radii, crystal-like behavior is unstable and water remains amorphous for all non-zero temperatures. At low enough temperatures, these states are glasses. Several experimental results for supercooled water can be understood in terms of the phase diagram we present.
Slow Dynamics and Structure of Supercooled Water in Confinement
Directory of Open Access Journals (Sweden)
Gaia Camisasca
2017-04-01
Full Text Available We review our simulation results on properties of supercooled confined water. We consider two situations: water confined in a hydrophilic pore that mimics an MCM-41 environment and water at interface with a protein. The behavior upon cooling of the α relaxation of water in both environments is well interpreted in terms of the Mode Coupling Theory of glassy dynamics. Moreover, we find a crossover from a fragile to a strong regime. We relate this crossover to the crossing of the Widom line emanating from the liquid-liquid critical point, and in confinement we connect this crossover also to a crossover of the two body excess entropy of water upon cooling. Hydration water exhibits a second, distinctly slower relaxation caused by its dynamical coupling with the protein. The crossover upon cooling of this long relaxation is related to the protein dynamics.
Dynamics of supercooled confined water measured by deep inelastic neutron scattering
De Michele, Vincenzo; Romanelli, Giovanni; Cupane, Antonio
2018-02-01
In this paper, we present the results of deep inelastic neutron scattering (DINS) measurements on supercooled water confined within the pores (average pore diameter 20 Å) of a disordered hydrophilic silica matrix obtained through hydrolysis and polycondensation of the alkoxide precursor Tetra-Methyl-Ortho-Silicate via the sol-gel method. Experiments were performed at two temperatures (250 K and 210 K, i.e., before and after the putative liquid-liquid transition of supercooled confined water) on a "wet" sample with hydration h 40% w/w, which is high enough to have water-filled pores but low enough to avoid water crystallization. A virtually "dry" sample at h 7% was also investigated to measure the contribution of the silica matrix to the neutron scattering signal. As is well known, DINS measurements allow the determination of the mean kinetic energy and the momentum distribution of the hydrogen atoms in the system and therefore, allow researchers to probe the local structure of supercooled confined water. The main result obtained is that at 210 K the hydrogen mean kinetic energy is equal or even slightly higher than at 250 K. This is at odds with the predictions of a semiempirical harmonic model recently proposed to describe the temperature dependence of the kinetic energy of hydrogen in water. This is a new and very interesting result, which suggests that at 210 K, the water hydrogens experience a stiffer intermolecular potential than at 250 K. This is in agreement with the liquid-liquid transition hypothesis.
Markov stochasticity coordinates
International Nuclear Information System (INIS)
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Abdulla, Parosh Aziz; Henda, Noomene Ben; Mayr, Richard
2007-01-01
We consider qualitative and quantitative verification problems for infinite-state Markov chains. We call a Markov chain decisive w.r.t. a given set of target states F if it almost certainly eventually reaches either F or a state from which F can no longer be reached. While all finite Markov chains are trivially decisive (for every set F), this also holds for many classes of infinite Markov chains. Infinite Markov chains which contain a finite attractor are decisive w.r.t. every set F. In part...
Markov stochasticity coordinates
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: iddo.eliazar@intel.com
2017-01-15
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
DEFF Research Database (Denmark)
Adrjanowicz, Karolina; Kaminski, Kamil; Paluch, Marian
2015-01-01
In this paper, we study crystallization behavior and molecular dynamics in the supercooled liquid state of the pharmaceutically important compound ketoprofen at various thermodynamic conditions. Dielectric relaxation for a racemic mixture was investigated in a wide range of temperatures and press...
Gelation on heating of supercooled gelatin solutions.
Guigo, Nathanaël; Sbirrazzuoli, Nicolas; Vyazovkin, Sergey
2012-04-23
Diluted (1.0-1.5 wt%) aqueous gelatin solutions have been cooled to -10 °C at a cooling rate 20 °C min(-1) without freezing and detectable gelation. When heated at a constant heating rate (0.5 -2 °C min(-1)), the obtained supercooled solutions demonstrate an atypical process of gelation that has been characterized by regular and stochastically modulated differential scanning calorimetry (DSC) as well as by isoconversional kinetic analysis. The process is detectable as an exothermic peak in the total heat flow of regular DSC and in the nonreversing heat flow of stochastically modulated DSC. Isoconversional kinetic analysis applied to DSC data reveals that the effective activation energy of the process increases from approximately 75 to 200 kJ mol(-1) as a supercooled solution transforms to gel on continuous heating. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Grabski
2014-01-01
Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. Clearly defines the properties and
Tellinghuisen, Joel
2010-01-01
Liquid-vapor, solid-vapor, and solid-liquid-vapor equilibria are studied for the pure substance water, using modern equipment that includes specially fabricated glass cells. Samples are evaporatively frozen initially, during which they typically supercool to -5 to -10 [degrees]C before spontaneously freezing. Vacuum pumping lowers the temperature…
DEFF Research Database (Denmark)
Justesen, Jørn
2005-01-01
A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly.......A simple construction of two-dimensional (2-D) fields is presented. Rows and columns are outcomes of the same Markov chain. The entropy can be calculated explicitly....
janssen, Anja; Segers, Johan
2013-01-01
The extremes of a univariate Markov chain with regularly varying stationary marginal distribution and asymptotically linear behavior are known to exhibit a multiplicative random walk structure called the tail chain. In this paper we extend this fact to Markov chains with multivariate regularly varying marginal distributions in Rd. We analyze both the forward and the backward tail process and show that they mutually determine each other through a kind of adjoint relation. In ...
Supercooling of Water Controlled by Nanoparticles and Ultrasound
Cui, Wei; Jia, Lisi; Chen, Ying; Li, Yi'ang; Li, Jun; Mo, Songping
2018-05-01
Nanoparticles, including Al2O3 and SiO2, and ultrasound were adopted to improve the solidification properties of water. The effects of nanoparticle concentration, contact angle, and ultrasonic intensity on the supercooling degree of water were investigated, as well as the dispersion stability of nanoparticles in water during solidification. Experimental results show that the supercooling degree of water is reduced under the combined effect of ultrasound and nanoparticles. Consequently, the reduction of supercooling degree increases with the increase of ultrasonic intensity and nanoparticle concentration and decrease of contact angle of nanoparticles. Moreover, the reduction of supercooling degree caused by ultrasound and nanoparticles together do not exceed the sum of the supercooling degree reductions caused by ultrasound and nanoparticles separately; the reduction is even smaller than that caused by ultrasound individually under certain conditions of controlled nanoparticle concentration and contact angle and ultrasonic intensity. The dispersion stability of nanoparticles during solidification can be maintained only when the nanoparticles and ultrasound together show a superior effect on reducing the supercooling degree of water to the single operation of ultrasound. Otherwise, the aggregation of nanoparticles appears in water solidification, which results in failure. The relationships among the meaningful nanoparticle concentration, contact angle, and ultrasonic intensity, at which the requirements of low supercooling and high stability could be satisfied, were obtained. The control mechanisms for these phenomena were analyzed.
Surface Tension of Supercooled Water: No Inflection Point down to-25 degrees C
Czech Academy of Sciences Publication Activity Database
Hrubý, Jan; Vinš, Václav; Mareš, R.; Hykl, Jiří; Kalová, J.
2014-01-01
Roč. 5, č. 3 (2014), s. 425-428 ISSN 1948-7185 R&D Projects: GA AV ČR(CZ) IAA200760905; GA ČR(CZ) GPP101/11/P046; GA MŠk(CZ) LG13056 Grant - others:Rada Programu interní podpory projektů mezinárodní spolupráce AV ČR(CZ) M100761201 Institutional support: RVO:61388998 Keywords : liquid * metastable * supercooled Subject RIV: JE - Non-nuclear Energetics, Energy Consumption ; Use Impact factor: 7.458, year: 2014
DEFF Research Database (Denmark)
Kong, Weiqiang; Dannemand, Mark; Johansen, Jakob Berg
2016-01-01
Sodium acetate trihydrate is a phase change material that can be used for long term heat storage in solar heating systems because of its relatively high heat of fusion, a melting temperature of 58 °C and its ability to supercool stable. In practical applications sodium acetate trihydrate tend to ......, 0.3–0.5 % (wt.%) Xanthan Gum or 1–2% (wt.%) of some solid or liquid polymers as additives had significantly higher heat contents compared to samples of sodium acetate trihydrate suffering from phase separation....
Fundamental research on supercooling phenomenon on heat transfer surface
International Nuclear Information System (INIS)
Saito, A.; Okawa, S.; Koganezawa, S.
1991-01-01
In relation to the problem of supercooling for ice storage devices, experiments on freezing a relatively large volume of supercooled water is carried out. In the experiment, an experimental method to determine a probability of freezing a large volume of supercooled water with a uniform temperature distribution is introduced. It is accomplished by dividing the water into many smaller droplets. In a statistical analysis, a method to improve an accuracy in a case of having a limited number of experiments is introduced, and the probability of freezing is calculated for each degree of supercooling. The average freezing temperature for the experiment is placed just at the extended region of the other researchers results worked on small droplets. By relating the value with the probability of freezing on various kinds of heat transfer surfaces, the probability of freezing which is independent of the surface is calculated. In this paper it is confirmed to be negligible compared with the one on the surface
El Yazid Boudaren, Mohamed; Monfrini, Emmanuel; Pieczynski, Wojciech; Aïssani, Amar
2014-11-01
Hidden Markov chains have been shown to be inadequate for data modeling under some complex conditions. In this work, we address the problem of statistical modeling of phenomena involving two heterogeneous system states. Such phenomena may arise in biology or communications, among other fields. Namely, we consider that a sequence of meaningful words is to be searched within a whole observation that also contains arbitrary one-by-one symbols. Moreover, a word may be interrupted at some site to be carried on later. Applying plain hidden Markov chains to such data, while ignoring their specificity, yields unsatisfactory results. The Phasic triplet Markov chain, proposed in this paper, overcomes this difficulty by means of an auxiliary underlying process in accordance with the triplet Markov chains theory. Related Bayesian restoration techniques and parameters estimation procedures according to the new model are then described. Finally, to assess the performance of the proposed model against the conventional hidden Markov chain model, experiments are conducted on synthetic and real data.
Czech Academy of Sciences Publication Activity Database
Vinš, Václav; Hošek, Jan; Hykl, Jiří; Hrubý, Jan
2017-01-01
Roč. 62, č. 11 (2017), s. 3823-3832 ISSN 0021-9568 R&D Projects: GA ČR(CZ) GJ15-07129Y Institutional support: RVO:61388998 Keywords : horizontal technique * metastable liquid * supercooled Subject RIV: BJ - Thermodynamics OBOR OECD: Thermodynamics Impact factor: 2.323, year: 2016 http://pubs.acs.org/doi/pdf/10.1021/acs.jced.7b00519
Hartfiel, Darald J
1998-01-01
In this study extending classical Markov chain theory to handle fluctuating transition matrices, the author develops a theory of Markov set-chains and provides numerous examples showing how that theory can be applied. Chapters are concluded with a discussion of related research. Readers who can benefit from this monograph are those interested in, or involved with, systems whose data is imprecise or that fluctuate with time. A background equivalent to a course in linear algebra and one in probability theory should be sufficient.
Confluence reduction for Markov automata
Timmer, Mark; Katoen, Joost P.; van de Pol, Jaco; Stoelinga, Mariëlle Ida Antoinette
2016-01-01
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. As expected, the state space explosion threatens the analysability of these models. We therefore introduce confluence reduction for Markov automata, a powerful reduction
Amorphous ices explained in terms of nonequilibrium phase transitions in supercooled water
Limmer, David; Chandler, David
2013-03-01
We analyze the phase diagram of supercooled water out-of-equilibrium using concepts from space-time thermodynamics and the dynamic facilitation theory of the glass transition, together with molecular dynamics simulations. We find that when water is driven out-of-equilibrium, it can exist in multiple amorphous states. In contrast, we find that when water is at equilibrium, it can exist in only one liquid state. The amorphous non-equilibrium states are solids, distinguished from the liquid by their lack of mobility, and distinguished from each other by their different densities and local structure. This finding explains the experimentally observed polyamorphism of water as a class of nonequilibrium phenomena involving glasses of different densities. While the amorphous solids can be long lived, they are thermodynamically unstable. When allowed to relax to equilibrium, they crystallize with pathways that pass first through liquid state configurations and then to ordered ice.
Process Algebra and Markov Chains
Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Process algebra and Markov chains
Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.
2001-01-01
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Indian Academy of Sciences (India)
be obtained as a limiting value of a sample path of a suitable ... makes a mathematical model of chance and deals with the problem by .... Is the Markov chain aperiodic? It is! Here is how you can see it. Suppose that after you do the cut, you hold the top half in your right hand, and the bottom half in your left. Then there.
Composable Markov Building Blocks
Evers, S.; Fokkinga, M.M.; Apers, Peter M.G.; Prade, H.; Subrahmanian, V.S.
2007-01-01
In situations where disjunct parts of the same process are described by their own first-order Markov models and only one model applies at a time (activity in one model coincides with non-activity in the other models), these models can be joined together into one. Under certain conditions, nearly all
Composable Markov Building Blocks
Evers, S.; Fokkinga, M.M.; Apers, Peter M.G.
2007-01-01
In situations where disjunct parts of the same process are described by their own first-order Markov models, these models can be joined together under the constraint that there can only be one activity at a time, i.e. the activities of one model coincide with non-activity in the other models. Under
Solan, Eilon; Vieille, Nicolas
2015-01-01
We study irreducible time-homogenous Markov chains with finite state space in discrete time. We obtain results on the sensitivity of the stationary distribution and other statistical quantities with respect to perturbations of the transition matrix. We define a new closeness relation between transition matrices, and use graph-theoretic techniques, in contrast with the matrix analysis techniques previously used.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 3. Markov Chain Monte Carlo - Examples. Arnab Chakraborty. General Article Volume 7 Issue 3 March 2002 pp 25-34. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/007/03/0025-0034. Keywords.
Partially Hidden Markov Models
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Rissanen, Jorma
1996-01-01
Partially Hidden Markov Models (PHMM) are introduced. They differ from the ordinary HMM's in that both the transition probabilities of the hidden states and the output probabilities are conditioned on past observations. As an illustration they are applied to black and white image compression where...
On the pressure evolution of dynamic properties of supercooled liquids
Energy Technology Data Exchange (ETDEWEB)
Drozd-Rzoska, Aleksandra; Rzoska, Sylwester J [Institute of Physics, Silesian University, ulica Uniwersytecka 4, 40-007 Katowice (Poland); Roland, C Michael [Naval Research Laboratory, Chemistry Division, Code 6120, Washington, DC 20375-5342 (United States); Imre, Attila R [KFKI Atomic Energy Research Institute, 1525 Budapest, POB 49 (Hungary)
2008-06-18
A pressure counterpart of the Vogel-Fulcher-Tammann (VFT) equation for representing the evolution of dielectric relaxation times or related dynamic properties is discussed: {tau}(P) = {tau}{sub 0}{sup P}exp[D{sub P}{delta}P(P{sub 0}-{delta}P)], where {delta}P = P-P{sub SL}, P{sub 0} is the ideal glass pressure estimation, D{sub P} is the pressure fragility strength coefficient, and the prefactor {tau}{sub 0}{sup P} is related to the relaxation time at the stability limit (P{sub SL}) in the negative pressure domain. The discussion is extended to the Avramov model (AvM) relation {tau}(T,P) = {tau}{sub 0}exp[{epsilon}(T{sub g}(P)/T){sup D}], supplemented with a modified Simon-Glatzel-type equation for the pressure dependence of the glass temperature (T{sub g}(P)), enabling an insight into the negative pressure region. A recently postulated (Dyre 2006 Rev. Mod. Phys. 78 953) comparison between the VFT and the AvM-type descriptions is examined, for both the temperature and the pressure paths. Finally, we address the question 'Does fragility depend on pressure?' from the title of Paluch M et al (2001 J. Chem. Phys. 114 8048) and propose a pressure counterpart for the 'Angell plot'.
Quasi-elastic neutron scattering studies of the slow dynamics of supercooled and glassy aspirin
International Nuclear Information System (INIS)
Zhang Yang; Mamontov, Eugene; Tyagi, Madhusudan; Chen, Sow-Hsin
2012-01-01
Aspirin, also known as acetylsalicylic acid (ASA), is not only a wonderful drug, but also a good glass former. Therefore, it serves as an important molecular system to study the near-arrest and arrested phenomena. In this paper, a high-resolution quasi-elastic neutron scattering (QENS) technique is used to investigate the slow dynamics of supercooled liquid and glassy aspirin from 410 down to 350 K. The measured QENS spectra can be analyzed with a stretched exponential model. We find that (i) the stretched exponent β(Q) is independent of the wavevector transfer Q in the measured Q range and (ii) the structural relaxation time τ(Q) follows a power-law dependence on Q. Consequently, the Q-independent structural relaxation time τ 0 can be extracted for each temperature to characterize the slow dynamics of aspirin. The temperature dependence of τ 0 can be fitted with the mode-coupling power law, the Vogel-Fulcher-Tammann equation and a universal equation for fragile glass forming liquids recently proposed by Tokuyama in the measured temperature range. The calculated dynamic response function χ T (Q, t) using the experimentally determined self-intermediate scattering function of the hydrogen atoms of aspirin shows direct evidence of the enhanced dynamic fluctuations as the aspirin is increasingly supercooled, in agreement with the fixed-time mean squared displacement (x 2 ) and the non-Gaussian parameter α 2 extracted from the elastic scattering.
Quasi-Elastic Neutron Scattering Studies of the Slow Dynamics of Supercooled and Glassy Aspirin
Energy Technology Data Exchange (ETDEWEB)
Zhang, Yang [ORNL; Tyagi, M. [NCNR and University of Maryland; Mamontov, Eugene [ORNL; Chen, Sow-hsin H [ORNL
2011-01-01
Aspirin, also known as acetylsalicylic acid (ASA), is not only a wonderful drug, but also a good glass former. Therefore, it serves as an important molecular system to study the near-arrest and arrested phenomena. In this paper, a high-resolution quasi-elastic neutron scattering (QENS) technique is used to investigate the slow dynamics of supercooled liquid and glassy aspirin from 410 K down to 350 K. The measured QENS spectra can be analyzed with a stretched exponential model. We find that (i) the stretched exponent (Q) is independent of the wave vector transfer Q in the measured Q-range, and (ii) the structural relaxation time (Q) follows a power law dependence on Q. Consequently, the Q-independent structural relaxation time 0 can be extracted for each temperature to characterize the slow dynamics of aspirin. The temperature dependence of 0 can be fitted with the mode coupling power law, the Vogel-Fulcher-Tammann equation and a universal equation for fragile glass forming liquids recently proposed by M. Tokuyama in the measured temperature range. The calculated dynamic response function T(Q,t) using the experimentally determined self-intermediate scattering function of the hydrogen atoms of aspirin shows a direct evidence of the enhanced dynamic fluctuations as the aspirin is increasingly supercooled, in agreement with the fixed-time mean squared displacement x2 and non-Gaussian parameter 2 extracted from the elastic scattering.
Quasi-elastic neutron scattering studies of the slow dynamics of supercooled and glassy aspirin
Zhang, Yang; Tyagi, Madhusudan; Mamontov, Eugene; Chen, Sow-Hsin
2012-02-01
Aspirin, also known as acetylsalicylic acid (ASA), is not only a wonderful drug, but also a good glass former. Therefore, it serves as an important molecular system to study the near-arrest and arrested phenomena. In this paper, a high-resolution quasi-elastic neutron scattering (QENS) technique is used to investigate the slow dynamics of supercooled liquid and glassy aspirin from 410 down to 350 K. The measured QENS spectra can be analyzed with a stretched exponential model. We find that (i) the stretched exponent β(Q) is independent of the wavevector transfer Q in the measured Q range and (ii) the structural relaxation time τ(Q) follows a power-law dependence on Q. Consequently, the Q-independent structural relaxation time τ0 can be extracted for each temperature to characterize the slow dynamics of aspirin. The temperature dependence of τ0 can be fitted with the mode-coupling power law, the Vogel-Fulcher-Tammann equation and a universal equation for fragile glass forming liquids recently proposed by Tokuyama in the measured temperature range. The calculated dynamic response function χT(Q, t) using the experimentally determined self-intermediate scattering function of the hydrogen atoms of aspirin shows direct evidence of the enhanced dynamic fluctuations as the aspirin is increasingly supercooled, in agreement with the fixed-time mean squared displacement langx2rang and the non-Gaussian parameter α2 extracted from the elastic scattering.
Energy Technology Data Exchange (ETDEWEB)
Seppaelae, Ari; Merilaeinen, Arttu [Helsinki University of Technology, Department of Energy Technology, Applied Thermodynamics, P.O. Box 4400, 02015 TKK (Finland); Wikstroem, Lisa; Kauranen, Pertti [VTT Technical Research Centre of Finland, Advanced Materials, P.O. Box 1300, 33101 Tampere (Finland)
2010-07-15
Some liquids can be kept in a supercooled or supersaturated metastable state for substantially long periods. Such liquids can be applied as long-term heat storage where the latent heat can be released when needed. As xylitol possesses a relatively high value of latent heat and as it can be easily supercooled, it has promising properties for this application. However, the speed of the crystallization of xylitol is low, leading to a low release rate of latent heat. Several additives have been experimentally tested for the purpose of accelerating the crystallization speed. The effect of the additives on the latent heat, on the melting temperatures, and on the long-term durability of the supercooled state was also measured. The highest speeds of the crystallization front, at a temperature of 22 C, were achieved with methanol as an additive leading to speeds 33 times higher in vertical experiments and in 170 times higher in horizontal ones than with pure xylitol. The improved speed of the crystallization front is mostly caused by the methanol flow currents generated as a result of the separation of methanol during crystallization, and to a lesser extent, as a result of the increase in the speed of the growth of the crystals. (author)
Effects of PVA(Polyvinyl Alcohol) on Supercooling Phenomena of Water
Kumano, Hiroyuki; Saito, Akio; Okawa, Seiji; Takizawa, Hiroshi
In this paper, effects of polymer additive on supercooling of water were investigated experimentally. Poly-vinyl alcohol (PVA) were used as the polymer, and the samples were prepared by dissolving PVA in ultra pure water. Concentration, degree of polymerization and saponification of PVA were varied as the experimental parameters. The sample was cooled, and the temperature at the instant when ice appears was measured. Since freezing of supercooled water is statistical phenomenon, many experiments were carried out and average degrees of supercooling were obtained for each experimental condition. As the result, it was found that PVA affects nucleation of supercooling and the degree of supercooling increases by adding the PVA. Especially, it is found that the average degree of supercooling increases and the standard deviation of average degree of supercooling decreases with increase of degree of saponification of PVA. However, the average degree of supercooling are independent of the degree of polymerization of PVA in the range of this study.
Generalized Markov branching models
Li, Junping
2005-01-01
In this thesis, we first considered a modified Markov branching process incorporating both state-independent immigration and resurrection. After establishing the criteria for regularity and uniqueness, explicit expressions for the extinction probability and mean extinction time are presented. The criteria for recurrence and ergodicity are also established. In addition, an explicit expression for the equilibrium distribution is presented.\\ud \\ud We then moved on to investigate the basic proper...
Ragain, Stephen; Ugander, Johan
2016-01-01
As datasets capturing human choices grow in richness and scale---particularly in online domains---there is an increasing need for choice models that escape traditional choice-theoretic axioms such as regularity, stochastic transitivity, and Luce's choice axiom. In this work we introduce the Pairwise Choice Markov Chain (PCMC) model of discrete choice, an inferentially tractable model that does not assume any of the above axioms while still satisfying the foundational axiom of uniform expansio...
Distinguishing Hidden Markov Chains
Kiefer, Stefan; Sistla, A. Prasad
2015-01-01
Hidden Markov Chains (HMCs) are commonly used mathematical models of probabilistic systems. They are employed in various fields such as speech recognition, signal processing, and biological sequence analysis. We consider the problem of distinguishing two given HMCs based on an observation sequence that one of the HMCs generates. More precisely, given two HMCs and an observation sequence, a distinguishing algorithm is expected to identify the HMC that generates the observation sequence. Two HM...
Fannes, Mark; Wouters, Jeroen
2012-01-01
We study a quantum process that can be considered as a quantum analogue for the classical Markov process. We specifically construct a version of these processes for free Fermions. For such free Fermionic processes we calculate the entropy density. This can be done either directly using Szeg\\"o's theorem for asymptotic densities of functions of Toeplitz matrices, or through an extension of said theorem to rates of functions, which we present in this article.
Pemodelan Markov Switching Autoregressive
Ariyani, Fiqria Devi; Warsito, Budi; Yasin, Hasbi
2014-01-01
Transition from depreciation to appreciation of exchange rate is one of regime switching that ignored by classic time series model, such as ARIMA, ARCH, or GARCH. Therefore, economic variables are modeled by Markov Switching Autoregressive (MSAR) which consider the regime switching. MLE is not applicable to parameters estimation because regime is an unobservable variable. So that filtering and smoothing process are applied to see the regime probabilities of observation. Using this model, tran...
Hambye, Thomas; Teresi, Daniele
In dimension-less theories of dynamical generation of the weak scale, the Universe can undergo a period of low-scale inflation during which all particles are massless and super-cool. This leads to a new mechanism of generation of the cosmological Dark Matter (DM) relic density: super-cooling can easily suppress the amount of DM to the desired level. This is achieved for TeV-scale DM, if super-cooling ends when quark condensates form at the QCD phase transition. Along this scenario, the baryon asymmetry can be generated either at the phase transition or through leptogenesis. We show that the above mechanism takes place in old and new dimension-less models.
Approximate quantum Markov chains
Sutter, David
2018-01-01
This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...
Communication: Diffusion constant in supercooled water as the Widom line is crossed in no man's land
Ni, Yicun; Hestand, Nicholas J.; Skinner, J. L.
2018-05-01
According to the liquid-liquid critical point (LLCP) hypothesis, there are two distinct phases of supercooled liquid water, namely, high-density liquid and low-density liquid, separated by a coexistence line that terminates in an LLCP. If the LLCP is real, it is located within No Man's Land (NML), the region of the metastable phase diagram that is difficult to access using conventional experimental techniques due to rapid homogeneous nucleation to the crystal. However, a recent ingenious experiment has enabled measurement of the diffusion constant deep inside NML. In the current communication, these recent measurements are compared, with good agreement, to the diffusion constant of E3B3 water, a classical water model that explicitly includes three-body interactions. The behavior of the diffusion constant as the system crosses the Widom line (the extension of the liquid-liquid coexistence line into the one-phase region) is analyzed to derive information about the presence and location of the LLCP. Calculations over a wide range of temperatures and pressures show that the new experimental measurements are consistent with an LLCP having a critical pressure of over 0.6 kbar.
DEFF Research Database (Denmark)
Dyre, Jeppe
1999-01-01
Recent NMR experiments on supercooled toluene and glycerol by Hinze and Böhmer show that small rotation angles dominate with only a few large molecular rotations. These results are here interpreted by assuming that viscous liquids are solidlike on short length scales. A characteristic length...
A relation between non-Markov and Markov processes
International Nuclear Information System (INIS)
Hara, H.
1980-01-01
With the aid of a transformation technique, it is shown that some memory effects in the non-Markov processes can be eliminated. In other words, some non-Markov processes are rewritten in a form obtained by the random walk process; the Markov process. To this end, two model processes which have some memory or correlation in the random walk process are introduced. An explanation of the memory in the processes is given. (orig.)
Mallak, Saed
1996-01-01
Ankara : Department of Mathematics and Institute of Engineering and Sciences of Bilkent University, 1996. Thesis (Master's) -- Bilkent University, 1996. Includes bibliographical references leaves leaf 29 In thi.s work, we studierl the Ergodicilv of Non-Stationary .Markov chains. We gave several e.xainples with different cases. We proved that given a sec[uence of Markov chains such that the limit of this sec|uence is an Ergodic Markov chain, then the limit of the combination ...
Markov Chain Monte Carlo Methods
Indian Academy of Sciences (India)
Keywords. Markov chain; state space; stationary transition probability; stationary distribution; irreducibility; aperiodicity; stationarity; M-H algorithm; proposal distribution; acceptance probability; image processing; Gibbs sampler.
Droplet-Sizing Liquid Water Content Sensor, Phase II
National Aeronautics and Space Administration — Icing is one of the most significant hazards to aircraft. A sizing supercooled liquid water content (SSLWC) sonde is being developed to meet a directly related need...
Pach, E; Rodriguez, L; Verdaguer, A
2018-01-18
The freezing of supercooled water films on different substrates was investigated using a high-speed camera coupled to an optical microscope, obtaining details of the freezing process not described in the literature before. We observed the two well known freezing stages (fast dendritic growth and slow freezing of the water liquid left after the dendritic growth), but we separated the process into different phenomena that were studied separately: two-dimensional dendrite growth on the substrate interface, vertical dendrite growth, formation and evolution of ice domains, trapping of air bubbles and freezing of the water film surface. We found all of these processes to be dependent on both the supercooling temperature and the substrate used. Ice dendrite (or ice front) growth during the first stage was found to be dependent on thermal properties of the substrate but could not be unequivocally related to them. Finally, for low supercooling, a direct relationship was observed between the morphology of the dendrites formed in the first stage, which depends on the substrate, and the roughness and the shape of the surface of the ice, when freezing of the film was completed. This opens the possibility of using surfaces and coatings to control ice morphology beyond anti-icing properties.
Volchenkov, Dima; Dawin, Jean René
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
DEFF Research Database (Denmark)
Kohlenbach, Ulrich Wilhelm
2002-01-01
We show that the so-called weak Markov's principle (WMP) which states that every pseudo-positive real number is positive is underivable in E-HA + AC. Since allows one to formalize (atl eastl arge parts of) Bishop's constructive mathematics, this makes it unlikely that WMP can be proved within...... the framework of Bishop-style mathematics (which has been open for about 20 years). The underivability even holds if the ine.ective schema of full comprehension (in all types) for negated formulas (in particular for -free formulas) is added, which allows one to derive the law of excluded middle...
LISA data analysis using Markov chain Monte Carlo methods
International Nuclear Information System (INIS)
Cornish, Neil J.; Crowder, Jeff
2005-01-01
The Laser Interferometer Space Antenna (LISA) is expected to simultaneously detect many thousands of low-frequency gravitational wave signals. This presents a data analysis challenge that is very different to the one encountered in ground based gravitational wave astronomy. LISA data analysis requires the identification of individual signals from a data stream containing an unknown number of overlapping signals. Because of the signal overlaps, a global fit to all the signals has to be performed in order to avoid biasing the solution. However, performing such a global fit requires the exploration of an enormous parameter space with a dimension upwards of 50 000. Markov Chain Monte Carlo (MCMC) methods offer a very promising solution to the LISA data analysis problem. MCMC algorithms are able to efficiently explore large parameter spaces, simultaneously providing parameter estimates, error analysis, and even model selection. Here we present the first application of MCMC methods to simulated LISA data and demonstrate the great potential of the MCMC approach. Our implementation uses a generalized F-statistic to evaluate the likelihoods, and simulated annealing to speed convergence of the Markov chains. As a final step we supercool the chains to extract maximum likelihood estimates, and estimates of the Bayes factors for competing models. We find that the MCMC approach is able to correctly identify the number of signals present, extract the source parameters, and return error estimates consistent with Fisher information matrix predictions
Liquid-liquid phase transition in Stillinger-Weber silicon
International Nuclear Information System (INIS)
Beaucage, Philippe; Mousseau, Normand
2005-01-01
It was recently demonstrated that Stillinger-Weber silicon undergoes a liquid-liquid first-order phase transition deep into the supercooled region (Sastry and Angell 2003 Nat. Mater. 2 739). Here we study the effects of perturbations on this phase transition. We show that the order of the liquid-liquid transition changes with negative pressure. We also find that the liquid-liquid transition disappears when the three-body term of the potential is strengthened by as little as 5%. This implies that the details of the potential could affect strongly the nature and even the existence of the liquid-liquid phase
Analysis of supercooling activity of tannin-related polyphenols.
Kuwabara, Chikako; Wang, Donghui; Endoh, Keita; Fukushi, Yukiharu; Arakawa, Keita; Fujikawa, Seizo
2013-08-01
Based on the discovery of novel supercooling-promoting hydrolyzable gallotannins from deep supercooling xylem parenchyma cells (XPCs) in Katsura tree (see Wang et al. (2012) [38]), supercooling capability of a wide variety of tannin-related polyphenols (TRPs) was examined in order to find more effective supercooling-promoting substances for their applications. The TRPs examined were single compounds including six kinds of hydrolyzable tannins, 11 kinds of catechin derivatives, two kinds of structural analogs of catechin and six kinds of phenolcarboxylic acid derivatives, 11 kinds of polyphenol mixtures and five kinds of crude plant tannin extracts. The effects of these TRPs on freezing were examined by droplet freezing assays using various solutions containing different kinds of identified ice nucleators such as the ice nucleation bacterium (INB) Erwinia ananas, the INB Xanthomonas campestris, silver iodide and phloroglucinol as well as a solution containing only unintentionally included unidentified airborne ice nucleators. Among the 41 kinds of TRPs examined, all of the hydrolyzable tannins, catechin derivatives, polyphenol mixtures and crude plant tannin extracts as well as a few structural analogs of catechin and phenolcarboxylic acid derivatives exhibited supercooling-promoting activity (SCA) with significant differences (p>0.05) from at least one of the solutions containing different kinds of ice nucleators. It should be noted that there were no TRPs exhibiting ice nucleation-enhancing activity (INA) in all solutions containing identified ice nucleators, whereas there were many TRPs exhibiting INA with significant differences in solutions containing unidentified ice nucleators alone. An emulsion freezing assay confirmed that these TRPs did not essentially affect homogeneous ice nucleation temperatures. It is thought that not only SCA but also INA in the TRPs are produced by interactions with heterogeneous ice nucleators, not by direct interaction with water
Evaluating the Liquid Liquid Phase Transition Hypothesis of Supercoooled Water
Limmer, David; Chandler, David
2011-03-01
To explain the anomalous behavior of supercooled water it has been conjectured that buried within an experimentally inaccessible region of liquid water's phase diagram there exists a second critical point, which is the terminus of a first order transition line between two distinct liquid phases. The so-called liquid-liquid phase transition (LLPT) has since generated much study, though to date there is no consensus on its existence. In this talk, we will discuss our efforts to systematically study the metastable phase diagram of supercooled water through computer simulation. By employing importance-sampling techniques, we have calculated free energies as a function of the density and long-range order to determine unambiguously if two distinct liquid phases exist. We will argue that, contrary to the LLPT hypothesis, the observed phenomenology can be understood as a consequence of the limit of stability of the liquid far away from coexistence. Our results suggest that homogeneous nucleation is the cause of the increased fluctuations present upon supercooling. Further we will show how this understanding can be extended to explain experimental observations of hysteresis in confined supercooled water systems.
Nonlinear Markov processes: Deterministic case
International Nuclear Information System (INIS)
Frank, T.D.
2008-01-01
Deterministic Markov processes that exhibit nonlinear transition mechanisms for probability densities are studied. In this context, the following issues are addressed: Markov property, conditional probability densities, propagation of probability densities, multistability in terms of multiple stationary distributions, stability analysis of stationary distributions, and basin of attraction of stationary distribution
Constructing Dynamic Event Trees from Markov Models
International Nuclear Information System (INIS)
Paolo Bucci; Jason Kirschenbaum; Tunc Aldemir; Curtis Smith; Ted Wood
2006-01-01
In the probabilistic risk assessment (PRA) of process plants, Markov models can be used to model accurately the complex dynamic interactions between plant physical process variables (e.g., temperature, pressure, etc.) and the instrumentation and control system that monitors and manages the process. One limitation of this approach that has prevented its use in nuclear power plant PRAs is the difficulty of integrating the results of a Markov analysis into an existing PRA. In this paper, we explore a new approach to the generation of failure scenarios and their compilation into dynamic event trees from a Markov model of the system. These event trees can be integrated into an existing PRA using software tools such as SAPHIRE. To implement our approach, we first construct a discrete-time Markov chain modeling the system of interest by: (a) partitioning the process variable state space into magnitude intervals (cells), (b) using analytical equations or a system simulator to determine the transition probabilities between the cells through the cell-to-cell mapping technique, and, (c) using given failure/repair data for all the components of interest. The Markov transition matrix thus generated can be thought of as a process model describing the stochastic dynamic behavior of the finite-state system. We can therefore search the state space starting from a set of initial states to explore all possible paths to failure (scenarios) with associated probabilities. We can also construct event trees of arbitrary depth by tracing paths from a chosen initiating event and recording the following events while keeping track of the probabilities associated with each branch in the tree. As an example of our approach, we use the simple level control system often used as benchmark in the literature with one process variable (liquid level in a tank), and three control units: a drain unit and two supply units. Each unit includes a separate level sensor to observe the liquid level in the tank
International Nuclear Information System (INIS)
Floriani, Elena; Lima, Ricardo; Ourrad, Ouerdia; Spinelli, Lionel
2016-01-01
Highlights: • The flux through a Markov chain of a conserved quantity (mass) is studied. • Mass is supplied by an external source and ends in the absorbing states of the chain. • Meaningful for modeling open systems whose dynamics has a Markov property. • The analytical expression of mass distribution is given for a constant source. • The expression of mass distribution is given for periodic or random sources. - Abstract: In this paper we study the flux through a finite Markov chain of a quantity, that we will call mass, which moves through the states of the chain according to the Markov transition probabilities. Mass is supplied by an external source and accumulates in the absorbing states of the chain. We believe that studying how this conserved quantity evolves through the transient (non-absorbing) states of the chain could be useful for the modelization of open systems whose dynamics has a Markov property.
Marco-Jimenez, F; Jimenez-Trigos, E; Lavara, R; Vicente, J S
2014-01-01
Ice growth and recrystallisation are considered important factors in determining vitrification outcomes. Synthetic polymers inhibit ice formation during cooling or warming of the vitrification process. The aim of this study was to assess the effect of adding commercially available synthetic polymers SuperCool X-1000 and SuperCool Z-1000 to vitrification media on in vivo development competence of rabbit embryos. Four hundred and thirty morphologically normal embryos recovered at 72 h of gestation were used. The vitrification media contained 20% dimethyl sulphoxide and 20% ethylene glycol, either alone or in combination with 1% of SuperCool X-1000 and 1% SuperCool. Our results show that embryos can be successfully vitrified using SuperCool X-1000 and SuperCool Z-1000 and when embryos are transferred, live offspring can be successfully produced. In conclusion, our results demonstrated that we succeeded for the first time in obtaining live offspring after vitrification of embryos using SuperCool X-1000 and SuperCool Z-1000 polymers.
Decompression-induced melting of ice IV and the liquid-liquid transition in water
Mishima, Osamu; Stanley, H. Eugene
1998-03-01
Although liquid water has been the focus of intensive research for over 100 years, a coherent physical picture that unifies all of the known anomalies of this liquid, is still lacking. Some of these anomalies occur in the supercooled region, and have been rationalized on the grounds of a possible retracing of the liquid-gas spinodal (metastability limit) line into the supercooled liquid region, or alternatively the presence of a line of first-order liquid-liquid phase transitions in this region which ends in a critical point,. But these ideas remain untested experimentally, in part because supercooled water can be probed only above the homogeneous nucleation temperature TH at which water spontaneously crystallizes. Here we report an experimental approach that is not restricted by the barrier imposed by TH, involving measurement of the decompression-induced melting curves of several high-pressure phases of ice in small emulsified droplets. We find that the melting curve for ice IV seems to undergo a discontinuity at precisely the location proposed for the line of liquid-liquid phase transitions. This is consistent with, but does not prove, the coexistence of two different phases of (supercooled) liquid water. From the experimental data we calculate a possible Gibbs potential surface and a corresponding equation of state for water, from the forms of which we estimate the coordinates of the liquid-liquid critical point to be at pressure Pc ~ 0.1GPa and temperature Tc ~ 220K.
Regeneration and general Markov chains
Directory of Open Access Journals (Sweden)
Vladimir V. Kalashnikov
1994-01-01
Full Text Available Ergodicity, continuity, finite approximations and rare visits of general Markov chains are investigated. The obtained results permit further quantitative analysis of characteristics, such as, rates of convergence, continuity (measured as a distance between perturbed and non-perturbed characteristics, deviations between Markov chains, accuracy of approximations and bounds on the distribution function of the first visit time to a chosen subset, etc. The underlying techniques use the embedding of the general Markov chain into a wide sense regenerative process with the help of splitting construction.
Markov chains theory and applications
Sericola, Bruno
2013-01-01
Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest.The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the
Quadratic Variation by Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard; Horel, Guillaume
We introduce a novel estimator of the quadratic variation that is based on the the- ory of Markov chains. The estimator is motivated by some general results concerning filtering contaminated semimartingales. Specifically, we show that filtering can in prin- ciple remove the effects of market...... microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the dis- crete Markov chain model that is well suited for the analysis of financial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analyti...
Effects of poly-vinyl alcohol on supercooling phenomena of water
Energy Technology Data Exchange (ETDEWEB)
Kumano, Hiroyuki; Hirata, Tetsuo; Kudoh, Tomoya [Department of Mechanical Systems Engineering, Shinshu University, 4-17-1, Wakasato, Nagano City, 380-8553 (Japan)
2009-05-15
The effects of a polymer additive on the supercooling of water were investigated experimentally. Poly-vinyl alcohols (PVAs) were used as the additives, and samples were prepared by dissolving the PVA in water. Since the characteristics of PVA are decided by its degrees of polymerization and saponification, these were varied along with the concentration as the experimental parameters. Moreover, the effect of purity of the water was also considered. Each sample was cooled and the temperature at the instant when ice appeared was measured. Since the freezing of supercooled water is a statistical phenomenon, many experiments were carried out and the average degree of supercooling was obtained. It was found that PVA affects the nucleation of ice in supercooled water and the degree of supercooling increases with the addition of PVA even for water with low purity. The average degree of supercooling increases with an increase in the degree of saponification of PVA. (author)
Markov Chain Monte Carlo Methods
Indian Academy of Sciences (India)
Systat Software Asia-Pacific. Ltd., in Bangalore, where the technical work for the development of the statistical software Systat takes ... In Part 4, we discuss some applications of the Markov ... one can construct the joint probability distribution of.
Reviving Markov processes and applications
International Nuclear Information System (INIS)
Cai, H.
1988-01-01
In this dissertation we study a procedure which restarts a Markov process when the process is killed by some arbitrary multiplicative functional. The regenerative nature of this revival procedure is characterized through a Markov renewal equation. An interesting duality between the revival procedure and the classical killing operation is found. Under the condition that the multiplicative functional possesses an intensity, the generators of the revival process can be written down explicitly. An intimate connection is also found between the perturbation of the sample path of a Markov process and the perturbation of a generator (in Kato's sense). The applications of the theory include the study of the processes like piecewise-deterministic Markov process, virtual waiting time process and the first entrance decomposition (taboo probability)
Confluence reduction for Markov automata
Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models
Confluence Reduction for Markov Automata
Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Braberman, Victor; Fribourg, Laurent
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models
Kim, Yiseul; Hong, Geun-Pyo
2016-01-01
This study investigated the effects of artificial supercooling followed by still air freezing (SSF) on the qualities of pork loin. The qualities of pork frozen by SSF were compared with the fresh control (CT, stored at 4? for 24 h), slow freezing (SAF, still air freezing) and rapid freezing (EIF, ethanol immersion freezing) treatments. Compared with no supercooling phenomena of SAF and EIF, the extent of supercooling obtained by SSF treatment was 1.4?. Despite that SSF was conducted with the ...
Rotational dynamics in supercooled water from nuclear spin relaxation and molecular simulations.
Qvist, Johan; Mattea, Carlos; Sunde, Erik P; Halle, Bertil
2012-05-28
Structural dynamics in liquid water slow down dramatically in the supercooled regime. To shed further light on the origin of this super-Arrhenius temperature dependence, we report high-precision (17)O and (2)H NMR relaxation data for H(2)O and D(2)O, respectively, down to 37 K below the equilibrium freezing point. With the aid of molecular dynamics (MD) simulations, we provide a detailed analysis of the rotational motions probed by the NMR experiments. The NMR-derived rotational correlation time τ(R) is the integral of a time correlation function (TCF) that, after a subpicosecond librational decay, can be described as a sum of two exponentials. Using a coarse-graining algorithm to map the MD trajectory on a continuous-time random walk (CTRW) in angular space, we show that the slowest TCF component can be attributed to large-angle molecular jumps. The mean jump angle is ∼48° at all temperatures and the waiting time distribution is non-exponential, implying dynamical heterogeneity. We have previously used an analogous CTRW model to analyze quasielastic neutron scattering data from supercooled water. Although the translational and rotational waiting times are of similar magnitude, most translational jumps are not synchronized with a rotational jump of the same molecule. The rotational waiting time has a stronger temperature dependence than the translation one, consistent with the strong increase of the experimentally derived product τ(R) D(T) at low temperatures. The present CTRW jump model is related to, but differs in essential ways from the extended jump model proposed by Laage and co-workers. Our analysis traces the super-Arrhenius temperature dependence of τ(R) to the rotational waiting time. We present arguments against interpreting this temperature dependence in terms of mode-coupling theory or in terms of mixture models of water structure.
Empirical Formulae for The Calculation of Austenite Supercooled Transformation Temperatures
Directory of Open Access Journals (Sweden)
Trzaska J.
2015-04-01
Full Text Available The paper presents empirical formulae for the calculation of austenite supercooled transformation temperatures, basing on the chemical composition, austenitising temperature and cooling rate. The multiple regression method was used. Four equations were established allowing to calculate temperature of the start area of ferrite, perlite, bainite and martensite at the given cooling rate. The calculation results obtained do not allow to determine the cooling rate range of ferritic, pearlitic, bainitic and martensite transformations. Classifiers based on logistic regression or neural network were established to solve this problem.
The freezing and supercooling of garlic (Allium sativum L.)
Energy Technology Data Exchange (ETDEWEB)
James, Christian; Seignemartin, Violaine; James, Stephen J. [Food Refrigeration and Process Engineering Research Centre (FRPERC), University of Bristol, Churchill Building, Langford, Bristol BS40 5DU (United Kingdom)
2009-03-15
This work shows that peeled garlic cloves demonstrate significant supercooling during freezing under standard conditions and can be stored at temperatures well below their freezing point (-2.7 C) without freezing. The nucleation point or 'metastable limit temperature' (the point at which ice crystal nucleation is initiated) of peeled garlic cloves was found to be between -7.7 and -14.6 C. Peeled garlic cloves were stored under static air conditions at temperatures between -6 and -9 C for up to 69 h without freezing, and unpeeled whole garlic bulbs and cloves were stored for 1 week at -6 C without freezing. (author)
Maximizing Entropy over Markov Processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2013-01-01
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of an system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code....
Maximizing entropy over Markov processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2014-01-01
The channel capacity of a deterministic system with confidential data is an upper bound on the amount of bits of data an attacker can learn from the system. We encode all possible attacks to a system using a probabilistic specification, an Interval Markov Chain. Then the channel capacity...... as a reward function, a polynomial algorithm to verify the existence of a system maximizing entropy among those respecting a specification, a procedure for the maximization of reward functions over Interval Markov Chains and its application to synthesize an implementation maximizing entropy. We show how...... to use Interval Markov Chains to model abstractions of deterministic systems with confidential data, and use the above results to compute their channel capacity. These results are a foundation for ongoing work on computing channel capacity for abstractions of programs derived from code. © 2014 Elsevier...
Markov Networks in Evolutionary Computation
Shakya, Siddhartha
2012-01-01
Markov networks and other probabilistic graphical modes have recently received an upsurge in attention from Evolutionary computation community, particularly in the area of Estimation of distribution algorithms (EDAs). EDAs have arisen as one of the most successful experiences in the application of machine learning methods in optimization, mainly due to their efficiency to solve complex real-world optimization problems and their suitability for theoretical analysis. This book focuses on the different steps involved in the conception, implementation and application of EDAs that use Markov networks, and undirected models in general. It can serve as a general introduction to EDAs but covers also an important current void in the study of these algorithms by explaining the specificities and benefits of modeling optimization problems by means of undirected probabilistic models. All major developments to date in the progressive introduction of Markov networks based EDAs are reviewed in the book. Hot current researc...
Xia, Ted
2010-01-01
This thesis presents two lines of research. On the one hand, we investigate heterogeneity in supercooled glycerol by means of rheometry, small-angle neutron scattering, and fluorescence imaging. We find from the rheological experiments that supercooled glycerol can behave like weak solids at
Bud primordia of Picea abies, despite a frozen shoot, stay ice free down to -50 °C by a mechanism termed supercooling whose biophysical and biochemical requirements are poorly understood. Bud architecture was assessed by 3D-reconstruction, supercooling and freezing patterns by infrared video thermog...
Comment on "Spontaneous liquid-liquid phase separation of water"
Limmer, David T.; Chandler, David
2015-01-01
Yagasaki et al. [Phys. Rev. E 89, 020301 (2014), 10.1103/PhysRevE.89.020301] present results from a molecular dynamics trajectory illustrating coarsening of ice, which they interpret as evidence of transient coexistence between two distinct supercooled phases of liquid water. We point out that neither two distinct liquids nor criticality are demonstrated in this simulation study. Instead, the illustrated trajectory is consistent with coarsening behaviors analyzed and predicted in earlier work by others.
Comment on "Spontaneous liquid-liquid phase separation of water".
Limmer, David T; Chandler, David
2015-01-01
Yagasaki et al. [Phys. Rev. E 89, 020301 (2014)] present results from a molecular dynamics trajectory illustrating coarsening of ice, which they interpret as evidence of transient coexistence between two distinct supercooled phases of liquid water. We point out that neither two distinct liquids nor criticality are demonstrated in this simulation study. Instead, the illustrated trajectory is consistent with coarsening behaviors analyzed and predicted in earlier work by others.
Deuteron-NMR investigation on the dynamics of supercooled, confined water
Energy Technology Data Exchange (ETDEWEB)
Sattig, Matthias; Vogel, Michael [TU Darmstadt, Institut fuer Festkoerperphysik (Germany)
2013-07-01
The dynamical behaviour of water in the regime of the supercooled liquid is a topic of large interest. In particular, the existence of a fragile-to-strong transition (FST) at T=225K related to the transition between two distinct phases of liquid water is controversially discussed. Due to crystallization the temperature range proposed for the FST is hardly accessible in bulk water. Therefore, we confine heavy water to narrow pores in the mesoporous silicate MCM-41. This suppresses the freezing of a substantial fraction of water, enabling direct investigation of the interesting temperatures. Deuteron-NMR methods are utilised to determine the rotational correlation times τ of water on time scales from ns up to s. The spin-lattice-relaxation time T{sub 1} exhibits a typical minimum at about T = 230 K. Above this minimum the correlation times follow a Vogel-Fulcher-Tammann law. Below the minimum, two relaxation processes could be observed. The low-temperature processes show a different temperature dependence, where the curves τ(T) of all processes intersect at about T = 230 K. A comparison with literature data from neutron scattering and dielectric spectroscopy gives rise to the idea that the observed crossover is due to this intersection of processes rather than to a FST. To test this idea studies on water confined to MCM-41 with different pore sizes and fillings are in progress.
Markov chains and mixing times
Levin, David A; Wilmer, Elizabeth L
2009-01-01
This book is an introduction to the modern approach to the theory of Markov chains. The main goal of this approach is to determine the rate of convergence of a Markov chain to the stationary distribution as a function of the size and geometry of the state space. The authors develop the key tools for estimating convergence times, including coupling, strong stationary times, and spectral methods. Whenever possible, probabilistic methods are emphasized. The book includes many examples and provides brief introductions to some central models of statistical mechanics. Also provided are accounts of r
Markov Models for Handwriting Recognition
Plotz, Thomas
2011-01-01
Since their first inception, automatic reading systems have evolved substantially, yet the recognition of handwriting remains an open research problem due to its substantial variation in appearance. With the introduction of Markovian models to the field, a promising modeling and recognition paradigm was established for automatic handwriting recognition. However, no standard procedures for building Markov model-based recognizers have yet been established. This text provides a comprehensive overview of the application of Markov models in the field of handwriting recognition, covering both hidden
Xylem development in prunus flower buds and the relationship to deep supercooling.
Ashworth, E N
1984-04-01
Xylem development in eight Prunus species was examined and the relationship to deep supercooling assessed. Dormant buds of six species, P. armeniaca, P. avium, P. cerasus, P. persica, P. salicina, and P. sargentii deep supercooled. Xylem vessel elements were not observed within the dormant floral primordia of these species. Instead, discrete bundles containing procambial cells were observed. Vascular differentiation resumed and xylem continuity was established during the time that the capacity to deep supercool was lost. In P. serotina and P. virginiana, two species which do not supercool, xylem vessels ran the length of the inflorescence and presumably provided a conduit for the spread of ice into the bud. The results support the hypothesis that the lack of xylem continuity is an important feature of buds which deep supercool.
Consistency and refinement for Interval Markov Chains
DEFF Research Database (Denmark)
Delahaye, Benoit; Larsen, Kim Guldstrand; Legay, Axel
2012-01-01
Interval Markov Chains (IMC), or Markov Chains with probability intervals in the transition matrix, are the base of a classic specification theory for probabilistic systems [18]. The standard semantics of IMCs assigns to a specification the set of all Markov Chains that satisfy its interval...
Katoen, Joost P.; Maneesh Khattri, M.; Zapreev, I.S.; Zapreev, I.S.
2005-01-01
This short tool paper introduces MRMC, a model checker for discrete-time and continuous-time Markov reward models. It supports reward extensions of PCTL and CSL, and allows for the automated verification of properties concerning long-run and instantaneous rewards as well as cumulative rewards. In
Adaptive Partially Hidden Markov Models
DEFF Research Database (Denmark)
Forchhammer, Søren Otto; Rasmussen, Tage
1996-01-01
Partially Hidden Markov Models (PHMM) have recently been introduced. The transition and emission probabilities are conditioned on the past. In this report, the PHMM is extended with a multiple token version. The different versions of the PHMM are applied to bi-level image coding....
Markov Decision Processes in Practice
Boucherie, Richardus J.; van Dijk, N.M.
2017-01-01
It is over 30 years ago since D.J. White started his series of surveys on practical applications of Markov decision processes (MDP), over 20 years after the phenomenal book by Martin Puterman on the theory of MDP, and over 10 years since Eugene A. Feinberg and Adam Shwartz published their Handbook
A metastable liquid melted from a crystalline solid under decompression
Lin, Chuanlong; Smith, Jesse S.; Sinogeikin, Stanislav V.; Kono, Yoshio; Park, Changyong; Kenney-Benson, Curtis; Shen, Guoyin
2017-01-01
A metastable liquid may exist under supercooling, sustaining the liquid below the melting point such as supercooled water and silicon. It may also exist as a transient state in solid-solid transitions, as demonstrated in recent studies of colloidal particles and glass-forming metallic systems. One important question is whether a crystalline solid may directly melt into a sustainable metastable liquid. By thermal heating, a crystalline solid will always melt into a liquid above the melting point. Here we report that a high-pressure crystalline phase of bismuth can melt into a metastable liquid below the melting line through a decompression process. The decompression-induced metastable liquid can be maintained for hours in static conditions, and transform to crystalline phases when external perturbations, such as heating and cooling, are applied. It occurs in the pressure-temperature region similar to where the supercooled liquid Bi is observed. Akin to supercooled liquid, the pressure-induced metastable liquid may be more ubiquitous than we thought.
Supercooling of aqueous NaCl and KCl solutions under acoustic levitation.
Lü, Y J; Wei, B
2006-10-14
The supercooling capability of aqueous NaCl and KCl solutions is investigated at containerless state by using acoustic levitation method. The supercooling of water is obviously enhanced by the alkali metal ions and increases linearly with the augmentation of concentrations. Furthermore, the supercooling depends on the nature of ions and is 2-3 K larger for NaCl solution than that for KCl solution in the present concentration range: Molecular dynamics simulations are performed to reveal the intrinsic correlation between supercoolability and microstructure. The translational and orientational order parameters are applied to quantitatively demonstrate the effect of ionic concentration on the hydrogen-bond network and ice melting point. The disrupted hydrogen-bond structure determines essentially the concentration dependence of supercooling. On the other hand, the introduced acoustic pressure suppresses the increase of supercooling by promoting the growth and coalescence of microbubbles, the effective nucleation catalysts, in water. However, the dissolved ions can weaken this effect, and moreover the degree varies with the ion type. This results in the different supercoolability for NaCl and KCl solutions under the acoustic levitation conditions.
Seasonal change in the capacity for supercooling by neonatal painted turtles.
Packard, G C; Packard, M J; McDaniel, L L
2001-05-01
Hatchlings of the North American painted turtle (Chrysemys picta) typically spend their first winter of life inside the shallow, subterranean nest where they completed incubation the preceding summer. This facet of their natural history commonly causes neonates in northerly populations to be exposed in mid-winter to ice and cold, which many animals survive by remaining unfrozen and supercooled. We measured the limit of supercooling in samples of turtles taken shortly after hatching and in other samples after 2 months of acclimation (or acclimatization) to a reduced temperature in the laboratory or field. Animals initially had only a limited capacity for supercooling, but they acquired an ability to undergo deeper supercooling during the course of acclimation. The gut of most turtles was packed with particles of soil and eggshell shortly after hatching, but not after acclimation. Thus, the relatively high limit of supercooling for turtles in the days immediately after hatching may have resulted from the ingestion of soil (and associated nucleating agents) by the animals as they were freeing themselves from their eggshell, whereas the relatively low limit of supercooling attained by acclimated turtles may have resulted from their purging their gut of its contents. Parallels may, therefore, exist between the natural-history strategy expressed by hatchling painted turtles and that expressed by numerous terrestrial arthropods that withstand the cold of winter by sustaining a state of supercooling.
Kanno, H.; Kajiwara, K.; Miyata, K.
2010-05-01
Supercooling behavior of aqueous dimethylsulfoxide (DMSO) solution was investigated as a function of DMSO concentration and at high pressures. A linear relationship was observed for TH (homogeneous ice nucleation temperature) and Tm (melting temperature) for the supercooling of aqueous DMSO solution at normal pressure. Analysis of the DTA (differential thermal analysis) traces for homogeneous ice crystallization in the bottom region of the TH curve for a DMSO solution of R =20 (R: moles of water/moles of DMSO) at high pressures supported the contention that the second critical point (SCP) of liquid water should exist at Pc2=˜200 MPa and at Tc2pressure of SCP, Tc2: temperature of SCP). The presence of two TH peaks for DMSO solutions (R =15, 12, and 10) suggests that phase separation occurs in aqueous DMSO solution (R ≤15) at high pressures and low temperatures (pressure dependence of the two TH curves for DMSO solutions of R =10 and 12 indicates that the two phase-separated components in the DMSO solution of R =10 have different liquid water structures [LDL-like and HDL-like structures (LDL: low-density liquid water, HDL: high-density liquid water)] in the pressure range of 120-230 MPa.
Superheating and supercooling of Ge nanocrystals embedded in SiO2
International Nuclear Information System (INIS)
Xu, Q; Sharp, I D; Yuan, C W; Yi, D O; Liao, C Y; Glaeser, A M; Minor, A M; Beeman, J W; Ridgway, M C; Kluth, P; Iii, J W Ager; Chrzan, D C; Haller, E E
2007-01-01
Free-standing nanocrystals exhibit a size-dependant thermodynamic melting point reduction relative to the bulk melting point that is governed by the surface free energy. The presence of an encapsulating matrix, however, alters the interface free energy of nanocrystals and their thermodynamic melting point can either increase or decrease relative to bulk. Furthermore, kinetic contributions can significantly alter the melting behaviours of embedded nanoscale materials. To study the effect of an encapsulating matrix on the melting behaviour of nanocrystals, we performed in situ electron diffraction measurements on Ge nanocrystals embedded in a silicon dioxide matrix. Ge nanocrystals were formed by multi-energy ion implantation into a 500 nm thick silica thin film on a silicon substrate followed by thermal annealing at 900 deg. C for 1 h. We present results demonstrating that Ge nanocrystals embedded in SiO 2 exhibit a 470 K melting/solidification hysteresis that is approximately symmetric about the bulk melting point. This unique behaviour, which is thought to be impossible for bulk materials, is well described using a classical thermodynamic model that predicts both kinetic supercooling and kinetic superheating. The presence of the silica matrix suppresses surface pre-melting of nanocrystals. Therefore, heterogeneous nucleation of both the liquid phase and the solid phase are required during the heating and cooling cycle. The magnitude of melting hysteresis is governed primarily by the value of the liquid Ge/solid Ge interface free energy, whereas the relative values of the solid Ge/matrix and liquid Ge/matrix interface free energies govern the position of the hysteresis loop in absolute temperature
DEFF Research Database (Denmark)
Dannemand, Mark; Johansen, Jakob Berg; Kong, Weiqiang
2016-01-01
Latent heat storage units utilizing stable supercooling of sodium acetate trihydrate (SAT) composites were tested in a laboratory. The stainless steel units were 1.5 m high cylinders with internal heat exchangers of tubes with fins. One unit was tested with 116 kg SAT with 6% extra water. Another...... in the thickened phase change material after melting. The heat content in the fully charged state and the heat released after solidification of the supercooled SAT mixtures at ambient temperature was higher for the unit with the thickened SAT mixture. The heat discharged after solidification of the supercooled SAT...
DEFF Research Database (Denmark)
Dannemand, Mark; Kong, Weiqiang; Fan, Jianhua
2015-01-01
Laboratory test of a long term heat storage module utilizing the principle of stable supercooling of 199.5 kg of sodium acetate water mixture has been carried out. Avoiding phase separation of the incongruently melting salt hydrate by using the extra water principle increased the heat storage...... capacity. An external expansion vessel minimized the pressure built up in the module while heating and reduced the risk of instable supercooling. The module was stable supercooled at indoor ambient temperature for up to two months after which it was discharged. The energy discharged after activating...
Long term thermal energy storage with stable supercooled sodium acetate trihydrate
DEFF Research Database (Denmark)
Dannemand, Mark; Schultz, Jørgen M.; Johansen, Jakob Berg
2015-01-01
Utilizing stable supercooling of sodium acetate trihydrate makes it possible to store thermal energy partly loss free. This principle makes seasonal heat storage in compact systems possible. To keep high and stable energy content and cycling stability phase separation of the storage material must...... it expands and will cause a pressure built up in a closed chamber which might compromise stability of the supercooling. This can be avoided by having an air volume above the phase change material connected to an external pressure less expansion tank. Supercooled sodium acetate trihydrate at 20 °C stores up...
Theory of terahertz electric oscillations by supercooled superconductors
Energy Technology Data Exchange (ETDEWEB)
Mishonov, Todor M; Mishonov, Mihail T [Department of Theoretical Physics, Faculty of Physics, University of Sofia St Kliment Ohridski, 5 J Bourchier Boulevard, 1164 Sofia (Bulgaria); Laboratorium voor Vaste-Stoffysica en Magnetisme, Katholieke Universiteit Leuven, Celestijnenlaan 200 D B-3001 Leuven (Belgium)
2005-11-15
We predict that below T{sub c} a regime of negative differential conductivity (NDC) can be reached. The superconductor should be supercooled to T
Markov chains and mixing times
Levin, David A
2017-01-01
Markov Chains and Mixing Times is a magical book, managing to be both friendly and deep. It gently introduces probabilistic techniques so that an outsider can follow. At the same time, it is the first book covering the geometric theory of Markov chains and has much that will be new to experts. It is certainly THE book that I will use to teach from. I recommend it to all comers, an amazing achievement. -Persi Diaconis, Mary V. Sunseri Professor of Statistics and Mathematics, Stanford University Mixing times are an active research topic within many fields from statistical physics to the theory of algorithms, as well as having intrinsic interest within mathematical probability and exploiting discrete analogs of important geometry concepts. The first edition became an instant classic, being accessible to advanced undergraduates and yet bringing readers close to current research frontiers. This second edition adds chapters on monotone chains, the exclusion process and hitting time parameters. Having both exercises...
Markov Chain Ontology Analysis (MCOA).
Frost, H Robert; McCray, Alexa T
2012-02-03
Biomedical ontologies have become an increasingly critical lens through which researchers analyze the genomic, clinical and bibliographic data that fuels scientific research. Of particular relevance are methods, such as enrichment analysis, that quantify the importance of ontology classes relative to a collection of domain data. Current analytical techniques, however, remain limited in their ability to handle many important types of structural complexity encountered in real biological systems including class overlaps, continuously valued data, inter-instance relationships, non-hierarchical relationships between classes, semantic distance and sparse data. In this paper, we describe a methodology called Markov Chain Ontology Analysis (MCOA) and illustrate its use through a MCOA-based enrichment analysis application based on a generative model of gene activation. MCOA models the classes in an ontology, the instances from an associated dataset and all directional inter-class, class-to-instance and inter-instance relationships as a single finite ergodic Markov chain. The adjusted transition probability matrix for this Markov chain enables the calculation of eigenvector values that quantify the importance of each ontology class relative to other classes and the associated data set members. On both controlled Gene Ontology (GO) data sets created with Escherichia coli, Drosophila melanogaster and Homo sapiens annotations and real gene expression data extracted from the Gene Expression Omnibus (GEO), the MCOA enrichment analysis approach provides the best performance of comparable state-of-the-art methods. A methodology based on Markov chain models and network analytic metrics can help detect the relevant signal within large, highly interdependent and noisy data sets and, for applications such as enrichment analysis, has been shown to generate superior performance on both real and simulated data relative to existing state-of-the-art approaches.
Scaling of viscous dynamics in simple liquids
DEFF Research Database (Denmark)
Bøhling, Lasse; Ingebrigtsen, Trond; Grzybowski, A.
2012-01-01
Supercooled liquids are characterized by relaxation times that increase dramatically by cooling or compression. From a single assumption follows a scaling law according to which the relaxation time is a function of h(ρ) over temperature, where ρ is the density and the function h(ρ) depends on the...
Markov processes characterization and convergence
Ethier, Stewart N
2009-01-01
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists."[A]nyone who works with Markov processes whose state space is uncountably infinite will need this most impressive book as a guide and reference."-American Scientist"There is no question but that space should immediately be reserved for [this] book on the library shelf. Those who aspire to mastery of the contents should also reserve a large number of long winter evenings."-Zentralblatt f?r Mathematik und ihre Grenzgebiete/Mathematics Abstracts"Ethier and Kurtz have produced an excellent treatment of the modern theory of Markov processes that [is] useful both as a reference work and as a graduate textbook."-Journal of Statistical PhysicsMarkov Proce...
Supercooling release of micro-size water droplets on microporous surfaces with cooling
Energy Technology Data Exchange (ETDEWEB)
Park, Chun Wan; Kang, Chae Dong [Chonbuk National University, Jeonju (Korea, Republic of)
2012-06-15
The gas diffusion layer (GDL) of polymer electrolyte membrane fuel cells plays a key role in controlling moisture in these cells. When the GDL is exposed to a cold environment, the water droplets or water nets in the GDL freeze. This work observed the supercooling and freezing behaviors of water droplets under low temperature. A GDL made of carbon fiber was coated with a waterproof material with 0%, 40%, and 60% PTFE (polytetrafluoroethylene) contents. The cooling process was investigated according to temperature, and the water droplets on the GDL were supercooled and frozen. Delay in the supercooling release was correlated with the size of water droplets on the GDL and the coating rate of the layer. Moreover, the supercooling degree of the droplets decreased as the number of freeze thaw cycles in the GDL increased.
Effect of freeze-thaw repetitions upon the supercooling release ability of ice-nucleating bacteria
International Nuclear Information System (INIS)
Tsuchiya, Yooko; Hasegawa, Hiromi; Sasaki, Kazuhiro
2004-01-01
We have studied the durability of ice-nucleating bacteria with a potent supercooling release capacity through repeated freeze-thaw cycles. Through experiment, we confirmed that UV sterilized Erwinia ananas maintains a superior supercooling release capacity at around -1degC through 2000 freeze-thaw cycles. We also found that γ-ray sterilization, which is more suitable than UV for large-scale sterilization treatment, has a similar effect at appropriately selected doses. (author)
Computer simulations of supercooled polymer melts in the bulk and in confined geometry
International Nuclear Information System (INIS)
Baschnagel, J; Varnik, F
2005-01-01
We survey results of computer simulations for the structure and dynamics of supercooled polymer melts and films. Our survey is mainly concerned with features of a coarse grained polymer model-a bead-spring model-in the temperature regime above the critical glass temperature T c of the ideal mode-coupling theory (MCT). We divide our discussion into two parts: a part devoted to bulk properties and a part dealing with thin films. The discussion of the bulk properties focuses on two aspects: a comparison of the simulation results with MCT and an analysis of dynamic heterogeneities. We explain in detail how the analyses are performed and what results may be obtained, and we critically assess their strengths and weaknesses. In discussing the application of MCT we also present first results of a quantitative comparison which does not rely on fits, but exploits static input from the simulation to predict the relaxation dynamics. The second part of this review is devoted to extensions of the simulations from the bulk to thin films. We explore in detail the influence of the boundary condition, imposed by smooth or rough walls, on the structure and dynamics of the polymer melt. Geometric confinement is found to shift the glass transition temperature T g (or T c in our case) relative to the bulk. We compare our and other simulation results for the T g shift with experimental data, briefly survey some theoretical ideas for explaining these shifts and discuss related simulation work on the glass transition of confined liquids. Finally, we also present some technical details of how to perform fits to MCT and give a brief introduction to another approach to the glass transition based on the potential energy landscape of a liquid. (topical review)
Verification of Open Interactive Markov Chains
Brazdil, Tomas; Hermanns, Holger; Krcal, Jan; Kretinsky, Jan; Rehak, Vojtech
2012-01-01
Interactive Markov chains (IMC) are compositional behavioral models extending both labeled transition systems and continuous-time Markov chains. IMC pair modeling convenience - owed to compositionality properties - with effective verification algorithms and tools - owed to Markov properties. Thus far however, IMC verification did not consider compositionality properties, but considered closed systems. This paper discusses the evaluation of IMC in an open and thus compositional interpretation....
Spectral methods for quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Szehr, Oleg
2014-05-08
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
Spectral methods for quantum Markov chains
International Nuclear Information System (INIS)
Szehr, Oleg
2014-01-01
The aim of this project is to contribute to our understanding of quantum time evolutions, whereby we focus on quantum Markov chains. The latter constitute a natural generalization of the ubiquitous concept of a classical Markov chain to describe evolutions of quantum mechanical systems. We contribute to the theory of such processes by introducing novel methods that allow us to relate the eigenvalue spectrum of the transition map to convergence as well as stability properties of the Markov chain.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelli; Robert, Philippe
2012-01-01
If ($C_n$) a Markov chain on a discrete state space $S$, a Markov chain ($C_n, M_n$) on the product space $S \\times S$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain behaves like the original Markov chain and the second component changes only when both
Criterion of Semi-Markov Dependent Risk Model
Institute of Scientific and Technical Information of China (English)
Xiao Yun MO; Xiang Qun YANG
2014-01-01
A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi-Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.
Markov Decision Process Measurement Model.
LaMar, Michelle M
2018-03-01
Within-task actions can provide additional information on student competencies but are challenging to model. This paper explores the potential of using a cognitive model for decision making, the Markov decision process, to provide a mapping between within-task actions and latent traits of interest. Psychometric properties of the model are explored, and simulation studies report on parameter recovery within the context of a simple strategy game. The model is then applied to empirical data from an educational game. Estimates from the model are found to correlate more strongly with posttest results than a partial-credit IRT model based on outcome data alone.
Directory of Open Access Journals (Sweden)
Jean B. Lasserre
2000-01-01
Full Text Available We consider the class of Markov kernels for which the weak or strong Feller property fails to hold at some discontinuity set. We provide a simple necessary and sufficient condition for existence of an invariant probability measure as well as a Foster-Lyapunov sufficient condition. We also characterize a subclass, the quasi (weak or strong Feller kernels, for which the sequences of expected occupation measures share the same asymptotic properties as for (weak or strong Feller kernels. In particular, it is shown that the sequences of expected occupation measures of strong and quasi strong-Feller kernels with an invariant probability measure converge setwise to an invariant measure.
Markov process of muscle motors
International Nuclear Information System (INIS)
Kondratiev, Yu; Pechersky, E; Pirogov, S
2008-01-01
We study a Markov random process describing muscle molecular motor behaviour. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spends an exponential time depending on the state. The thin filament moves at a velocity proportional to the average of all displacements of all motors. We assume that the time which a motor stays in the bound state does not depend on its displacement. Then one can find an exact solution of a nonlinear equation appearing in the limit of an infinite number of motors
Barbu, Vlad
2008-01-01
Semi-Markov processes are much more general and better adapted to applications than the Markov ones because sojourn times in any state can be arbitrarily distributed, as opposed to the geometrically distributed sojourn time in the Markov case. This book concerns with the estimation of discrete-time semi-Markov and hidden semi-Markov processes
Metastable liquid-liquid transition in a molecular model of water
Palmer, Jeremy C.; Martelli, Fausto; Liu, Yang; Car, Roberto; Panagiotopoulos, Athanassios Z.; Debenedetti, Pablo G.
2014-06-01
Liquid water's isothermal compressibility and isobaric heat capacity, and the magnitude of its thermal expansion coefficient, increase sharply on cooling below the equilibrium freezing point. Many experimental, theoretical and computational studies have sought to understand the molecular origin and implications of this anomalous behaviour. Of the different theoretical scenarios put forward, one posits the existence of a first-order phase transition that involves two forms of liquid water and terminates at a critical point located at deeply supercooled conditions. Some experimental evidence is consistent with this hypothesis, but no definitive proof of a liquid-liquid transition in water has been obtained to date: rapid ice crystallization has so far prevented decisive measurements on deeply supercooled water, although this challenge has been overcome recently. Computer simulations are therefore crucial for exploring water's structure and behaviour in this regime, and have shown that some water models exhibit liquid-liquid transitions and others do not. However, recent work has argued that the liquid-liquid transition has been mistakenly interpreted, and is in fact a liquid-crystal transition in all atomistic models of water. Here we show, by studying the liquid-liquid transition in the ST2 model of water with the use of six advanced sampling methods to compute the free-energy surface, that two metastable liquid phases and a stable crystal phase exist at the same deeply supercooled thermodynamic condition, and that the transition between the two liquids satisfies the thermodynamic criteria of a first-order transition. We follow the rearrangement of water's coordination shell and topological ring structure along a thermodynamically reversible path from the low-density liquid to cubic ice. We also show that the system fluctuates freely between the two liquid phases rather than crystallizing. These findings provide unambiguous evidence for a liquid-liquid transition in
Supercooling and cold energy storage characteristics of nano-media in ball-packed porous structures
Directory of Open Access Journals (Sweden)
Zhao Qunzhi
2015-04-01
Full Text Available The presented experiments aimed to study the supercooling and cold-energy storage characteristics of nanofluids and water-based nano-media in ball-packed porous structures (BPS. Titanium dioxide nanoparticles (TiO2 NPs measuring 20nm and 80nm were used as additives and sodium dodecyl benzene sulphonate (SDBS was used as anionic surfactant. The experiments used different concentrations of nanofluid, distilled with BPS of different spherical diameter and different concentrations of nano-media, and were conducted 20 times. Experimental results of supercooling were analysed by statistical methods. Results show that the average and peak supercooling degrees of nanofluids and nano-media in BPS are lower than those of distilled water. For the distilled water in BPS, the supercooling degree decreases on the whole with the decrease of the ball diameter. With the same spherical diameter (8mm of BPS, the supercooling degree of TiO2 NPs measuring 20nm is lower than the supercooling degree of distilled water in BPS. Step-cooling experiments of different concentrations of nanofluids and nano-media in BPS were also conducted. Results showed that phase transition time is reduced because of the presence of TiO2 NPs. The BPS substrate and the NPs enhance the heat transfer. Distilled water with a porous solid base and nanoparticles means the amount of cold-energy storage increases and the supercooling degree and the total time are greatly reduced. The phase transition time of distilled water is about 3.5 times that of nano-media in BPS.
Timed Comparisons of Semi-Markov Processes
DEFF Research Database (Denmark)
Pedersen, Mathias Ruggaard; Larsen, Kim Guldstrand; Bacci, Giorgio
2018-01-01
-Markov processes, and investigate the question of how to compare two semi-Markov processes with respect to their time-dependent behaviour. To this end, we introduce the relation of being “faster than” between processes and study its algorithmic complexity. Through a connection to probabilistic automata we obtain...
Probabilistic Reachability for Parametric Markov Models
DEFF Research Database (Denmark)
Hahn, Ernst Moritz; Hermanns, Holger; Zhang, Lijun
2011-01-01
Given a parametric Markov model, we consider the problem of computing the rational function expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression...
Inhomogeneous Markov point processes by transformation
DEFF Research Database (Denmark)
Jensen, Eva B. Vedel; Nielsen, Linda Stougaard
2000-01-01
We construct parametrized models for point processes, allowing for both inhomogeneity and interaction. The inhomogeneity is obtained by applying parametrized transformations to homogeneous Markov point processes. An interesting model class, which can be constructed by this transformation approach......, is that of exponential inhomogeneous Markov point processes. Statistical inference For such processes is discussed in some detail....
Markov-modulated and feedback fluid queues
Scheinhardt, Willem R.W.
1998-01-01
In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short
Classification Using Markov Blanket for Feature Selection
DEFF Research Database (Denmark)
Zeng, Yifeng; Luo, Jian
2009-01-01
Selecting relevant features is in demand when a large data set is of interest in a classification task. It produces a tractable number of features that are sufficient and possibly improve the classification performance. This paper studies a statistical method of Markov blanket induction algorithm...... for filtering features and then applies a classifier using the Markov blanket predictors. The Markov blanket contains a minimal subset of relevant features that yields optimal classification performance. We experimentally demonstrate the improved performance of several classifiers using a Markov blanket...... induction as a feature selection method. In addition, we point out an important assumption behind the Markov blanket induction algorithm and show its effect on the classification performance....
Quantum Markov Chain Mixing and Dissipative Engineering
DEFF Research Database (Denmark)
Kastoryano, Michael James
2012-01-01
This thesis is the fruit of investigations on the extension of ideas of Markov chain mixing to the quantum setting, and its application to problems of dissipative engineering. A Markov chain describes a statistical process where the probability of future events depends only on the state...... of the system at the present point in time, but not on the history of events. Very many important processes in nature are of this type, therefore a good understanding of their behaviour has turned out to be very fruitful for science. Markov chains always have a non-empty set of limiting distributions...... (stationary states). The aim of Markov chain mixing is to obtain (upper and/or lower) bounds on the number of steps it takes for the Markov chain to reach a stationary state. The natural quantum extensions of these notions are density matrices and quantum channels. We set out to develop a general mathematical...
The Bacterial Sequential Markov Coalescent.
De Maio, Nicola; Wilson, Daniel J
2017-05-01
Bacteria can exchange and acquire new genetic material from other organisms directly and via the environment. This process, known as bacterial recombination, has a strong impact on the evolution of bacteria, for example, leading to the spread of antibiotic resistance across clades and species, and to the avoidance of clonal interference. Recombination hinders phylogenetic and transmission inference because it creates patterns of substitutions (homoplasies) inconsistent with the hypothesis of a single evolutionary tree. Bacterial recombination is typically modeled as statistically akin to gene conversion in eukaryotes, i.e. , using the coalescent with gene conversion (CGC). However, this model can be very computationally demanding as it needs to account for the correlations of evolutionary histories of even distant loci. So, with the increasing popularity of whole genome sequencing, the need has emerged for a faster approach to model and simulate bacterial genome evolution. We present a new model that approximates the coalescent with gene conversion: the bacterial sequential Markov coalescent (BSMC). Our approach is based on a similar idea to the sequential Markov coalescent (SMC)-an approximation of the coalescent with crossover recombination. However, bacterial recombination poses hurdles to a sequential Markov approximation, as it leads to strong correlations and linkage disequilibrium across very distant sites in the genome. Our BSMC overcomes these difficulties, and shows a considerable reduction in computational demand compared to the exact CGC, and very similar patterns in simulated data. We implemented our BSMC model within new simulation software FastSimBac. In addition to the decreased computational demand compared to previous bacterial genome evolution simulators, FastSimBac provides more general options for evolutionary scenarios, allowing population structure with migration, speciation, population size changes, and recombination hotspots. FastSimBac is
Mechanism of Supercooled Water Droplet Breakup near the Leading Edge of an Airfoil
Veras-Alba, Belen; Palacios, Jose; Vargas, Mario; Ruggeri, Charles; Bartkus, Tadas P.
2017-01-01
This work presents the results of an experimental study on supercooled droplet deformation and breakup near the leading edge of an airfoil. The results are compared to prior room temperature droplet deformation results to explore the effects of droplet supercooling. The experiments were conducted in the Adverse Environment Rotor Test Stand (AERTS) at The Pennsylvania State University. An airfoil model placed at the end of the rotor blades mounted onto the hub in the AERTS chamber was moved at speeds ranging between 50 and 80 m/sec. The temperature of the chamber was set at -20°C. A monotonic droplet generator was used to produce droplets that fell from above, perpendicular to the path of the airfoil. The supercooled state of the droplets was determined by measurement of the temperature of the drops at various locations below the droplet generator exit. A temperature prediction code was also used to estimate the temperature of the droplets based on vertical velocity and the distance traveled by droplets from the droplet generator to the airfoil stagnation line. High speed imaging was employed to observe the interaction between the droplets and the airfoil. The high speed imaging provided droplet deformation information as the droplet approached the airfoil near the stagnation line. A tracking software program was used to measure the horizontal and vertical displacement of the droplet against time. It was demonstrated that to compare the effects of water supercooling on droplet deformation, the ratio of the slip velocity and the initial droplet velocity must be equal. A case with equal slip velocity to initial velocity ratios was selected for room temperature and supercooled droplet conditions. The airfoil velocity was 60 m/s and the slip velocity for both sets of data was 40 m/s. In these cases, the deformation of the weakly supercooled and warm droplets did not present different trends. The similar behavior for both environmental conditions indicates that water
2016-01-01
This study investigated the effects of artificial supercooling followed by still air freezing (SSF) on the qualities of pork loin. The qualities of pork frozen by SSF were compared with the fresh control (CT, stored at 4℃ for 24 h), slow freezing (SAF, still air freezing) and rapid freezing (EIF, ethanol immersion freezing) treatments. Compared with no supercooling phenomena of SAF and EIF, the extent of supercooling obtained by SSF treatment was 1.4℃. Despite that SSF was conducted with the same method with SAF, application of artificial supercooling accelerated the phase transition (traverse from -0.6℃ to -5℃) from 3.07 h (SAF) to 2.23 h (SSF). The observation of a microstructure indicated that the SSF prevented tissue damage caused by ice crystallization and maintained the structural integrity. The estimated quality parameters reflected that SSF exhibited superior meat quality compared with slow freezing (SAF). SSF showed better water-holding capacity (lower thawing loss, cooking loss and expressible moisture) and tenderness than SAF, and these quality parameters of SSF were not significantly different with ultra-fast freezing treatment (EIF). Consequently, the results demonstrated that the generation of supercooling followed by conventional freezing potentially had the advantage of minimizing the quality deterioration caused by the slow freezing of meat. PMID:27857541
Kim, Yiseul; Hong, Geun-Pyo
2016-10-31
This study investigated the effects of artificial supercooling followed by still air freezing (SSF) on the qualities of pork loin. The qualities of pork frozen by SSF were compared with the fresh control (CT, stored at 4℃ for 24 h), slow freezing (SAF, still air freezing) and rapid freezing (EIF, ethanol immersion freezing) treatments. Compared with no supercooling phenomena of SAF and EIF, the extent of supercooling obtained by SSF treatment was 1.4℃. Despite that SSF was conducted with the same method with SAF, application of artificial supercooling accelerated the phase transition (traverse from -0.6℃ to -5℃) from 3.07 h (SAF) to 2.23 h (SSF). The observation of a microstructure indicated that the SSF prevented tissue damage caused by ice crystallization and maintained the structural integrity. The estimated quality parameters reflected that SSF exhibited superior meat quality compared with slow freezing (SAF). SSF showed better water-holding capacity (lower thawing loss, cooking loss and expressible moisture) and tenderness than SAF, and these quality parameters of SSF were not significantly different with ultra-fast freezing treatment (EIF). Consequently, the results demonstrated that the generation of supercooling followed by conventional freezing potentially had the advantage of minimizing the quality deterioration caused by the slow freezing of meat.
Experimental evidence for stochastic switching of supercooled phases in NdNiO3 nanostructures
Kumar, Devendra; Rajeev, K. P.; Alonso, J. A.
2018-03-01
A first-order phase transition is a dynamic phenomenon. In a multi-domain system, the presence of multiple domains of coexisting phases averages out the dynamical effects, making it nearly impossible to predict the exact nature of phase transition dynamics. Here, we report the metal-insulator transition in samples of sub-micrometer size NdNiO3 where the effect of averaging is minimized by restricting the number of domains under study. We observe the presence of supercooled metallic phases with supercooling of 40 K or more. The transformation from the supercooled metallic to the insulating state is a stochastic process that happens at different temperatures and times in different experimental runs. The experimental results are understood without incorporating material specific properties, suggesting that the behavior is of universal nature. The size of the sample needed to observe individual switching of supercooled domains, the degree of supercooling, and the time-temperature window of switching are expected to depend on the parameters such as quenched disorder, strain, and magnetic field.
Schmidt games and Markov partitions
International Nuclear Information System (INIS)
Tseng, Jimmy
2009-01-01
Let T be a C 2 -expanding self-map of a compact, connected, C ∞ , Riemannian manifold M. We correct a minor gap in the proof of a theorem from the literature: the set of points whose forward orbits are nondense has full Hausdorff dimension. Our correction allows us to strengthen the theorem. Combining the correction with Schmidt games, we generalize the theorem in dimension one: given a point x 0 in M, the set of points whose forward orbit closures miss x 0 is a winning set. Finally, our key lemma, the no matching lemma, may be of independent interest in the theory of symbolic dynamics or the theory of Markov partitions
The Putative Liquid-Liquid Transition is a Liquid-Solid Transition in Atomistic Models of Water
Chandler, David; Limmer, David
2013-03-01
Our detailed and controlled studies of free energy surfaces for models of water find no evidence for reversible polyamorphism, and a general theoretical analysis of the phase behavior of cold water in nano pores shows that measured behaviors of these systems reflect surface modulation and dynamics of ice, not a liquid-liquid critical point. A few workers reach different conclusions, reporting evidence of a liquid-liquid critical point in computer simulations of supercooled water. In some cases, it appears that these contrary results are based upon simulation algorithms that are inconsistent with principles of statistical mechanics, such as using barostats that do not reproduce the correct distribution of volume fluctuations. In other cases, the results appear to be associated with difficulty equilibrating the supercooled material and mistaking metastability for coarsening of the ordered ice phase. In this case, sufficient information is available for us to reproduce the contrary results and to establish that they are artifacts of finite time sampling. This finding leads us to the conclusion that two distinct, reversible liquid phases do not exist in models of supercooled water.
Development of seasonal heat storage based on stable supercooling of a sodium acetate water mixture
DEFF Research Database (Denmark)
Furbo, Simon; Fan, Jianhua; Andersen, Elsa
2012-01-01
A number of heat storage modules for seasonal heat storages based on stable supercooling of a sodium acetate water mixture have been tested by means of experiments in a heat storage test facility. The modules had different volumes and designs. Further, different methods were used to transfer heat...... to and from the sodium acetate water mixture in the modules. By means of the experiments: • The heat exchange capacity rates to and from the sodium acetate water mixture in the heat storage modules were determined for different volume flow rates. • The heat content of the heat storage modules were determined....... • The reliability of the supercooling was elucidated for the heat storage modules for different operation conditions. • The reliability of a cooling method used to start solidification of the supercooled sodium acetate water mixture was elucidated. The method is making use of boiling CO2 in a small tank in good...
Limited Impact of Subglacial Supercooling Freeze-on for Greenland Ice Sheet Stratigraphy
Dow, Christine F.; Karlsson, Nanna B.; Werder, Mauro A.
2018-02-01
Large units of disrupted radiostratigraphy (UDR) are visible in many radio-echo sounding data sets from the Greenland Ice Sheet. This study investigates whether supercooling freeze-on rates at the bed can cause the observed UDR. We use a subglacial hydrology model to calculate both freezing and melting rates at the base of the ice sheet in a distributed sheet and within basal channels. We find that while supercooling freeze-on is a phenomenon that occurs in many areas of the ice sheet, there is no discernible correlation with the occurrence of UDR. The supercooling freeze-on rates are so low that it would require tens of thousands of years with minimal downstream ice motion to form the hundreds of meters of disrupted radiostratigraphy. Overall, the melt rates at the base of the ice sheet greatly overwhelm the freeze-on rates, which has implications for mass balance calculations of Greenland ice.
Finite Markov processes and their applications
Iosifescu, Marius
2007-01-01
A self-contained treatment of finite Markov chains and processes, this text covers both theory and applications. Author Marius Iosifescu, vice president of the Romanian Academy and director of its Center for Mathematical Statistics, begins with a review of relevant aspects of probability theory and linear algebra. Experienced readers may start with the second chapter, a treatment of fundamental concepts of homogeneous finite Markov chain theory that offers examples of applicable models.The text advances to studies of two basic types of homogeneous finite Markov chains: absorbing and ergodic ch
Markov chains models, algorithms and applications
Ching, Wai-Ki; Ng, Michael K; Siu, Tak-Kuen
2013-01-01
This new edition of Markov Chains: Models, Algorithms and Applications has been completely reformatted as a text, complete with end-of-chapter exercises, a new focus on management science, new applications of the models, and new examples with applications in financial risk management and modeling of financial data.This book consists of eight chapters. Chapter 1 gives a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory will also be highlighted. Some classical iterative methods
Markov chains analytic and Monte Carlo computations
Graham, Carl
2014-01-01
Markov Chains: Analytic and Monte Carlo Computations introduces the main notions related to Markov chains and provides explanations on how to characterize, simulate, and recognize them. Starting with basic notions, this book leads progressively to advanced and recent topics in the field, allowing the reader to master the main aspects of the classical theory. This book also features: Numerous exercises with solutions as well as extended case studies.A detailed and rigorous presentation of Markov chains with discrete time and state space.An appendix presenting probabilistic notions that are nec
Weis, David D; Nardozzi, Jonathan D
2005-04-15
The rate of the alkaline phosphatase-catalyzed hydrolysis of 4-methylumbelliferone phosphate was measured in acoustically levitated droplets of aqueous tris (50 mM) at pH 8.5 at 22 +/- 2 degrees C and in supercooled solution at -6 +/- 2 degrees C. At 22 degrees C, the rate of product formation was in excellent agreement with the rate observed in bulk solution in a cuvette, indicating that the acoustic levitation process does not alter the enzyme activity. The rate of the reaction decreased 6-fold in supercooled solution at -6 +/- 2 degrees C. The acoustic levitator apparatus is described in detail.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelli; Robert, Philippe
Motivated by an original on-line page-ranking algorithm, starting from an arbitrary Markov chain $(C_n)$ on a discrete state space ${\\cal S}$, a Markov chain $(C_n,M_n)$ on the product space ${\\cal S}^2$, the cat and mouse Markov chain, is constructed. The first coordinate of this Markov chain
Qvist, Johan; Schober, Helmut; Halle, Bertil
2011-04-14
One of the outstanding challenges presented by liquid water is to understand how molecules can move on a picosecond time scale despite being incorporated in a three-dimensional network of relatively strong H-bonds. This challenge is exacerbated in the supercooled state, where the dramatic slowing down of structural dynamics is reminiscent of the, equally poorly understood, generic behavior of liquids near the glass transition temperature. By probing single-molecule dynamics on a wide range of time and length scales, quasielastic neutron scattering (QENS) can potentially reveal the mechanistic details of water's structural dynamics, but because of interpretational ambiguities this potential has not been fully realized. To resolve these issues, we present here an extensive set of high-quality QENS data from water in the range 253-293 K and a corresponding set of molecular dynamics (MD) simulations to facilitate and validate the interpretation. Using a model-free approach, we analyze the QENS data in terms of two motional components. Based on the dynamical clustering observed in MD trajectories, we identify these components with two distinct types of structural dynamics: picosecond local (L) structural fluctuations within dynamical basins and slower interbasin jumps (J). The Q-dependence of the dominant QENS component, associated with J dynamics, can be quantitatively rationalized with a continuous-time random walk (CTRW) model with an apparent jump length that depends on low-order moments of the jump length and waiting time distributions. Using a simple coarse-graining algorithm to quantitatively identify dynamical basins, we map the newtonian MD trajectory on a CTRW trajectory, from which the jump length and waiting time distributions are computed. The jump length distribution is gaussian and the rms jump length increases from 1.5 to 1.9 Å as the temperature increases from 253 to 293 K. The rms basin radius increases from 0.71 to 0.75 Å over the same range. The
New Mexico cloud super cooled liquid water survey final report 2009.
Energy Technology Data Exchange (ETDEWEB)
Beavis, Nick; Roskovensky, John K.; Ivey, Mark D.
2010-02-01
Los Alamos and Sandia National Laboratories are partners in an effort to survey the super-cooled liquid water in clouds over the state of New Mexico in a project sponsored by the New Mexico Small Business Assistance Program. This report summarizes the scientific work performed at Sandia National Laboratories during the 2009. In this second year of the project a practical methodology for estimating cloud super-cooled liquid water was created. This was accomplished through the analysis of certain MODIS sensor satellite derived cloud products and vetted parameterizations techniques. A software code was developed to analyze multiple cases automatically. The eighty-one storm events identified in the previous year effort from 2006-2007 were again the focus. Six derived MODIS products were obtained first through careful MODIS image evaluation. Both cloud and clear-sky properties from this dataset were determined over New Mexico. Sensitivity studies were performed that identified the parameters which most influenced the estimation of cloud super-cooled liquid water. Limited validation was undertaken to ensure the soundness of the cloud super-cooled estimates. Finally, a path forward was formulized to insure the successful completion of the initial scientific goals which include analyzing different of annual datasets, validation of the developed algorithm, and the creation of a user-friendly and interactive tool for estimating cloud super-cooled liquid water.
Observation uncertainty in reversible Markov chains.
Metzner, Philipp; Weber, Marcus; Schütte, Christof
2010-09-01
In many applications one is interested in finding a simplified model which captures the essential dynamical behavior of a real life process. If the essential dynamics can be assumed to be (approximately) memoryless then a reasonable choice for a model is a Markov model whose parameters are estimated by means of Bayesian inference from an observed time series. We propose an efficient Monte Carlo Markov chain framework to assess the uncertainty of the Markov model and related observables. The derived Gibbs sampler allows for sampling distributions of transition matrices subject to reversibility and/or sparsity constraints. The performance of the suggested sampling scheme is demonstrated and discussed for a variety of model examples. The uncertainty analysis of functions of the Markov model under investigation is discussed in application to the identification of conformations of the trialanine molecule via Robust Perron Cluster Analysis (PCCA+) .
Generated dynamics of Markov and quantum processes
Janßen, Martin
2016-01-01
This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state. Quantum processes apply to systems where all variables, that control reversibility, are taken as relevant variables, while Markov processes emerge when some of those variables cannot be followed and are thus irrelevant for the dynamic description. Their absence renders the dynamic irreversible. A further aim is to demonstrate that almost any subdiscipline of theoretical physics can conceptually be put in...
Confluence reduction for Markov automata (extended version)
Timmer, Mark; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette
Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models
Semi-Markov Arnason-Schwarz models.
King, Ruth; Langrock, Roland
2016-06-01
We consider multi-state capture-recapture-recovery data where observed individuals are recorded in a set of possible discrete states. Traditionally, the Arnason-Schwarz model has been fitted to such data where the state process is modeled as a first-order Markov chain, though second-order models have also been proposed and fitted to data. However, low-order Markov models may not accurately represent the underlying biology. For example, specifying a (time-independent) first-order Markov process involves the assumption that the dwell time in each state (i.e., the duration of a stay in a given state) has a geometric distribution, and hence that the modal dwell time is one. Specifying time-dependent or higher-order processes provides additional flexibility, but at the expense of a potentially significant number of additional model parameters. We extend the Arnason-Schwarz model by specifying a semi-Markov model for the state process, where the dwell-time distribution is specified more generally, using, for example, a shifted Poisson or negative binomial distribution. A state expansion technique is applied in order to represent the resulting semi-Markov Arnason-Schwarz model in terms of a simpler and computationally tractable hidden Markov model. Semi-Markov Arnason-Schwarz models come with only a very modest increase in the number of parameters, yet permit a significantly more flexible state process. Model selection can be performed using standard procedures, and in particular via the use of information criteria. The semi-Markov approach allows for important biological inference to be drawn on the underlying state process, for example, on the times spent in the different states. The feasibility of the approach is demonstrated in a simulation study, before being applied to real data corresponding to house finches where the states correspond to the presence or absence of conjunctivitis. © 2015, The International Biometric Society.
A Bayesian model for binary Markov chains
Directory of Open Access Journals (Sweden)
Belkheir Essebbar
2004-02-01
Full Text Available This note is concerned with Bayesian estimation of the transition probabilities of a binary Markov chain observed from heterogeneous individuals. The model is founded on the Jeffreys' prior which allows for transition probabilities to be correlated. The Bayesian estimator is approximated by means of Monte Carlo Markov chain (MCMC techniques. The performance of the Bayesian estimates is illustrated by analyzing a small simulated data set.
Bayesian analysis of Markov point processes
DEFF Research Database (Denmark)
Berthelsen, Kasper Klitgaard; Møller, Jesper
2006-01-01
Recently Møller, Pettitt, Berthelsen and Reeves introduced a new MCMC methodology for drawing samples from a posterior distribution when the likelihood function is only specified up to a normalising constant. We illustrate the method in the setting of Bayesian inference for Markov point processes...... a partially ordered Markov point process as the auxiliary variable. As the method requires simulation from the "unknown" likelihood, perfect simulation algorithms for spatial point processes become useful....
Subharmonic projections for a quantum Markov semigroup
International Nuclear Information System (INIS)
Fagnola, Franco; Rebolledo, Rolando
2002-01-01
This article introduces a concept of subharmonic projections for a quantum Markov semigroup, in view of characterizing the support projection of a stationary state in terms of the semigroup generator. These results, together with those of our previous article [J. Math. Phys. 42, 1296 (2001)], lead to a method for proving the existence of faithful stationary states. This is often crucial in the analysis of ergodic properties of quantum Markov semigroups. The method is illustrated by applications to physical models
Transition Effect Matrices and Quantum Markov Chains
Gudder, Stan
2009-06-01
A transition effect matrix (TEM) is a quantum generalization of a classical stochastic matrix. By employing a TEM we obtain a quantum generalization of a classical Markov chain. We first discuss state and operator dynamics for a quantum Markov chain. We then consider various types of TEMs and vector states. In particular, we study invariant, equilibrium and singular vector states and investigate projective, bistochastic, invertible and unitary TEMs.
Energy Technology Data Exchange (ETDEWEB)
Frank, T D [Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269 (United States)
2008-07-18
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
International Nuclear Information System (INIS)
Frank, T D
2008-01-01
We discuss nonlinear Markov processes defined on discrete time points and discrete state spaces using Markov chains. In this context, special attention is paid to the distinction between linear and nonlinear Markov processes. We illustrate that the Chapman-Kolmogorov equation holds for nonlinear Markov processes by a winner-takes-all model for social conformity. (fast track communication)
Markov Processes in Image Processing
Petrov, E. P.; Kharina, N. L.
2018-05-01
Digital images are used as an information carrier in different sciences and technologies. The aspiration to increase the number of bits in the image pixels for the purpose of obtaining more information is observed. In the paper, some methods of compression and contour detection on the basis of two-dimensional Markov chain are offered. Increasing the number of bits on the image pixels will allow one to allocate fine object details more precisely, but it significantly complicates image processing. The methods of image processing do not concede by the efficiency to well-known analogues, but surpass them in processing speed. An image is separated into binary images, and processing is carried out in parallel with each without an increase in speed, when increasing the number of bits on the image pixels. One more advantage of methods is the low consumption of energy resources. Only logical procedures are used and there are no computing operations. The methods can be useful in processing images of any class and assignment in processing systems with a limited time and energy resources.
Adaptive Markov Chain Monte Carlo
Jadoon, Khan
2016-08-08
A substantial interpretation of electromagnetic induction (EMI) measurements requires quantifying optimal model parameters and uncertainty of a nonlinear inverse problem. For this purpose, an adaptive Bayesian Markov chain Monte Carlo (MCMC) algorithm is used to assess multi-orientation and multi-offset EMI measurements in an agriculture field with non-saline and saline soil. In the MCMC simulations, posterior distribution was computed using Bayes rule. The electromagnetic forward model based on the full solution of Maxwell\\'s equations was used to simulate the apparent electrical conductivity measured with the configurations of EMI instrument, the CMD mini-Explorer. The model parameters and uncertainty for the three-layered earth model are investigated by using synthetic data. Our results show that in the scenario of non-saline soil, the parameters of layer thickness are not well estimated as compared to layers electrical conductivity because layer thicknesses in the model exhibits a low sensitivity to the EMI measurements, and is hence difficult to resolve. Application of the proposed MCMC based inversion to the field measurements in a drip irrigation system demonstrate that the parameters of the model can be well estimated for the saline soil as compared to the non-saline soil, and provide useful insight about parameter uncertainty for the assessment of the model outputs.
Fitting Hidden Markov Models to Psychological Data
Directory of Open Access Journals (Sweden)
Ingmar Visser
2002-01-01
Full Text Available Markov models have been used extensively in psychology of learning. Applications of hidden Markov models are rare however. This is partially due to the fact that comprehensive statistics for model selection and model assessment are lacking in the psychological literature. We present model selection and model assessment statistics that are particularly useful in applying hidden Markov models in psychology. These statistics are presented and evaluated by simulation studies for a toy example. We compare AIC, BIC and related criteria and introduce a prediction error measure for assessing goodness-of-fit. In a simulation study, two methods of fitting equality constraints are compared. In two illustrative examples with experimental data we apply selection criteria, fit models with constraints and assess goodness-of-fit. First, data from a concept identification task is analyzed. Hidden Markov models provide a flexible approach to analyzing such data when compared to other modeling methods. Second, a novel application of hidden Markov models in implicit learning is presented. Hidden Markov models are used in this context to quantify knowledge that subjects express in an implicit learning task. This method of analyzing implicit learning data provides a comprehensive approach for addressing important theoretical issues in the field.
DEFF Research Database (Denmark)
Dannemand, Mark; Dragsted, Janne; Fan, Jianhua
2016-01-01
Laboratory tests of two heat storage units based on the principle of stable supercooling of sodium acetate trihydrate (SAT) mixtures were carried out. One unit was filled with 199.5 kg of SAT with 9% extra water to avoid phase separation of the incongruently melting salt hydrate. The other unit...
Crystallization in diblock copolymer thin films at different degrees of supercooling
DEFF Research Database (Denmark)
Darko, C.; Botiz, I.; Reiter, G.
2009-01-01
The crystalline structures in thin films of polystyrene-b-poly(ethylene oxide) (PS-b-PEO) diblock copolymers were studied in dependence on the degree of supercooling. Atomic force microscopy showed that the crystalline domains (lamellae) consist of grains, which are macroscopic at low and interme...
Hoffmann, Nadine; Duft, Denis; Kiselev, Alexei; Leisner, Thomas
2013-04-01
The contact freezing of supercooled cloud droplets is one of the potentially important and the least investigated heterogeneous mechanism of ice formation in the tropospheric clouds [1]. On the time scales of cloud lifetime the freezing of supercooled water droplets via contact mechanism may occur at higher temperature compared to the same IN immersed in the droplet. However, the laboratory experiments of contact freezing are very challenging due to the number of factors affecting the probability of ice formation. In our experiment we study single water droplets freely levitated in the laminar flow of mineral dust particles acting as the contact freezing nuclei. By repeating the freezing experiment sufficient number of times we are able to reproduce statistical freezing behavior of large ensembles of supercooled droplets and measure the average rate of freezing events. We show that the rate of freezing at given temperature is governed only by the rate of droplet -particle collision and by the properties of the contact ice nuclei. In this contribution we investigate the relationship between the freezing probability and the size of mineral dust particle (represented by illite) and show that their IN efficiency scales with the particle size. Based on this observation, we discuss the similarity between the freezing of supercooled water droplets in immersion and contact modes and possible mechanisms of apparent enhancement of the contact freezing efficiency. [1] - K.C. Young, The role of contact nucleation in ice phase initiation in clouds, Journal of the Atmospheric Sciences 31, 1974
Costanzo, Jon P; Baker, Patrick J; Dinkelacker, Stephen A; Lee, Richard E
2003-02-01
Hatchlings of the painted turtle (Chrysemys picta) commonly hibernate in their shallow, natal nests. Survival at temperatures below the limit of freeze tolerance (approximately -4 degrees C) apparently depends on their ability to remain supercooled, and, whereas previous studies have reported that supercooling capacity improves markedly with cold acclimation, the mechanistic basis for this change is incompletely understood. We report that the crystallization temperature (T(c)) of recently hatched (summer) turtles acclimated to 22 degrees C and reared on a substratum of vermiculite or nesting soil was approximately 5 degrees C higher than the T(c) determined for turtles acclimated to 4 degrees C and tested in winter. This increase in supercooling capacity coincided with elimination of substratum (and, in fewer cases, eggshell) that the hatchlings had ingested; however, this association was not necessarily causal because turtles reared on a paper-covered substratum did not ingest exogenous matter but nevertheless showed a similar increase in supercooling capacity. Our results for turtles reared on paper revealed that seasonal development of supercooling capacity fundamentally requires elimination of ice-nucleating agents (INA) of endogenous origin: summer turtles, but not winter turtles, produced feces (perhaps derived from residual yolk) that expressed ice-nucleating activity. Ingestion of vermiculite or eggshell, which had modest ice-nucleating activity, had no effect on the T(c), whereas ingestion of nesting soil, which contained two classes of potent INA, markedly reduced the supercooling capacity of summer turtles. This effect persisted long after the turtles had purged their guts of soil particles, because the T(c) of winter turtles reared on nesting soil (mean +/- S.E.M.=-11.6+/-1.4 degrees C) was approximately 6 degrees C higher than the T(c) of winter turtles reared on vermiculite or paper. Experiments in which winter turtles were fed INA commonly found in
Influence of Nanoparticles and Graphite Foam on the Supercooling of Acetamide
International Nuclear Information System (INIS)
Yu, J.; Chen, X.; Ma, X.; Song, Q.; Zhao, Y.; Cao, J.
2014-01-01
Acetamide is a promising phase change materials (PCMs) for thermal storage,but the large supercooling during the freezing process has limited its application. In this study, we prepared acetamide-SiO 2 composites by adding nano-SiO 2 into acetamide. This modified PCM was then impregnated into the porous graphite foam forming acetamide-SiO 2 -graphite foam form-stable composites. These composites were subjected to melting-solidification cycles 50 times; the time-temperature curves were tracked and recorded during these cycles. The time-temperature curves showed that, for the acetamide containing 2 wt. % SiO 2 , the supercooling phenomenon was eliminated and the material’s performance was stable for 50 cycles. The solidification temperature of the acetamide-SiO 2 -graphite foam samples was 65°C and the melting temperature was lowered to 65°C. The samples exhibited almost no supercooling and the presence of SiO 2 had no significant effect on the melting-solidification temperature. The microscopic supercooling of the acetamide-SiO 2 composite was measured using differential scanning calorimetry (DSC). The results indicated that when the content of SiO 2 was 1 wt. to 2 wt. %, the supercooling could be reduced to less than 10°C and heat was sufficiently released during solidification. Finally, a set of algorithms was derived using MATLAB software for simulating the crystallization of samples based on the classical nucleation theory. The results of the simulation agreed with the experiment results.
Influence of Nanoparticles and Graphite Foam on the Supercooling of Acetamide
Directory of Open Access Journals (Sweden)
Jia Yu
2014-01-01
Full Text Available Acetamide is a promising phase change materials (PCMs for thermal storage,but the large supercooling during the freezing process has limited its application. In this study, we prepared acetamide-SiO2 composites by adding nano-SiO2 into acetamide. This modified PCM was then impregnated into the porous graphite foam forming acetamide-SiO2-graphite foam form-stable composites. These composites were subjected to melting-solidification cycles 50 times; the time-temperature curves were tracked and recorded during these cycles. The time-temperature curves showed that, for the acetamide containing 2 wt. % SiO2, the supercooling phenomenon was eliminated and the material’s performance was stable for 50 cycles. The solidification temperature of the acetamide-SiO2-graphite foam samples was 65°C and the melting temperature was lowered to 65°C. The samples exhibited almost no supercooling and the presence of SiO2 had no significant effect on the melting-solidification temperature. The microscopic supercooling of the acetamide-SiO2 composite was measured using differential scanning calorimetry (DSC. The results indicated that when the content of SiO2 was 1 wt. to 2 wt. %, the supercooling could be reduced to less than 10°C and heat was sufficiently released during solidification. Finally, a set of algorithms was derived using MATLAB software for simulating the crystallization of samples based on the classical nucleation theory. The results of the simulation agreed with the experiment results.
International Nuclear Information System (INIS)
Tang, Xiaofen; Li, Wei; Zhang, Xingxiang; Shi, Haifeng
2014-01-01
Microencapsulated phase change material with a low supercooling degree is one of the increasing important researches as well as industrial application for thermal energy storage. This study develops a novel and low supercooling microencapsulated n-octadecane (MicroC18) with n-octadecyl methacrylate (ODMA)–methacrylic acid (MAA) copolymer as shell using suspension-like polymerization. The fabrication and properties of MicroC18 were characterized by using a field-emission scanning electron microscope (FE-SEM), Fourier transformed infrared spectroscopy (FTIR), particle size distribution analysis, differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA). The MicroC18 with spherical shapes and an average diameter of 1.60–1.68 μm are fabricated. The onset crystallizing temperatures of MicroC18 are only 4 °C below that of n-octadecane. The unique copolymer shell has a significant impact on the low supercooling of MicroC18. The n-octadecane in all of the samples crystalizes by heterogeneous nucleation. The content of n-octadecane in the microcapsules is low; however, the microcapsules still exhibit high enthalpy through the contribution of the shells. At a monomers/n-octadecane mass ratio is 2:1, as used in the recipes, the MicroC18 with highest phase change enthalpy was obtained. The temperature of thermal resistant of MicroC18 is approximately 235.6 °C, which is affected by the thickness of the polymer shell. - Highlights: • Microencapsulated n-octadecane with comb-like copolymer shell has low supercooling. • The unique shell plays a significant role in suppressing supercooling. • The types of cross-linker affect morphologies and heat enthalpies of microcapsules. • Microcapsules exhibit high phase change enthalpies and thermal stabilities
Zipf exponent of trajectory distribution in the hidden Markov model
Bochkarev, V. V.; Lerner, E. Yu
2014-03-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.
Zipf exponent of trajectory distribution in the hidden Markov model
International Nuclear Information System (INIS)
Bochkarev, V V; Lerner, E Yu
2014-01-01
This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different
Performance Modeling of Communication Networks with Markov Chains
Mo, Jeonghoon
2010-01-01
This book is an introduction to Markov chain modeling with applications to communication networks. It begins with a general introduction to performance modeling in Chapter 1 where we introduce different performance models. We then introduce basic ideas of Markov chain modeling: Markov property, discrete time Markov chain (DTMe and continuous time Markov chain (CTMe. We also discuss how to find the steady state distributions from these Markov chains and how they can be used to compute the system performance metric. The solution methodologies include a balance equation technique, limiting probab
The putative liquid-liquid transition is a liquid-solid transition in atomistic models of water. II
Limmer, David T.; Chandler, David
2013-06-01
This paper extends our earlier studies of free energy functions of density and crystalline order parameters for models of supercooled water, which allows us to examine the possibility of two distinct metastable liquid phases [D. T. Limmer and D. Chandler, J. Chem. Phys. 135, 134503 (2011), 10.1063/1.3643333 and preprint arXiv:1107.0337 (2011)]. Low-temperature reversible free energy surfaces of several different atomistic models are computed: mW water, TIP4P/2005 water, Stillinger-Weber silicon, and ST2 water, the last of these comparing three different treatments of long-ranged forces. In each case, we show that there is one stable or metastable liquid phase, and there is an ice-like crystal phase. The time scales for crystallization in these systems far exceed those of structural relaxation in the supercooled metastable liquid. We show how this wide separation in time scales produces an illusion of a low-temperature liquid-liquid transition. The phenomenon suggesting metastability of two distinct liquid phases is actually coarsening of the ordered ice-like phase, which we elucidate using both analytical theory and computer simulation. For the latter, we describe robust methods for computing reversible free energy surfaces, and we consider effects of electrostatic boundary conditions. We show that sensible alterations of models and boundary conditions produce no qualitative changes in low-temperature phase behaviors of these systems, only marginal changes in equations of state. On the other hand, we show that altering sampling time scales can produce large and qualitative non-equilibrium effects. Recent reports of evidence of a liquid-liquid critical point in computer simulations of supercooled water are considered in this light.
The putative liquid-liquid transition is a liquid-solid transition in atomistic models of water. II
International Nuclear Information System (INIS)
Limmer, David T.; Chandler, David
2013-01-01
This paper extends our earlier studies of free energy functions of density and crystalline order parameters for models of supercooled water, which allows us to examine the possibility of two distinct metastable liquid phases [D. T. Limmer and D. Chandler, J. Chem. Phys.135, 134503 (2011) and preprint http://arxiv.org/abs/arXiv:1107.0337 (2011)]. Low-temperature reversible free energy surfaces of several different atomistic models are computed: mW water, TIP4P/2005 water, Stillinger-Weber silicon, and ST2 water, the last of these comparing three different treatments of long-ranged forces. In each case, we show that there is one stable or metastable liquid phase, and there is an ice-like crystal phase. The time scales for crystallization in these systems far exceed those of structural relaxation in the supercooled metastable liquid. We show how this wide separation in time scales produces an illusion of a low-temperature liquid-liquid transition. The phenomenon suggesting metastability of two distinct liquid phases is actually coarsening of the ordered ice-like phase, which we elucidate using both analytical theory and computer simulation. For the latter, we describe robust methods for computing reversible free energy surfaces, and we consider effects of electrostatic boundary conditions. We show that sensible alterations of models and boundary conditions produce no qualitative changes in low-temperature phase behaviors of these systems, only marginal changes in equations of state. On the other hand, we show that altering sampling time scales can produce large and qualitative non-equilibrium effects. Recent reports of evidence of a liquid-liquid critical point in computer simulations of supercooled water are considered in this light
The putative liquid-liquid transition is a liquid-solid transition in atomistic models of water. II
Energy Technology Data Exchange (ETDEWEB)
Limmer, David T.; Chandler, David, E-mail: chandler@berkeley.edu [Department of Chemistry, University of California, Berkeley, California 94720 (United States)
2013-06-07
This paper extends our earlier studies of free energy functions of density and crystalline order parameters for models of supercooled water, which allows us to examine the possibility of two distinct metastable liquid phases [D. T. Limmer and D. Chandler, J. Chem. Phys.135, 134503 (2011) and preprint http://arxiv.org/abs/arXiv:1107.0337 (2011)]. Low-temperature reversible free energy surfaces of several different atomistic models are computed: mW water, TIP4P/2005 water, Stillinger-Weber silicon, and ST2 water, the last of these comparing three different treatments of long-ranged forces. In each case, we show that there is one stable or metastable liquid phase, and there is an ice-like crystal phase. The time scales for crystallization in these systems far exceed those of structural relaxation in the supercooled metastable liquid. We show how this wide separation in time scales produces an illusion of a low-temperature liquid-liquid transition. The phenomenon suggesting metastability of two distinct liquid phases is actually coarsening of the ordered ice-like phase, which we elucidate using both analytical theory and computer simulation. For the latter, we describe robust methods for computing reversible free energy surfaces, and we consider effects of electrostatic boundary conditions. We show that sensible alterations of models and boundary conditions produce no qualitative changes in low-temperature phase behaviors of these systems, only marginal changes in equations of state. On the other hand, we show that altering sampling time scales can produce large and qualitative non-equilibrium effects. Recent reports of evidence of a liquid-liquid critical point in computer simulations of supercooled water are considered in this light.
The putative liquid-liquid transition is a liquid-solid transition in atomistic models of water. II.
Limmer, David T; Chandler, David
2013-06-07
This paper extends our earlier studies of free energy functions of density and crystalline order parameters for models of supercooled water, which allows us to examine the possibility of two distinct metastable liquid phases [D. T. Limmer and D. Chandler, J. Chem. Phys. 135, 134503 (2011) and preprint arXiv:1107.0337 (2011)]. Low-temperature reversible free energy surfaces of several different atomistic models are computed: mW water, TIP4P/2005 water, Stillinger-Weber silicon, and ST2 water, the last of these comparing three different treatments of long-ranged forces. In each case, we show that there is one stable or metastable liquid phase, and there is an ice-like crystal phase. The time scales for crystallization in these systems far exceed those of structural relaxation in the supercooled metastable liquid. We show how this wide separation in time scales produces an illusion of a low-temperature liquid-liquid transition. The phenomenon suggesting metastability of two distinct liquid phases is actually coarsening of the ordered ice-like phase, which we elucidate using both analytical theory and computer simulation. For the latter, we describe robust methods for computing reversible free energy surfaces, and we consider effects of electrostatic boundary conditions. We show that sensible alterations of models and boundary conditions produce no qualitative changes in low-temperature phase behaviors of these systems, only marginal changes in equations of state. On the other hand, we show that altering sampling time scales can produce large and qualitative non-equilibrium effects. Recent reports of evidence of a liquid-liquid critical point in computer simulations of supercooled water are considered in this light.
Coding with partially hidden Markov models
DEFF Research Database (Denmark)
Forchhammer, Søren; Rissanen, J.
1995-01-01
Partially hidden Markov models (PHMM) are introduced. They are a variation of the hidden Markov models (HMM) combining the power of explicit conditioning on past observations and the power of using hidden states. (P)HMM may be combined with arithmetic coding for lossless data compression. A general...... 2-part coding scheme for given model order but unknown parameters based on PHMM is presented. A forward-backward reestimation of parameters with a redefined backward variable is given for these models and used for estimating the unknown parameters. Proof of convergence of this reestimation is given....... The PHMM structure and the conditions of the convergence proof allows for application of the PHMM to image coding. Relations between the PHMM and hidden Markov models (HMM) are treated. Results of coding bi-level images with the PHMM coding scheme is given. The results indicate that the PHMM can adapt...
Markov and mixed models with applications
DEFF Research Database (Denmark)
Mortensen, Stig Bousgaard
This thesis deals with mathematical and statistical models with focus on applications in pharmacokinetic and pharmacodynamic (PK/PD) modelling. These models are today an important aspect of the drug development in the pharmaceutical industry and continued research in statistical methodology within...... or uncontrollable factors in an individual. Modelling using SDEs also provides new tools for estimation of unknown inputs to a system and is illustrated with an application to estimation of insulin secretion rates in diabetic patients. Models for the eect of a drug is a broader area since drugs may affect...... for non-parametric estimation of Markov processes are proposed to give a detailed description of the sleep process during the night. Statistically the Markov models considered for sleep states are closely related to the PK models based on SDEs as both models share the Markov property. When the models...
Consistent Estimation of Partition Markov Models
Directory of Open Access Journals (Sweden)
Jesús E. García
2017-04-01
Full Text Available The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns.
Pinney, Rhiannon; Liverpool, Tanniemola B; Royall, C Patrick
2016-12-21
We consider a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of particles organized into icosahedra under simple steady state shear. We recast this glassformer as an effective system of icosahedra [Pinney et al., J. Chem. Phys. 143, 244507 (2015)]. From the observed population of icosahedra in each steady state, we obtain an effective temperature which is linearly dependent on the shear rate in the range considered. Upon shear banding, the system separates into a region of high shear rate and a region of low shear rate. The effective temperatures obtained in each case show that the low shear regions correspond to a significantly lower temperature than the high shear regions. Taking a weighted average of the effective temperature of these regions (weight determined by region size) yields an estimate of the effective temperature which compares well with an effective temperature based on the global mesocluster population of the whole system.
COOPERATIVITY, CAGE EFFECT AND HOPPING DIFFUSION IN SUPERCOOLED LIQUIDS AND GLASSES
Directory of Open Access Journals (Sweden)
A.S.Bakai
2003-01-01
Full Text Available Molecular dynamic simulations of structure, thermodynamic and kinetic properties of model metallic Ag-Cu alloy are performed to elucidate its behavior at glass transition. In spite of small variations of inherent structure of the alloy the relaxation kinetics undergo dramatic changes at the glass transition. The time dependences of the mean square displacements and the non-Gaussianity parameter show the signs of anomalous diffusion in an intermediate time region. The analysis of time evolution of van Hove correlation function indicates the existence of both jump displacements and short-range cooperative atomic rearrangements. Below Tg these cooperative rearrangements do not contribute to a long-range diffusion but they still dominate the relaxation at short time.
Crystallization Kinetics of Supercooled Liquid Ge-Sb Based on Ultrafast Calorimetry
Chen, Bin; Momand, Jamo; Vermeulen, Paul A.; Kooi, Bart J.
The crystallization kinetics of phase-change materials (PCMs) entails a crucial aspect of phase-change memory technology, and their study is also of interest to advance the understanding of crystallization in general. Research on crystallization of PCMs remains challenging because of the short
Magnetic, electric and optic properties of liquid crystals
International Nuclear Information System (INIS)
Florea, St.C.
1980-01-01
We study the nematic liquid crystals of thermotrop type. We also studied the crystals whose mesomorphism occured both at temperature increasing and decreasing and during the supercooling phase (monotrope). Investigation results performed by us have had in view the following: clearing up and experimental support of a new mechanism of nuclear relaxation in liquid crystals, proposed by author; usage of experimental techniques and methods for to characterize and test some mesomorph media used in very important applications, such as color TV. (author)
Markov decision processes in artificial intelligence
Sigaud, Olivier
2013-01-01
Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision problems under uncertainty as well as Reinforcement Learning problems. Written by experts in the field, this book provides a global view of current research using MDPs in Artificial Intelligence. It starts with an introductory presentation of the fundamental aspects of MDPs (planning in MDPs, Reinforcement Learning, Partially Observable MDPs, Markov games and the use of non-classical criteria). Then it presents more advanced research trends in the domain and gives some concrete examples using illustr
Markov bridges, bisection and variance reduction
DEFF Research Database (Denmark)
Asmussen, Søren; Hobolth, Asger
. In this paper we firstly consider the problem of generating sample paths from a continuous-time Markov chain conditioned on the endpoints using a new algorithm based on the idea of bisection. Secondly we study the potential of the bisection algorithm for variance reduction. In particular, examples are presented......Time-continuous Markov jump processes is a popular modelling tool in disciplines ranging from computational finance and operations research to human genetics and genomics. The data is often sampled at discrete points in time, and it can be useful to simulate sample paths between the datapoints...
Inhomogeneous Markov Models for Describing Driving Patterns
DEFF Research Database (Denmark)
Iversen, Emil Banning; Møller, Jan K.; Morales, Juan Miguel
2017-01-01
. Specifically, an inhomogeneous Markov model that captures the diurnal variation in the use of a vehicle is presented. The model is defined by the time-varying probabilities of starting and ending a trip, and is justified due to the uncertainty associated with the use of the vehicle. The model is fitted to data...... collected from the actual utilization of a vehicle. Inhomogeneous Markov models imply a large number of parameters. The number of parameters in the proposed model is reduced using B-splines....
Inhomogeneous Markov Models for Describing Driving Patterns
DEFF Research Database (Denmark)
Iversen, Jan Emil Banning; Møller, Jan Kloppenborg; Morales González, Juan Miguel
. Specically, an inhomogeneous Markov model that captures the diurnal variation in the use of a vehicle is presented. The model is dened by the time-varying probabilities of starting and ending a trip and is justied due to the uncertainty associated with the use of the vehicle. The model is tted to data...... collected from the actual utilization of a vehicle. Inhomogeneous Markov models imply a large number of parameters. The number of parameters in the proposed model is reduced using B-splines....
Detecting Structural Breaks using Hidden Markov Models
DEFF Research Database (Denmark)
Ntantamis, Christos
Testing for structural breaks and identifying their location is essential for econometric modeling. In this paper, a Hidden Markov Model (HMM) approach is used in order to perform these tasks. Breaks are defined as the data points where the underlying Markov Chain switches from one state to another....... The estimation of the HMM is conducted using a variant of the Iterative Conditional Expectation-Generalized Mixture (ICE-GEMI) algorithm proposed by Delignon et al. (1997), that permits analysis of the conditional distributions of economic data and allows for different functional forms across regimes...
Predicting Protein Secondary Structure with Markov Models
DEFF Research Database (Denmark)
Fischer, Paul; Larsen, Simon; Thomsen, Claus
2004-01-01
we are considering here, is to predict the secondary structure from the primary one. To this end we train a Markov model on training data and then use it to classify parts of unknown protein sequences as sheets, helices or coils. We show how to exploit the directional information contained...... in the Markov model for this task. Classifications that are purely based on statistical models might not always be biologically meaningful. We present combinatorial methods to incorporate biological background knowledge to enhance the prediction performance....
Markov processes an introduction for physical scientists
Gillespie, Daniel T
1991-01-01
Markov process theory is basically an extension of ordinary calculus to accommodate functions whos time evolutions are not entirely deterministic. It is a subject that is becoming increasingly important for many fields of science. This book develops the single-variable theory of both continuous and jump Markov processes in a way that should appeal especially to physicists and chemists at the senior and graduate level.Key Features* A self-contained, prgamatic exposition of the needed elements of random variable theory* Logically integrated derviations of the Chapman-Kolmogorov e
Kwon, Su-Yong; Kim, Jong-Chul; Choi, Byung-Il
2007-10-01
Distinguishing between a supercooled dew and frost below 0 °C in dew/frost-point measurements is an important and challenging problem that has not yet been completely solved. This study presents a new method for the recognition of a supercooled dew in a dew/frost-point sensor. A quartz crystal microbalance (QCM) sensor was used as a dew/frost-point sensor to detect a dew and a supercooled dew as well as frost. The slip phenomenon occurring at an interface between the water droplet and the surface of the quartz crystal resonator of the QCM sensor gives a simple and accurate way of distinguishing between a supercooled dew and frost below 0 °C. This method can give a highly accurate measurement of the dew or the frost point without misreading in the dew-point sensor at temperatures below 0 °C.
Prediction of Annual Rainfall Pattern Using Hidden Markov Model ...
African Journals Online (AJOL)
ADOWIE PERE
Hidden Markov model is very influential in stochastic world because of its ... the earth from the clouds. The usual ... Rainfall modelling and ... Markov Models have become popular tools ... environment sciences, University of Jos, plateau state,.
Extending Markov Automata with State and Action Rewards
Guck, Dennis; Timmer, Mark; Blom, Stefan; Bertrand, N.; Bortolussi, L.
This presentation introduces the Markov Reward Automaton (MRA), an extension of the Markov automaton that allows the modelling of systems incorporating rewards in addition to nondeterminism, discrete probabilistic choice and continuous stochastic timing. Our models support both rewards that are
On abnormal decomposition of supercooled austenite in carbon and alloy steels
International Nuclear Information System (INIS)
Parusov, V.V.; Dolzhenkov, I.I.; Podobedov, L.V.; Vakulenko, I.A.
1980-01-01
Residual stresses which appear as a result of thermal cycling in the temperature range of 300-700 deg C are investigated in an austenitic class steel (03Kh18N11) to ground the assumption on the effect of plastic deformation, appearing due to thermal stresses, on the mechanism of supercooled austenite decomposition. The determination of residual stresses is carried out with the help of X-ray diffraction analysis. It is established that the deformation brings about an increase in density of dislocation the interaction of which leads to the formation of a typical austenite substructure which conditions the proceeding of the eutectoid transformation according to an abnormal mechanism. It is noted, that the grain pearlite formation due to plastic and microplastic deformation of supercooled austenite induced by thermal stresses should be taken into account when developing steel heat treatment shedules [ru
Perturbation theory for Markov chains via Wasserstein distance
Rudolf, Daniel; Schweizer, Nikolaus
2017-01-01
Perturbation theory for Markov chains addresses the question of how small differences in the transition probabilities of Markov chains are reflected in differences between their distributions. We prove powerful and flexible bounds on the distance of the nth step distributions of two Markov chains
Quantum Enhanced Inference in Markov Logic Networks.
Wittek, Peter; Gogolin, Christian
2017-04-19
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.
Markov Random Fields on Triangle Meshes
DEFF Research Database (Denmark)
Andersen, Vedrana; Aanæs, Henrik; Bærentzen, Jakob Andreas
2010-01-01
In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process label...
A Martingale Decomposition of Discrete Markov Chains
DEFF Research Database (Denmark)
Hansen, Peter Reinhard
We consider a multivariate time series whose increments are given from a homogeneous Markov chain. We show that the martingale component of this process can be extracted by a filtering method and establish the corresponding martingale decomposition in closed-form. This representation is useful fo...
Renewal characterization of Markov modulated Poisson processes
Directory of Open Access Journals (Sweden)
Marcel F. Neuts
1989-01-01
Full Text Available A Markov Modulated Poisson Process (MMPP M(t defined on a Markov chain J(t is a pure jump process where jumps of M(t occur according to a Poisson process with intensity λi whenever the Markov chain J(t is in state i. M(t is called strongly renewal (SR if M(t is a renewal process for an arbitrary initial probability vector of J(t with full support on P={i:λi>0}. M(t is called weakly renewal (WR if there exists an initial probability vector of J(t such that the resulting MMPP is a renewal process. The purpose of this paper is to develop general characterization theorems for the class SR and some sufficiency theorems for the class WR in terms of the first passage times of the bivariate Markov chain [J(t,M(t]. Relevance to the lumpability of J(t is also studied.
Evaluation of Usability Utilizing Markov Models
Penedo, Janaina Rodrigues; Diniz, Morganna; Ferreira, Simone Bacellar Leal; Silveira, Denis S.; Capra, Eliane
2012-01-01
Purpose: The purpose of this paper is to analyze the usability of a remote learning system in its initial development phase, using a quantitative usability evaluation method through Markov models. Design/methodology/approach: The paper opted for an exploratory study. The data of interest of the research correspond to the possible accesses of users…
Bayesian analysis for reversible Markov chains
Diaconis, P.; Rolles, S.W.W.
2006-01-01
We introduce a natural conjugate prior for the transition matrix of a reversible Markov chain. This allows estimation and testing. The prior arises from random walk with reinforcement in the same way the Dirichlet prior arises from Pólya’s urn. We give closed form normalizing constants, a simple
Bisimulation and Simulation Relations for Markov Chains
Baier, Christel; Hermanns, H.; Katoen, Joost P.; Wolf, Verena; Aceto, L.; Gordon, A.
2006-01-01
Formal notions of bisimulation and simulation relation play a central role for any kind of process algebra. This short paper sketches the main concepts for bisimulation and simulation relations for probabilistic systems, modelled by discrete- or continuous-time Markov chains.
Discounted Markov games : generalized policy iteration method
Wal, van der J.
1978-01-01
In this paper, we consider two-person zero-sum discounted Markov games with finite state and action spaces. We show that the Newton-Raphson or policy iteration method as presented by Pollats-chek and Avi-Itzhak does not necessarily converge, contradicting a proof of Rao, Chandrasekaran, and Nair.
Hidden Markov Models for Human Genes
DEFF Research Database (Denmark)
Baldi, Pierre; Brunak, Søren; Chauvin, Yves
1997-01-01
We analyse the sequential structure of human genomic DNA by hidden Markov models. We apply models of widely different design: conventional left-right constructs and models with a built-in periodic architecture. The models are trained on segments of DNA sequences extracted such that they cover com...
Markov Trends in Macroeconomic Time Series
R. Paap (Richard)
1997-01-01
textabstractMany macroeconomic time series are characterised by long periods of positive growth, expansion periods, and short periods of negative growth, recessions. A popular model to describe this phenomenon is the Markov trend, which is a stochastic segmented trend where the slope depends on the
Optimal dividend distribution under Markov regime switching
Jiang, Z.; Pistorius, M.
2012-01-01
We investigate the problem of optimal dividend distribution for a company in the presence of regime shifts. We consider a company whose cumulative net revenues evolve as a Brownian motion with positive drift that is modulated by a finite state Markov chain, and model the discount rate as a
Revisiting Weak Simulation for Substochastic Markov Chains
DEFF Research Database (Denmark)
Jansen, David N.; Song, Lei; Zhang, Lijun
2013-01-01
of the logic PCTL\\x, and its completeness was conjectured. We revisit this result and show that soundness does not hold in general, but only for Markov chains without divergence. It is refuted for some systems with substochastic distributions. Moreover, we provide a counterexample to completeness...
Fracture Mechanical Markov Chain Crack Growth Model
DEFF Research Database (Denmark)
Gansted, L.; Brincker, Rune; Hansen, Lars Pilegaard
1991-01-01
propagation process can be described by a discrete space Markov theory. The model is applicable to deterministic as well as to random loading. Once the model parameters for a given material have been determined, the results can be used for any structure as soon as the geometrical function is known....
Multi-dimensional quasitoeplitz Markov chains
Directory of Open Access Journals (Sweden)
Alexander N. Dudin
1999-01-01
Full Text Available This paper deals with multi-dimensional quasitoeplitz Markov chains. We establish a sufficient equilibrium condition and derive a functional matrix equation for the corresponding vector-generating function, whose solution is given algorithmically. The results are demonstrated in the form of examples and applications in queues with BMAP-input, which operate in synchronous random environment.
Markov chains with quasitoeplitz transition matrix
Directory of Open Access Journals (Sweden)
Alexander M. Dukhovny
1989-01-01
Full Text Available This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.
Markov Chain Estimation of Avian Seasonal Fecundity
To explore the consequences of modeling decisions on inference about avian seasonal fecundity we generalize previous Markov chain (MC) models of avian nest success to formulate two different MC models of avian seasonal fecundity that represent two different ways to model renestin...
Noise can speed convergence in Markov chains.
Franzke, Brandon; Kosko, Bart
2011-10-01
A new theorem shows that noise can speed convergence to equilibrium in discrete finite-state Markov chains. The noise applies to the state density and helps the Markov chain explore improbable regions of the state space. The theorem ensures that a stochastic-resonance noise benefit exists for states that obey a vector-norm inequality. Such noise leads to faster convergence because the noise reduces the norm components. A corollary shows that a noise benefit still occurs if the system states obey an alternate norm inequality. This leads to a noise-benefit algorithm that requires knowledge of the steady state. An alternative blind algorithm uses only past state information to achieve a weaker noise benefit. Simulations illustrate the predicted noise benefits in three well-known Markov models. The first model is a two-parameter Ehrenfest diffusion model that shows how noise benefits can occur in the class of birth-death processes. The second model is a Wright-Fisher model of genotype drift in population genetics. The third model is a chemical reaction network of zeolite crystallization. A fourth simulation shows a convergence rate increase of 64% for states that satisfy the theorem and an increase of 53% for states that satisfy the corollary. A final simulation shows that even suboptimal noise can speed convergence if the noise applies over successive time cycles. Noise benefits tend to be sharpest in Markov models that do not converge quickly and that do not have strong absorbing states.
Model Checking Infinite-State Markov Chains
Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Cloth, L.
2004-01-01
In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state
Model Checking Markov Chains: Techniques and Tools
Zapreev, I.S.
2008-01-01
This dissertation deals with four important aspects of model checking Markov chains: the development of efficient model-checking tools, the improvement of model-checking algorithms, the efficiency of the state-space reduction techniques, and the development of simulation-based model-checking
Nonlinearly perturbed semi-Markov processes
Silvestrov, Dmitrii
2017-01-01
The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will cont...
Quantum Enhanced Inference in Markov Logic Networks
Wittek, Peter; Gogolin, Christian
2017-04-01
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is essentially a first-order logic template to generate Markov networks. Inference in MLNs is probabilistic and it is often performed by approximate methods such as Markov chain Monte Carlo (MCMC) Gibbs sampling. An MLN has many regular, symmetric structures that can be exploited at both first-order level and in the generated Markov network. We analyze the graph structures that are produced by various lifting methods and investigate the extent to which quantum protocols can be used to speed up Gibbs sampling with state preparation and measurement schemes. We review different such approaches, discuss their advantages, theoretical limitations, and their appeal to implementations. We find that a straightforward application of a recent result yields exponential speedup compared to classical heuristics in approximate probabilistic inference, thereby demonstrating another example where advanced quantum resources can potentially prove useful in machine learning.
Markov chain of distances between parked cars
International Nuclear Information System (INIS)
Seba, Petr
2008-01-01
We describe the distribution of distances between parked cars as a solution of certain Markov processes and show that its solution is obtained with the help of a distributional fixed point equation. Under certain conditions the process is solved explicitly. The resulting probability density is compared with the actual parking data measured in the city. (fast track communication)
Continuity Properties of Distances for Markov Processes
DEFF Research Database (Denmark)
Jaeger, Manfred; Mao, Hua; Larsen, Kim Guldstrand
2014-01-01
In this paper we investigate distance functions on finite state Markov processes that measure the behavioural similarity of non-bisimilar processes. We consider both probabilistic bisimilarity metrics, and trace-based distances derived from standard Lp and Kullback-Leibler distances. Two desirable...
Model Checking Structured Infinite Markov Chains
Remke, Anne Katharina Ingrid
2008-01-01
In the past probabilistic model checking hast mostly been restricted to finite state models. This thesis explores the possibilities of model checking with continuous stochastic logic (CSL) on infinite-state Markov chains. We present an in-depth treatment of model checking algorithms for two special
Hidden Markov models for labeled sequences
DEFF Research Database (Denmark)
Krogh, Anders Stærmose
1994-01-01
A hidden Markov model for labeled observations, called a class HMM, is introduced and a maximum likelihood method is developed for estimating the parameters of the model. Instead of training it to model the statistics of the training sequences it is trained to optimize recognition. It resembles MMI...
Efficient Modelling and Generation of Markov Automata
Koutny, M.; Timmer, Mark; Ulidowski, I.; Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette
This paper introduces a framework for the efficient modelling and generation of Markov automata. It consists of (1) the data-rich process-algebraic language MAPA, allowing concise modelling of systems with nondeterminism, probability and Markovian timing; (2) a restricted form of the language, the
A Metrized Duality Theorem for Markov Processes
DEFF Research Database (Denmark)
Kozen, Dexter; Mardare, Radu Iulian; Panangaden, Prakash
2014-01-01
We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the wa...
Packard, Gary C; Packard, Mary J
2006-05-01
Painted turtles (Chrysemys picta) typically spend their first winter of life in a shallow, subterranean hibernaculum (the natal nest) where they seemingly withstand exposure to ice and cold by resisting freezing and becoming supercooled. However, turtles ingest soil and fragments of eggshell as they are hatching from their eggs, and the ingestate usually contains efficient nucleating agents that cause water to freeze at high subzero temperatures. Consequently, neonatal painted turtles have only a modest ability to undergo supercooling in the period immediately after hatching. We studied the limit for supercooling (SCP) in hatchlings that were acclimating to different thermal regimes and then related SCPs of the turtles to the amount of particulate matter in their gastrointestinal (GI) tract. Turtles that were transferred directly from 26 degrees C (the incubation temperature) to 2 degrees C did not purge soil from their gut, and SCPs for these animals remained near -4 degrees C for the 60 days of the study. Animals that were held at 26 degrees C for the duration of the experiment usually cleared soil from their GI tract within 24 days, but SCPs for these turtles were only slightly lower after 60 days than they were at the outset of the experiment. Hatchlings that were acclimating slowly to 2 degrees C cleared soil from their gut within 24 days and realized a modest reduction in their SCP. However, the limit of supercooling in the slowly acclimating animals continued to decline even after all particulate material had been removed from their GI tract, thereby indicating that factors intrinsic to the nucleating agents themselves also may have been involved in the acclimation of hatchlings to low temperature. The lowest SCPs for turtles that were acclimating slowly to 2 degrees C were similar to SCPs recorded in an earlier study of animals taken from natural nests in late autumn, so the current findings affirm the importance of seasonally declining temperatures in
International Nuclear Information System (INIS)
Cao, Fangyu; Yang, Bao
2014-01-01
Highlights: • A new method for supercooling suppression of microPCMs by optimizing the structure of the microcapsule shell. • Large effective latent heat (up to 213 J/g) of the microPCMs, much higher than those using additive as nucleating agents. • Change of shell composition and structure significantly affects the phase transition processes of the encapsulated PCMs. • The latent heat of the shell-induced phase transition is maximized, reaching 83.7% of the latent heat of bulk octadecane. • Hollow spheres with porous rather than solid resin shell are also formed when the SDS concentration is very high. - Abstract: A new method for supercooling suppression of microencapsulated phase change materials (PCMs) has been developed by optimizing the composition and structure of the microcapsule resin shell. The microcapsules comprising paraffin octadecane encapsulated in melamine–formaldehyde resin shell were synthesized with the use the oil-in-water emulsion technique. These PCM microcapsules are 5–15 μm in diameter. The supercooling of these octadecane microcapsules can be as large as 13.6 °C, when the homogeneous nucleation is dominant during the melt crystallization into the thermodynamically stable triclinic phase. It is discovered that the homogeneous nucleation can be mediated by shell-induced nucleation of the triclinic phase and the metastable rotator phase when the shell composition and structure are optimized, without need of any nucleating additives. The effects of synthesis parameters, such as ratio of melamine to formaldehyde, pH of pre-polymer, and pH of emulsion, on the phase transition properties of the octadecane microcapsules have been investigated systemically. The optimum synthesis conditions have been identified in terms of minimizing the supercooling while maintaining heat capacity. Potential applications of this type of phase changeable microcapsules include high heat capacity thermal fluids, thermal management in smart buildings
Dynamically slow processes in supercooled water confined between hydrophobic plates
Energy Technology Data Exchange (ETDEWEB)
Franzese, Giancarlo [Departamento de Fisica Fundamental, Universidad de Barcelona, Diagonal 647, Barcelona 08028 (Spain); Santos, Francisco de los, E-mail: gfranzese@ub.ed, E-mail: fdlsant@ugr.e [Departamento de Electromagnetismo y Fisica de la Materia, Universidad de Granada, Fuentenueva s/n, 18071 Granada (Spain)
2009-12-16
We study the dynamics of water confined between hydrophobic flat surfaces at low temperature. At different pressures, we observe different behaviors that we understand in terms of the hydrogen bond dynamics. At high pressure, the formation of the open structure of the hydrogen bond network is inhibited and the surfaces can be rapidly dried (dewetted) by formation of a large cavity with decreasing temperature. At lower pressure we observe strong non-exponential behavior of the correlation function, but with no strong increase of the correlation time. This behavior can be associated, on the one hand, to the rapid ordering of the hydrogen bonds that generates heterogeneities and, on the other hand, to the lack of a single timescale as a consequence of the cooperativity in the vicinity of the liquid-liquid critical point that characterizes the phase diagram at low temperature of the water model considered here. At very low pressures, the gradual formation of the hydrogen bond network is responsible for the large increase of the correlation time and, eventually, the dynamical arrest of the system, with a strikingly different dewetting process, characterized by the formation of many small cavities.
Dynamically slow processes in supercooled water confined between hydrophobic plates
International Nuclear Information System (INIS)
Franzese, Giancarlo; Santos, Francisco de los
2009-01-01
We study the dynamics of water confined between hydrophobic flat surfaces at low temperature. At different pressures, we observe different behaviors that we understand in terms of the hydrogen bond dynamics. At high pressure, the formation of the open structure of the hydrogen bond network is inhibited and the surfaces can be rapidly dried (dewetted) by formation of a large cavity with decreasing temperature. At lower pressure we observe strong non-exponential behavior of the correlation function, but with no strong increase of the correlation time. This behavior can be associated, on the one hand, to the rapid ordering of the hydrogen bonds that generates heterogeneities and, on the other hand, to the lack of a single timescale as a consequence of the cooperativity in the vicinity of the liquid-liquid critical point that characterizes the phase diagram at low temperature of the water model considered here. At very low pressures, the gradual formation of the hydrogen bond network is responsible for the large increase of the correlation time and, eventually, the dynamical arrest of the system, with a strikingly different dewetting process, characterized by the formation of many small cavities.
A simulation study of homogeneous ice nucleation in supercooled salty water
Soria, Guiomar D.; Espinosa, Jorge R.; Ramirez, Jorge; Valeriani, Chantal; Vega, Carlos; Sanz, Eduardo
2018-06-01
We use computer simulations to investigate the effect of salt on homogeneous ice nucleation. The melting point of the employed solution model was obtained both by direct coexistence simulations and by thermodynamic integration from previous calculations of the water chemical potential. Using a seeding approach, in which we simulate ice seeds embedded in a supercooled aqueous solution, we compute the nucleation rate as a function of temperature for a 1.85 NaCl mol per water kilogram solution at 1 bar. To improve the accuracy and reliability of our calculations, we combine seeding with the direct computation of the ice-solution interfacial free energy at coexistence using the Mold Integration method. We compare the results with previous simulation work on pure water to understand the effect caused by the solute. The model captures the experimental trend that the nucleation rate at a given supercooling decreases when adding salt. Despite the fact that the thermodynamic driving force for ice nucleation is higher for salty water for a given supercooling, the nucleation rate slows down with salt due to a significant increase of the ice-fluid interfacial free energy. The salty water model predicts an ice nucleation rate that is in good agreement with experimental measurements, bringing confidence in the predictive ability of the model. We expect that the combination of state-of-the-art simulation methods here employed to study ice nucleation from solution will be of much use in forthcoming numerical investigations of crystallization in mixtures.
Nonthermal ice nucleation observed at distorted contact lines of supercooled water drops.
Yang, Fan; Cruikshank, Owen; He, Weilue; Kostinski, Alex; Shaw, Raymond A
2018-02-01
Ice nucleation is the crucial step for ice formation in atmospheric clouds and therefore underlies climatologically relevant precipitation and radiative properties. Progress has been made in understanding the roles of temperature, supersaturation, and material properties, but an explanation for the efficient ice nucleation occurring when a particle contacts a supercooled water drop has been elusive for over half a century. Here, we explore ice nucleation initiated at constant temperature and observe that mechanical agitation induces freezing of supercooled water drops at distorted contact lines. Results show that symmetric motion of supercooled water on a vertically oscillating substrate does not freeze, no matter how we agitate it. However, when the moving contact line is distorted with the help of trace amounts of oil or inhomogeneous pinning on the substrate, freezing can occur at temperatures much higher than in a static droplet, equivalent to ∼10^{10} increase in nucleation rate. Several possible mechanisms are proposed to explain the observations. One plausible explanation among them, decreased pressure due to interface curvature, is explored theoretically and compared with the observational results quasiquantitatively. Indeed, the observed freezing-temperature increase scales with contact line speed in a manner consistent with the pressure hypothesis. Whatever the mechanism, the experiments demonstrate a strong preference for ice nucleation at three-phase contact lines compared to the two-phase interface, and they also show that movement and distortion of the contact line are necessary contributions to stimulating the nucleation process.
High density liquid structure enhancement in glass forming aqueous solution of LiCl
Camisasca, G.; De Marzio, M.; Rovere, M.; Gallo, P.
2018-06-01
We investigate using molecular dynamics simulations the dynamical and structural properties of LiCl:6H2O aqueous solution upon supercooling. This ionic solution is a glass forming liquid of relevant interest in connection with the study of the anomalies of supercooled water. The LiCl:6H2O solution is easily supercooled and the liquid state can be maintained over a large decreasing temperature range. We performed simulations from ambient to 200 K in order to investigate how the presence of the salt modifies the behavior of supercooled water. The study of the relaxation time of the self-density correlation function shows that the system follows the prediction of the mode coupling theory and behaves like a fragile liquid in all the range explored. The analysis of the changes in the water structure induced by the salt shows that while the salt preserves the water hydrogen bonds in the system, it strongly affects the tetrahedral hydrogen bond network. Following the interpretation of the anomalies of water in terms of a two-state model, the modifications of the oxygen radial distribution function and the angular distribution function of the hydrogen bonds in water indicate that LiCl has the role of enhancing the high density liquid component of water with respect to the low density component. This is in agreement with recent experiments on aqueous ionic solutions.
Nuclear security assessment with Markov model approach
International Nuclear Information System (INIS)
Suzuki, Mitsutoshi; Terao, Norichika
2013-01-01
Nuclear security risk assessment with the Markov model based on random event is performed to explore evaluation methodology for physical protection in nuclear facilities. Because the security incidences are initiated by malicious and intentional acts, expert judgment and Bayes updating are used to estimate scenario and initiation likelihood, and it is assumed that the Markov model derived from stochastic process can be applied to incidence sequence. Both an unauthorized intrusion as Design Based Threat (DBT) and a stand-off attack as beyond-DBT are assumed to hypothetical facilities, and performance of physical protection and mitigation and minimization of consequence are investigated to develop the assessment methodology in a semi-quantitative manner. It is shown that cooperation between facility operator and security authority is important to respond to the beyond-DBT incidence. (author)
An interlacing theorem for reversible Markov chains
International Nuclear Information System (INIS)
Grone, Robert; Salamon, Peter; Hoffmann, Karl Heinz
2008-01-01
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
An interlacing theorem for reversible Markov chains
Energy Technology Data Exchange (ETDEWEB)
Grone, Robert; Salamon, Peter [Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720 (United States); Hoffmann, Karl Heinz [Institut fuer Physik, Technische Universitaet Chemnitz, D-09107 Chemnitz (Germany)
2008-05-30
Reversible Markov chains are an indispensable tool in the modeling of a vast class of physical, chemical, biological and statistical problems. Examples include the master equation descriptions of relaxing physical systems, stochastic optimization algorithms such as simulated annealing, chemical dynamics of protein folding and Markov chain Monte Carlo statistical estimation. Very often the large size of the state spaces requires the coarse graining or lumping of microstates into fewer mesoscopic states, and a question of utmost importance for the validity of the physical model is how the eigenvalues of the corresponding stochastic matrix change under this operation. In this paper we prove an interlacing theorem which gives explicit bounds on the eigenvalues of the lumped stochastic matrix. (fast track communication)
Stochastic Dynamics through Hierarchically Embedded Markov Chains.
Vasconcelos, Vítor V; Santos, Fernando P; Santos, Francisco C; Pacheco, Jorge M
2017-02-03
Studying dynamical phenomena in finite populations often involves Markov processes of significant mathematical and/or computational complexity, which rapidly becomes prohibitive with increasing population size or an increasing number of individual configuration states. Here, we develop a framework that allows us to define a hierarchy of approximations to the stationary distribution of general systems that can be described as discrete Markov processes with time invariant transition probabilities and (possibly) a large number of states. This results in an efficient method for studying social and biological communities in the presence of stochastic effects-such as mutations in evolutionary dynamics and a random exploration of choices in social systems-including situations where the dynamics encompasses the existence of stable polymorphic configurations, thus overcoming the limitations of existing methods. The present formalism is shown to be general in scope, widely applicable, and of relevance to a variety of interdisciplinary problems.
Exact solution of the hidden Markov processes
Saakian, David B.
2017-11-01
We write a master equation for the distributions related to hidden Markov processes (HMPs) and solve it using a functional equation. Thus the solution of HMPs is mapped exactly to the solution of the functional equation. For a general case the latter can be solved only numerically. We derive an exact expression for the entropy of HMPs. Our expression for the entropy is an alternative to the ones given before by the solution of integral equations. The exact solution is possible because actually the model can be considered as a generalized random walk on a one-dimensional strip. While we give the solution for the two second-order matrices, our solution can be easily generalized for the L values of the Markov process and M values of observables: We should be able to solve a system of L functional equations in the space of dimension M -1 .
Handbook of Markov chain Monte Carlo
Brooks, Steve
2011-01-01
""Handbook of Markov Chain Monte Carlo"" brings together the major advances that have occurred in recent years while incorporating enough introductory material for new users of MCMC. Along with thorough coverage of the theoretical foundations and algorithmic and computational methodology, this comprehensive handbook includes substantial realistic case studies from a variety of disciplines. These case studies demonstrate the application of MCMC methods and serve as a series of templates for the construction, implementation, and choice of MCMC methodology.
Second Order Optimality in Markov Decision Chains
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2017-01-01
Roč. 53, č. 6 (2017), s. 1086-1099 ISSN 0023-5954 R&D Projects: GA ČR GA15-10331S Institutional support: RVO:67985556 Keywords : Markov decision chains * second order optimality * optimalilty conditions for transient, discounted and average models * policy and value iterations Subject RIV: BB - Applied Statistics, Operational Research OBOR OECD: Statistics and probability Impact factor: 0.379, year: 2016 http://library.utia.cas.cz/separaty/2017/E/sladky-0485146.pdf
Dynamical fluctuations for semi-Markov processes
Czech Academy of Sciences Publication Activity Database
Maes, C.; Netočný, Karel; Wynants, B.
2009-01-01
Roč. 42, č. 36 (2009), 365002/1-365002/21 ISSN 1751-8113 R&D Projects: GA ČR GC202/07/J051 Institutional research plan: CEZ:AV0Z10100520 Keywords : nonequilibrium fluctuations * semi-Markov processes Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.577, year: 2009 http://www.iop.org/EJ/abstract/1751-8121/42/36/365002
Analysis of a quantum Markov chain
International Nuclear Information System (INIS)
Marbeau, J.; Gudder, S.
1990-01-01
A quantum chain is analogous to a classical stationary Markov chain except that the probability measure is replaced by a complex amplitude measure and the transition probability matrix is replaced by a transition amplitude matrix. After considering the general situation, we study a particular example of a quantum chain whose transition amplitude matrix has the form of a Dirichlet matrix. Such matrices generate a discrete analog of the usual continuum Feynman amplitude. We then compute the probability distribution for these quantum chains
Modelling of cyclical stratigraphy using Markov chains
Energy Technology Data Exchange (ETDEWEB)
Kulatilake, P.H.S.W.
1987-07-01
State-of-the-art on modelling of cyclical stratigraphy using first-order Markov chains is reviewed. Shortcomings of the presently available procedures are identified. A procedure which eliminates all the identified shortcomings is presented. Required statistical tests to perform this modelling are given in detail. An example (the Oficina formation in eastern Venezuela) is given to illustrate the presented procedure. 12 refs., 3 tabs. 1 fig.
Markov Chains For Testing Redundant Software
White, Allan L.; Sjogren, Jon A.
1990-01-01
Preliminary design developed for validation experiment that addresses problems unique to assuring extremely high quality of multiple-version programs in process-control software. Approach takes into account inertia of controlled system in sense it takes more than one failure of control program to cause controlled system to fail. Verification procedure consists of two steps: experimentation (numerical simulation) and computation, with Markov model for each step.
Operational Markov Condition for Quantum Processes
Pollock, Felix A.; Rodríguez-Rosario, César; Frauenheim, Thomas; Paternostro, Mauro; Modi, Kavan
2018-01-01
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process or the experimental falsifiability of a Markovian hypothesis.
Markov and semi-Markov switching linear mixed models used to identify forest tree growth components.
Chaubert-Pereira, Florence; Guédon, Yann; Lavergne, Christian; Trottier, Catherine
2010-09-01
Tree growth is assumed to be mainly the result of three components: (i) an endogenous component assumed to be structured as a succession of roughly stationary phases separated by marked change points that are asynchronous among individuals, (ii) a time-varying environmental component assumed to take the form of synchronous fluctuations among individuals, and (iii) an individual component corresponding mainly to the local environment of each tree. To identify and characterize these three components, we propose to use semi-Markov switching linear mixed models, i.e., models that combine linear mixed models in a semi-Markovian manner. The underlying semi-Markov chain represents the succession of growth phases and their lengths (endogenous component) whereas the linear mixed models attached to each state of the underlying semi-Markov chain represent-in the corresponding growth phase-both the influence of time-varying climatic covariates (environmental component) as fixed effects, and interindividual heterogeneity (individual component) as random effects. In this article, we address the estimation of Markov and semi-Markov switching linear mixed models in a general framework. We propose a Monte Carlo expectation-maximization like algorithm whose iterations decompose into three steps: (i) sampling of state sequences given random effects, (ii) prediction of random effects given state sequences, and (iii) maximization. The proposed statistical modeling approach is illustrated by the analysis of successive annual shoots along Corsican pine trunks influenced by climatic covariates. © 2009, The International Biometric Society.
Modeling nonhomogeneous Markov processes via time transformation.
Hubbard, R A; Inoue, L Y T; Fann, J R
2008-09-01
Longitudinal studies are a powerful tool for characterizing the course of chronic disease. These studies are usually carried out with subjects observed at periodic visits giving rise to panel data. Under this observation scheme the exact times of disease state transitions and sequence of disease states visited are unknown and Markov process models are often used to describe disease progression. Most applications of Markov process models rely on the assumption of time homogeneity, that is, that the transition rates are constant over time. This assumption is not satisfied when transition rates depend on time from the process origin. However, limited statistical tools are available for dealing with nonhomogeneity. We propose models in which the time scale of a nonhomogeneous Markov process is transformed to an operational time scale on which the process is homogeneous. We develop a method for jointly estimating the time transformation and the transition intensity matrix for the time transformed homogeneous process. We assess maximum likelihood estimation using the Fisher scoring algorithm via simulation studies and compare performance of our method to homogeneous and piecewise homogeneous models. We apply our methodology to a study of delirium progression in a cohort of stem cell transplantation recipients and show that our method identifies temporal trends in delirium incidence and recovery.
Temperature scaling method for Markov chains.
Crosby, Lonnie D; Windus, Theresa L
2009-01-22
The use of ab initio potentials in Monte Carlo simulations aimed at investigating the nucleation kinetics of water clusters is complicated by the computational expense of the potential energy determinations. Furthermore, the common desire to investigate the temperature dependence of kinetic properties leads to an urgent need to reduce the expense of performing simulations at many different temperatures. A method is detailed that allows a Markov chain (obtained via Monte Carlo) at one temperature to be scaled to other temperatures of interest without the need to perform additional large simulations. This Markov chain temperature-scaling (TeS) can be generally applied to simulations geared for numerous applications. This paper shows the quality of results which can be obtained by TeS and the possible quantities which may be extracted from scaled Markov chains. Results are obtained for a 1-D analytical potential for which the exact solutions are known. Also, this method is applied to water clusters consisting of between 2 and 5 monomers, using Dynamical Nucleation Theory to determine the evaporation rate constant for monomer loss. Although ab initio potentials are not utilized in this paper, the benefit of this method is made apparent by using the Dang-Chang polarizable classical potential for water to obtain statistical properties at various temperatures.
Stencil method: a Markov model for transport in porous media
Delgoshaie, A. H.; Tchelepi, H.; Jenny, P.
2016-12-01
In porous media the transport of fluid is dominated by flow-field heterogeneity resulting from the underlying transmissibility field. Since the transmissibility is highly uncertain, many realizations of a geological model are used to describe the statistics of the transport phenomena in a Monte Carlo framework. One possible way to avoid the high computational cost of physics-based Monte Carlo simulations is to model the velocity field as a Markov process and use Markov Chain Monte Carlo. In previous works multiple Markov models for discrete velocity processes have been proposed. These models can be divided into two general classes of Markov models in time and Markov models in space. Both of these choices have been shown to be effective to some extent. However some studies have suggested that the Markov property cannot be confirmed for a temporal Markov process; Therefore there is not a consensus about the validity and value of Markov models in time. Moreover, previous spacial Markov models have only been used for modeling transport on structured networks and can not be readily applied to model transport in unstructured networks. In this work we propose a novel approach for constructing a Markov model in time (stencil method) for a discrete velocity process. The results form the stencil method are compared to previously proposed spacial Markov models for structured networks. The stencil method is also applied to unstructured networks and can successfully describe the dispersion of particles in this setting. Our conclusion is that both temporal Markov models and spacial Markov models for discrete velocity processes can be valid for a range of model parameters. Moreover, we show that the stencil model can be more efficient in many practical settings and is suited to model dispersion both on structured and unstructured networks.
Markov chains and semi-Markov models in time-to-event analysis.
Abner, Erin L; Charnigo, Richard J; Kryscio, Richard J
2013-10-25
A variety of statistical methods are available to investigators for analysis of time-to-event data, often referred to as survival analysis. Kaplan-Meier estimation and Cox proportional hazards regression are commonly employed tools but are not appropriate for all studies, particularly in the presence of competing risks and when multiple or recurrent outcomes are of interest. Markov chain models can accommodate censored data, competing risks (informative censoring), multiple outcomes, recurrent outcomes, frailty, and non-constant survival probabilities. Markov chain models, though often overlooked by investigators in time-to-event analysis, have long been used in clinical studies and have widespread application in other fields.
Derivation of Markov processes that violate detailed balance
Lee, Julian
2018-03-01
Time-reversal symmetry of the microscopic laws dictates that the equilibrium distribution of a stochastic process must obey the condition of detailed balance. However, cyclic Markov processes that do not admit equilibrium distributions with detailed balance are often used to model systems driven out of equilibrium by external agents. I show that for a Markov model without detailed balance, an extended Markov model can be constructed, which explicitly includes the degrees of freedom for the driving agent and satisfies the detailed balance condition. The original cyclic Markov model for the driven system is then recovered as an approximation at early times by summing over the degrees of freedom for the driving agent. I also show that the widely accepted expression for the entropy production in a cyclic Markov model is actually a time derivative of an entropy component in the extended model. Further, I present an analytic expression for the entropy component that is hidden in the cyclic Markov model.
English, Thomas
2005-01-01
A standard tool of reliability analysis used at NASA-JSC is the event tree. An event tree is simply a probability tree, with the probabilities determining the next step through the tree specified at each node. The nodal probabilities are determined by a reliability study of the physical system at work for a particular node. The reliability study performed at a node is typically referred to as a fault tree analysis, with the potential of a fault tree existing.for each node on the event tree. When examining an event tree it is obvious why the event tree/fault tree approach has been adopted. Typical event trees are quite complex in nature, and the event tree/fault tree approach provides a systematic and organized approach to reliability analysis. The purpose of this study was two fold. Firstly, we wanted to explore the possibility that a semi-Markov process can create dependencies between sojourn times (the times it takes to transition from one state to the next) that can decrease the uncertainty when estimating time to failures. Using a generalized semi-Markov model, we studied a four element reliability model and were able to demonstrate such sojourn time dependencies. Secondly, we wanted to study the use of semi-Markov processes to introduce a time variable into the event tree diagrams that are commonly developed in PRA (Probabilistic Risk Assessment) analyses. Event tree end states which change with time are more representative of failure scenarios than are the usual static probability-derived end states.
A Markov Process Inspired Cellular Automata Model of Road Traffic
Wang, Fa; Li, Li; Hu, Jianming; Ji, Yan; Yao, Danya; Zhang, Yi; Jin, Xuexiang; Su, Yuelong; Wei, Zheng
2008-01-01
To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process whose stationary distribution corresponds to the observed distribution of practical gaps. The multiformity of this Markov process provides the model enough flexibility to describe various driving behaviors. Two examples are given to show how to specialize i...
A New GMRES(m Method for Markov Chains
Directory of Open Access Journals (Sweden)
Bing-Yuan Pu
2013-01-01
Full Text Available This paper presents a class of new accelerated restarted GMRES method for calculating the stationary probability vector of an irreducible Markov chain. We focus on the mechanism of this new hybrid method by showing how to periodically combine the GMRES and vector extrapolation method into a much efficient one for improving the convergence rate in Markov chain problems. Numerical experiments are carried out to demonstrate the efficiency of our new algorithm on several typical Markov chain problems.
Context Tree Estimation in Variable Length Hidden Markov Models
Dumont, Thierry
2011-01-01
We address the issue of context tree estimation in variable length hidden Markov models. We propose an estimator of the context tree of the hidden Markov process which needs no prior upper bound on the depth of the context tree. We prove that the estimator is strongly consistent. This uses information-theoretic mixture inequalities in the spirit of Finesso and Lorenzo(Consistent estimation of the order for Markov and hidden Markov chains(1990)) and E.Gassiat and S.Boucheron (Optimal error exp...
Deteksi Fraud Menggunakan Metode Model Markov Tersembunyi Pada Proses Bisnis
Directory of Open Access Journals (Sweden)
Andrean Hutama Koosasi
2017-03-01
Full Text Available Model Markov Tersembunyi merupakan sebuah metode statistik berdasarkan Model Markov sederhana yang memodelkan sistem serta membaginya dalam 2 (dua state, state tersembunyi dan state observasi. Dalam pengerjaan tugas akhir ini, penulis mengusulkan penggunaan metode Model Markov Tersembunyi untuk menemukan fraud didalam sebuah pelaksanaan proses bisnis. Dengan penggunaan metode Model Markov Tersembunyi ini, maka pengamatan terhadap elemen penyusun sebuah kasus/kejadian, yakni beberapa aktivitas, akan diperoleh sebuah nilai peluang, yang sekaligus memberikan prediksi terhadap kasus/kejadian tersebut, sebuah fraud atau tidak. Hasil ekpserimen ini menunjukkan bahwa metode yang diusulkan mampu memberikan prediksi akhir dengan evaluasi TPR sebesar 87,5% dan TNR sebesar 99,4%.
International Nuclear Information System (INIS)
Kaetsu, I.; Yoshii, F.; Watanabe, Y.
1978-01-01
Radiation-induced polymerization of glass-forming monomers such as 2-hydroxyethyl methacrylate and glycidyl methacrylate under high pressure was studied. The glass transition temperature of these monomers was heightened by increased pressure. The temperature dependence of polymerizability showed a characteristic relation, similar to those in supercooled-phase polymerization under normal pressure, that had a maximum at T/sub ν/ which shifted to higher levels of temperature as well as to T/sub g/ under high pressure. Polymerizability in the supercooled state also increased under increased pressure
Perspective on the structure of liquid water
International Nuclear Information System (INIS)
Nilsson, A.; Pettersson, L.G.M.
2011-01-01
Graphical abstract: Liquid water can be described in a fluctuating inhomogeneous picture with two local structural motifs that are spatially separated. At ambient temperatures most molecules favor a closer packing than tetrahedral, with strongly distorted hydrogen bonds giving higher density (yellow), which allows the quantized librational modes to be excited and contribute to the entropy, but with enthalpically favored tetrahedrally bonded water patches appearing as fluctuations (blue), i.e. a competition between entropy and enthalpy. Upon cooling water the amount of molecules participating in tetrahedral structures and the size of the tetrahedral patches increase. Highlights: ► Two components maximizing either enthalpy (tetrahedral, low-density) or entropy (non-specific H-bonding, higher density). ► Interconvert discontinuously and ratio depends on temperature. ► Density fluctuations on 1 nm length scale. ► Increasing size in supercooled region. ► Connection to Widom line and 2nd critical point. - Abstract: We present a picture that combines discussions regarding the thermodynamic anomalies in ambient and supercooled water with recent interpretations of X-ray spectroscopy and scattering data of water in the ambient regime. At ambient temperatures most molecules favor a closer packing than tetrahedral, with strongly distorted hydrogen bonds, which allows the quantized librational modes to be excited and contribute to the entropy, but with enthalpically favored tetrahedrally bonded water patches appearing as fluctuations, i.e. a competition between entropy and enthalpy. Upon cooling water the amount of molecules participating in tetrahedral structures and the size of the tetrahedral patches increase. The two local structures are connected to the liquid–liquid critical point hypothesis in supercooled water corresponding to high density liquid and low density liquid. We will discuss the interpretation of X-ray absorption spectroscopy, X-ray emission
Markov Chain Analysis of Musical Dice Games
Volchenkov, D.; Dawin, J. R.
2012-07-01
A system for using dice to compose music randomly is known as the musical dice game. The discrete time MIDI models of 804 pieces of classical music written by 29 composers have been encoded into the transition matrices and studied by Markov chains. Contrary to human languages, entropy dominates over redundancy, in the musical dice games based on the compositions of classical music. The maximum complexity is achieved on the blocks consisting of just a few notes (8 notes, for the musical dice games generated over Bach's compositions). First passage times to notes can be used to resolve tonality and feature a composer.
Pruning Boltzmann networks and hidden Markov models
DEFF Research Database (Denmark)
Pedersen, Morten With; Stork, D.
1996-01-01
We present sensitivity-based pruning algorithms for general Boltzmann networks. Central to our methods is the efficient calculation of a second-order approximation to the true weight saliencies in a cross-entropy error. Building upon previous work which shows a formal correspondence between linear...... Boltzmann chains and hidden Markov models (HMMs), we argue that our method can be applied to HMMs as well. We illustrate pruning on Boltzmann zippers, which are equivalent to two HMMs with cross-connection links. We verify that our second-order approximation preserves the rank ordering of weight saliencies...
Decoding LDPC Convolutional Codes on Markov Channels
Directory of Open Access Journals (Sweden)
Kashyap Manohar
2008-01-01
Full Text Available Abstract This paper describes a pipelined iterative technique for joint decoding and channel state estimation of LDPC convolutional codes over Markov channels. Example designs are presented for the Gilbert-Elliott discrete channel model. We also compare the performance and complexity of our algorithm against joint decoding and state estimation of conventional LDPC block codes. Complexity analysis reveals that our pipelined algorithm reduces the number of operations per time step compared to LDPC block codes, at the expense of increased memory and latency. This tradeoff is favorable for low-power applications.
Decoding LDPC Convolutional Codes on Markov Channels
Directory of Open Access Journals (Sweden)
Chris Winstead
2008-04-01
Full Text Available This paper describes a pipelined iterative technique for joint decoding and channel state estimation of LDPC convolutional codes over Markov channels. Example designs are presented for the Gilbert-Elliott discrete channel model. We also compare the performance and complexity of our algorithm against joint decoding and state estimation of conventional LDPC block codes. Complexity analysis reveals that our pipelined algorithm reduces the number of operations per time step compared to LDPC block codes, at the expense of increased memory and latency. This tradeoff is favorable for low-power applications.
Evolving the structure of hidden Markov Models
DEFF Research Database (Denmark)
won, K. J.; Prugel-Bennett, A.; Krogh, A.
2006-01-01
A genetic algorithm (GA) is proposed for finding the structure of hidden Markov Models (HMMs) used for biological sequence analysis. The GA is designed to preserve biologically meaningful building blocks. The search through the space of HMM structures is combined with optimization of the emission...... and transition probabilities using the classic Baum-Welch algorithm. The system is tested on the problem of finding the promoter and coding region of C. jejuni. The resulting HMM has a superior discrimination ability to a handcrafted model that has been published in the literature....
Honest Importance Sampling with Multiple Markov Chains.
Tan, Aixin; Doss, Hani; Hobert, James P
2015-01-01
Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π 1 , is used to estimate an expectation with respect to another, π . The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π 1 is replaced by a Harris ergodic Markov chain with invariant density π 1 , then the resulting estimator remains strongly consistent. There is a price to be paid however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this paper, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general set up, where we assume that Markov chain samples from several probability densities, π 1 , …, π k , are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effects models under different priors. The second involves Bayesian variable
ANALYSING ACCEPTANCE SAMPLING PLANS BY MARKOV CHAINS
Directory of Open Access Journals (Sweden)
Mohammad Mirabi
2012-01-01
Full Text Available
ENGLISH ABSTRACT: In this research, a Markov analysis of acceptance sampling plans in a single stage and in two stages is proposed, based on the quality of the items inspected. In a stage of this policy, if the number of defective items in a sample of inspected items is more than the upper threshold, the batch is rejected. However, the batch is accepted if the number of defective items is less than the lower threshold. Nonetheless, when the number of defective items falls between the upper and lower thresholds, the decision-making process continues to inspect the items and collect further samples. The primary objective is to determine the optimal values of the upper and lower thresholds using a Markov process to minimise the total cost associated with a batch acceptance policy. A solution method is presented, along with a numerical demonstration of the application of the proposed methodology.
AFRIKAANSE OPSOMMING: In hierdie navorsing word ’n Markov-ontleding gedoen van aannamemonsternemingsplanne wat plaasvind in ’n enkele stap of in twee stappe na gelang van die kwaliteit van die items wat geïnspekteer word. Indien die eerste monster toon dat die aantal defektiewe items ’n boonste grens oorskry, word die lot afgekeur. Indien die eerste monster toon dat die aantal defektiewe items minder is as ’n onderste grens, word die lot aanvaar. Indien die eerste monster toon dat die aantal defektiewe items in die gebied tussen die boonste en onderste grense lê, word die besluitnemingsproses voortgesit en verdere monsters word geneem. Die primêre doel is om die optimale waardes van die booonste en onderste grense te bepaal deur gebruik te maak van ’n Markov-proses sodat die totale koste verbonde aan die proses geminimiseer kan word. ’n Oplossing word daarna voorgehou tesame met ’n numeriese voorbeeld van die toepassing van die voorgestelde oplossing.
Vulnerability of networks of interacting Markov chains.
Kocarev, L; Zlatanov, N; Trajanov, D
2010-05-13
The concept of vulnerability is introduced for a model of random, dynamical interactions on networks. In this model, known as the influence model, the nodes are arranged in an arbitrary network, while the evolution of the status at a node is according to an internal Markov chain, but with transition probabilities that depend not only on the current status of that node but also on the statuses of the neighbouring nodes. Vulnerability is treated analytically and numerically for several networks with different topological structures, as well as for two real networks--the network of infrastructures and the EU power grid--identifying the most vulnerable nodes of these networks.
Genetic Algorithms Principles Towards Hidden Markov Model
Directory of Open Access Journals (Sweden)
Nabil M. Hewahi
2011-10-01
Full Text Available In this paper we propose a general approach based on Genetic Algorithms (GAs to evolve Hidden Markov Models (HMM. The problem appears when experts assign probability values for HMM, they use only some limited inputs. The assigned probability values might not be accurate to serve in other cases related to the same domain. We introduce an approach based on GAs to find
out the suitable probability values for the HMM to be mostly correct in more cases than what have been used to assign the probability values.
Supercooling as a viable non-freezing cell preservation method of rat hepatocytes.
Directory of Open Access Journals (Sweden)
O Berk Usta
Full Text Available Supercooling preservation holds the potential to drastically extend the preservation time of organs, tissues and engineered tissue products, and fragile cell types that do not lend themselves well to cryopreservation or vitrification. Here, we investigate the effects of supercooling preservation (SCP at -4(oC on primary rat hepatocytes stored in cryovials and compare its success (high viability and good functional characteristics to that of static cold storage (CS at +4(oC and cryopreservation. We consider two prominent preservation solutions a Hypothermosol (HTS-FRS and b University of Wisconsin solution (UW and a range of preservation temperatures (-4 to -10 (oC. We find that there exists an optimum temperature (-4(oC for SCP of rat hepatocytes which yields the highest viability; at this temperature HTS-FRS significantly outperforms UW solution in terms of viability and functional characteristics (secretions and enzymatic activity in suspension and plate culture. With the HTS-FRS solution we show that the cells can be stored for up to a week with high viability (~56%; moreover we also show that the preservation can be performed in large batches (50 million cells with equal or better viability and no loss of functionality as compared to smaller batches (1.5 million cells performed in cryovials.
Hacker, Jürgen; Ladinig, Ursula; Wagner, Johanna; Neuner, Gilbert
2011-01-01
Freezing patterns in the high alpine cushion plants Saxifraga bryoides, Saxifraga caesia, Saxifraga moschata and Silene acaulis were studied by infrared thermography at three reproductive stages (bud, anthesis, fruit development). The single reproductive shoots of a cushion froze independently in all four species at every reproductive stage. Ice formation caused lethal damage to the respective inflorescence. After ice nucleation, which occurred mainly in the stalk or the base of the reproductive shoot, ice propagated throughout that entire shoot, but not into neighboring shoots. However, anatomical ice barriers within cushions were not detected. The naturally occurring temperature gradient within the cushion appeared to interrupt ice propagation thermally. Consequently, every reproductive shoot needed an autonomous ice nucleation event to initiate freezing. Ice nucleation was not only influenced by minimum temperatures but also by the duration of exposure. At moderate subzero exposure temperatures (−4.3 to −7.7 °C) the number of frozen inflorescences increased exponentially. Due to efficient supercooling, single reproductive shoots remained unfrozen down to −17.4 °C (cooling rate 6 K h−1). Hence, the observed freezing pattern may be advantageous for frost survival of individual inflorescences and reproductive success of high alpine cushion plants, when during episodic summer frosts damage can be avoided by supercooling. PMID:21151351
Space resolved x-ray diffraction measurements of the supercooled state of polymers
International Nuclear Information System (INIS)
Asano, Tsutomu; Yoshida, Shinya; Nishida, Akira; Mina, M.F.
2002-01-01
In order to measure an ordering process of polymers, the supercooled state near the crystallizing surface was observed by a space resolved X-ray diffraction method at Photon Factory (PF). Using temperature slope crystallization, low density polyethylene and even-number paraffins were examined during crystallization from the melt state. The results indicate that polyethylene shows a sharp b-axis orientation where the lamellar normal and crystalline c-axis are perpendicular to the temperature slope. The crystalline lamellae are well-developed with lamellar thickness of 180 A. The supercooled melt state just above the crystallizing plane shows some diffraction in the small angle region without any crystalline reflection in the wide angle. This fact suggests that a long-range ordering (lamellar structure) appears prior to the short-range one (crystalline structure). The in-situ crystallizing surface was observed by an optical microscope connected to a TV system. The crystallizing surface of even-number paraffins moves to upwards in the temperature slope. In-situ X-ray measurements at PF revealed that the crystalline c-axis and lamellar normal of the even number paraffins are parallel to the temperature slope. From these results, the crystalline ordering and the surface movement of even number paraffins are explained using special nucleation mechanism including a screw dislocation. (author)
Schwindt, Daniel; Kozák, Johanna-Luise; Kohlpaintner, Michael
2017-04-01
In the central European Alps, permafrost can be expected in altitudes above 2300 m a.s.l., where mean annual air temperatures are below -1°C. However, attributed to the thermally induced "chimney effect", isolated permafrost lenses can be found in scree slopes far below the timberline where mean annual air temperature is positive. Usually the supercooled subsurface appears as lenses at the foot of talus slopes, covered by a thick layer of organic material and a unique vegetation composition most obviously characterized by dwarf grown trees ("Hexenwäldli") and azonal plant species. The fact that mean annual air temperature is positive and therefore can be excluded as a driving factor makes these sites unique for studying interdependencies between a supercooled subsurface, plant adaptation and vegetation sociology as well as the soil development. Three study sites in the Swiss Alps, differing in altitude and substrate (granite, dolomite, limestone) were investigated. Studies covered the permafrost-affected central parts of the slope as well as the surrounding areas. For characterizing distribution and temporal variability of ground ice geophysical methods were applied (electrical resistivity- and seismic refraction tomography). Temperature data loggers were used for monitoring the thermal regime (air-, surface- and soil temperatures). Chemical parameters (pH, C/N ratio) and nutrient contents (N, P, Ca, Mg, Mn, K) were analyzed in different depth levels. Plant communities were analyzed with the Braun-Blanquet method. To characterize physiognomic adaptation of trees, transects have been determined parallel to slope, measuring tree height, diameter and age. Results show a strong spatial correlation between frozen ground, formation of a thick organic layer (Tangelhumus), azonal plant species distribution and pronounced dwarfing of trees. Surrounding areas with unfrozen subsurface show an - for the particular altitude - expected species and soil composition and normal
Review of solid–liquid phase change materials and their encapsulation technologies
Su, Weiguang; Darkwa, Jo; Kokogiannakis, Georgios
2017-01-01
Various types of solid–liquid phase change materials (PCMs) have been reviewed for thermal energy storage applications. The review has shown that organic solid–liquid PCMs have much more advantages and capabilities than inorganic PCMs but do possess low thermal conductivity and density as well as being flammable. Inorganic PCMs possess higher heat storage capacities and conductivities, cheaper and readily available as well as being non-flammable, but do experience supercooling and phase segre...
Experimental-statistical model of liquid-phase epitaxy for InP/InGaAsP/InP heterostructures
International Nuclear Information System (INIS)
Vasil'ev, M.G.; Selin, A.A.; Shelyakin, A.A.
1985-01-01
A mathematic model of the process of liquid-phase epitaxy for double InP/InGaAsP/InP heterostructures is constructed using statistical methods of experiment planning. The analysis of the model shows that the degree of In-P system melt supercooling affects considerably the characteristics of double heterostructures
Epitope discovery with phylogenetic hidden Markov models.
LENUS (Irish Health Repository)
Lacerda, Miguel
2010-05-01
Existing methods for the prediction of immunologically active T-cell epitopes are based on the amino acid sequence or structure of pathogen proteins. Additional information regarding the locations of epitopes may be acquired by considering the evolution of viruses in hosts with different immune backgrounds. In particular, immune-dependent evolutionary patterns at sites within or near T-cell epitopes can be used to enhance epitope identification. We have developed a mutation-selection model of T-cell epitope evolution that allows the human leukocyte antigen (HLA) genotype of the host to influence the evolutionary process. This is one of the first examples of the incorporation of environmental parameters into a phylogenetic model and has many other potential applications where the selection pressures exerted on an organism can be related directly to environmental factors. We combine this novel evolutionary model with a hidden Markov model to identify contiguous amino acid positions that appear to evolve under immune pressure in the presence of specific host immune alleles and that therefore represent potential epitopes. This phylogenetic hidden Markov model provides a rigorous probabilistic framework that can be combined with sequence or structural information to improve epitope prediction. As a demonstration, we apply the model to a data set of HIV-1 protein-coding sequences and host HLA genotypes.
Neyman, Markov processes and survival analysis.
Yang, Grace
2013-07-01
J. Neyman used stochastic processes extensively in his applied work. One example is the Fix and Neyman (F-N) competing risks model (1951) that uses finite homogeneous Markov processes to analyse clinical trials with breast cancer patients. We revisit the F-N model, and compare it with the Kaplan-Meier (K-M) formulation for right censored data. The comparison offers a way to generalize the K-M formulation to include risks of recovery and relapses in the calculation of a patient's survival probability. The generalization is to extend the F-N model to a nonhomogeneous Markov process. Closed-form solutions of the survival probability are available in special cases of the nonhomogeneous processes, like the popular multiple decrement model (including the K-M model) and Chiang's staging model, but these models do not consider recovery and relapses while the F-N model does. An analysis of sero-epidemiology current status data with recurrent events is illustrated. Fix and Neyman used Neyman's RBAN (regular best asymptotic normal) estimates for the risks, and provided a numerical example showing the importance of considering both the survival probability and the length of time of a patient living a normal life in the evaluation of clinical trials. The said extension would result in a complicated model and it is unlikely to find analytical closed-form solutions for survival analysis. With ever increasing computing power, numerical methods offer a viable way of investigating the problem.
Unmixing hyperspectral images using Markov random fields
International Nuclear Information System (INIS)
Eches, Olivier; Dobigeon, Nicolas; Tourneret, Jean-Yves
2011-01-01
This paper proposes a new spectral unmixing strategy based on the normal compositional model that exploits the spatial correlations between the image pixels. The pure materials (referred to as endmembers) contained in the image are assumed to be available (they can be obtained by using an appropriate endmember extraction algorithm), while the corresponding fractions (referred to as abundances) are estimated by the proposed algorithm. Due to physical constraints, the abundances have to satisfy positivity and sum-to-one constraints. The image is divided into homogeneous distinct regions having the same statistical properties for the abundance coefficients. The spatial dependencies within each class are modeled thanks to Potts-Markov random fields. Within a Bayesian framework, prior distributions for the abundances and the associated hyperparameters are introduced. A reparametrization of the abundance coefficients is proposed to handle the physical constraints (positivity and sum-to-one) inherent to hyperspectral imagery. The parameters (abundances), hyperparameters (abundance mean and variance for each class) and the classification map indicating the classes of all pixels in the image are inferred from the resulting joint posterior distribution. To overcome the complexity of the joint posterior distribution, Markov chain Monte Carlo methods are used to generate samples asymptotically distributed according to the joint posterior of interest. Simulations conducted on synthetic and real data are presented to illustrate the performance of the proposed algorithm.
Markov transitions and the propagation of chaos
International Nuclear Information System (INIS)
Gottlieb, A.
1998-01-01
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also show that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution
Asymptotic evolution of quantum Markov chains
Energy Technology Data Exchange (ETDEWEB)
Novotny, Jaroslav [FNSPE, CTU in Prague, 115 19 Praha 1 - Stare Mesto (Czech Republic); Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany)
2012-07-01
The iterated quantum operations, so called quantum Markov chains, play an important role in various branches of physics. They constitute basis for many discrete models capable to explore fundamental physical problems, such as the approach to thermal equilibrium, or the asymptotic dynamics of macroscopic physical systems far from thermal equilibrium. On the other hand, in the more applied area of quantum technology they also describe general characteristic properties of quantum networks or they can describe different quantum protocols in the presence of decoherence. A particularly, an interesting aspect of these quantum Markov chains is their asymptotic dynamics and its characteristic features. We demonstrate there is always a vector subspace (typically low-dimensional) of so-called attractors on which the resulting superoperator governing the iterative time evolution of quantum states can be diagonalized and in which the asymptotic quantum dynamics takes place. As the main result interesting algebraic relations are presented for this set of attractors which allow to specify their dual basis and to determine them in a convenient way. Based on this general theory we show some generalizations concerning the theory of fixed points or asymptotic evolution of random quantum operations.
Monotone measures of ergodicity for Markov chains
Directory of Open Access Journals (Sweden)
J. Keilson
1998-01-01
Full Text Available The following paper, first written in 1974, was never published other than as part of an internal research series. Its lack of publication is unrelated to the merits of the paper and the paper is of current importance by virtue of its relation to the relaxation time. A systematic discussion is provided of the approach of a finite Markov chain to ergodicity by proving the monotonicity of an important set of norms, each measures of egodicity, whether or not time reversibility is present. The paper is of particular interest because the discussion of the relaxation time of a finite Markov chain [2] has only been clean for time reversible chains, a small subset of the chains of interest. This restriction is not present here. Indeed, a new relaxation time quoted quantifies the relaxation time for all finite ergodic chains (cf. the discussion of Q1(t below Equation (1.7]. This relaxation time was developed by Keilson with A. Roy in his thesis [6], yet to be published.
Approximating Markov Chains: What and why
International Nuclear Information System (INIS)
Pincus, S.
1996-01-01
Much of the current study of dynamical systems is focused on geometry (e.g., chaos and bifurcations) and ergodic theory. Yet dynamical systems were originally motivated by an attempt to open-quote open-quote solve,close-quote close-quote or at least understand, a discrete-time analogue of differential equations. As such, numerical, analytical solution techniques for dynamical systems would seem desirable. We discuss an approach that provides such techniques, the approximation of dynamical systems by suitable finite state Markov Chains. Steady state distributions for these Markov Chains, a straightforward calculation, will converge to the true dynamical system steady state distribution, with appropriate limit theorems indicated. Thus (i) approximation by a computable, linear map holds the promise of vastly faster steady state solutions for nonlinear, multidimensional differential equations; (ii) the solution procedure is unaffected by the presence or absence of a probability density function for the attractor, entirely skirting singularity, fractal/multifractal, and renormalization considerations. The theoretical machinery underpinning this development also implies that under very general conditions, steady state measures are weakly continuous with control parameter evolution. This means that even though a system may change periodicity, or become chaotic in its limiting behavior, such statistical parameters as the mean, standard deviation, and tail probabilities change continuously, not abruptly with system evolution. copyright 1996 American Institute of Physics
International Nuclear Information System (INIS)
Gao Zhong-Ke; Hu Li-Dan; Jin Ning-De
2013-01-01
We generate a directed weighted complex network by a method based on Markov transition probability to represent an experimental two-phase flow. We first systematically carry out gas—liquid two-phase flow experiments for measuring the time series of flow signals. Then we construct directed weighted complex networks from various time series in terms of a network generation method based on Markov transition probability. We find that the generated network inherits the main features of the time series in the network structure. In particular, the networks from time series with different dynamics exhibit distinct topological properties. Finally, we construct two-phase flow directed weighted networks from experimental signals and associate the dynamic behavior of gas-liquid two-phase flow with the topological statistics of the generated networks. The results suggest that the topological statistics of two-phase flow networks allow quantitative characterization of the dynamic flow behavior in the transitions among different gas—liquid flow patterns. (general)
Pathwise duals of monotone and additive Markov processes
Czech Academy of Sciences Publication Activity Database
Sturm, A.; Swart, Jan M.
-, - (2018) ISSN 0894-9840 R&D Projects: GA ČR GAP201/12/2613 Institutional support: RVO:67985556 Keywords : pathwise duality * monotone Markov process * additive Markov process * interacting particle system Subject RIV: BA - General Mathematics Impact factor: 0.854, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/swart-0465436.pdf
An introduction to hidden Markov models for biological sequences
DEFF Research Database (Denmark)
Krogh, Anders Stærmose
1998-01-01
A non-matematical tutorial on hidden Markov models (HMMs) plus a description of one of the applications of HMMs: gene finding.......A non-matematical tutorial on hidden Markov models (HMMs) plus a description of one of the applications of HMMs: gene finding....
Asymptotics for Estimating Equations in Hidden Markov Models
DEFF Research Database (Denmark)
Hansen, Jørgen Vinsløv; Jensen, Jens Ledet
Results on asymptotic normality for the maximum likelihood estimate in hidden Markov models are extended in two directions. The stationarity assumption is relaxed, which allows for a covariate process influencing the hidden Markov process. Furthermore a class of estimating equations is considered...
Efficient Incorporation of Markov Random Fields in Change Detection
DEFF Research Database (Denmark)
Aanæs, Henrik; Nielsen, Allan Aasbjerg; Carstensen, Jens Michael
2009-01-01
of noise, implying that the pixel-wise classifier is also noisy. There is thus a need for incorporating local homogeneity constraints into such a change detection framework. For this modelling task Markov Random Fields are suitable. Markov Random Fields have, however, previously been plagued by lack...
Markov trace on the Yokonuma-Hecke algebra
International Nuclear Information System (INIS)
Juyumaya, J.
2002-11-01
The objective of this note is to prove that there exists a Markov trace on the Yokonuma-Hecke algebra. A motivation to define a Markov trace is to get polynomial invariants for knots in the sense of Jones construction. (author)
Compositionality for Markov reward chains with fast and silent transitions
Markovski, J.; Sokolova, A.; Trcka, N.; Vink, de E.P.
2009-01-01
A parallel composition is defined for Markov reward chains with stochastic discontinuity, and with fast and silent transitions. In this setting, compositionality with respect to the relevant aggregation preorders is established. For Markov reward chains with fast transitions the preorders are
Model Checking Markov Reward Models with Impulse Rewards
Cloth, Lucia; Katoen, Joost-Pieter; Khattri, Maneesh; Pulungan, Reza; Bondavalli, Andrea; Haverkort, Boudewijn; Tang, Dong
This paper considers model checking of Markov reward models (MRMs), continuous-time Markov chains with state rewards as well as impulse rewards. The reward extension of the logic CSL (Continuous Stochastic Logic) is interpreted over such MRMs, and two numerical algorithms are provided to check the
Recursive smoothers for hidden discrete-time Markov chains
Directory of Open Access Journals (Sweden)
Lakhdar Aggoun
2005-01-01
Full Text Available We consider a discrete-time Markov chain observed through another Markov chain. The proposed model extends models discussed by Elliott et al. (1995. We propose improved recursive formulae to update smoothed estimates of processes related to the model. These recursive estimates are used to update the parameter of the model via the expectation maximization (EM algorithm.
First hitting probabilities for semi markov chains and estimation
DEFF Research Database (Denmark)
Georgiadis, Stylianos
2017-01-01
We first consider a stochastic system described by an absorbing semi-Markov chain with finite state space and we introduce the absorption probability to a class of recurrent states. Afterwards, we study the first hitting probability to a subset of states for an irreducible semi-Markov chain...
ANALYTIC WORD RECOGNITION WITHOUT SEGMENTATION BASED ON MARKOV RANDOM FIELDS
Coisy, C.; Belaid, A.
2004-01-01
In this paper, a method for analytic handwritten word recognition based on causal Markov random fields is described. The words models are HMMs where each state corresponds to a letter; each letter is modelled by a NSHPHMM (Markov field). Global models are build dynamically, and used for recognition
A Markov decision model for optimising economic production lot size ...
African Journals Online (AJOL)
Adopting such a Markov decision process approach, the states of a Markov chain represent possible states of demand. The decision of whether or not to produce additional inventory units is made using dynamic programming. This approach demonstrates the existence of an optimal state-dependent EPL size, and produces ...
Portfolio allocation under the vendor managed inventory: A Markov ...
African Journals Online (AJOL)
Portfolio allocation under the vendor managed inventory: A Markov decision process. ... Journal of Applied Sciences and Environmental Management ... This study provides a review of Markov decision processes and investigates its suitability for solutions to portfolio allocation problems under vendor managed inventory in ...
Logics and Models for Stochastic Analysis Beyond Markov Chains
DEFF Research Database (Denmark)
Zeng, Kebin
, because of the generality of ME distributions, we have to leave the world of Markov chains. To support ME distributions with multiple exits, we introduce a multi-exits ME distribution together with a process algebra MEME to express the systems having the semantics as Markov renewal processes with ME...
Arias, Nadia S; Bucci, Sandra J; Scholz, Fabian G; Goldstein, Guillermo
2015-10-01
Plants can avoid freezing damage by preventing extracellular ice formation below the equilibrium freezing temperature (supercooling). We used Olea europaea cultivars to assess which traits contribute to avoid ice nucleation at sub-zero temperatures. Seasonal leaf water relations, non-structural carbohydrates, nitrogen and tissue damage and ice nucleation temperatures in different plant parts were determined in five cultivars growing in the Patagonian cold desert. Ice seeding in roots occurred at higher temperatures than in stems and leaves. Leaves of cold acclimated cultivars supercooled down to -13 °C, substantially lower than the minimum air temperatures observed in the study site. During winter, leaf ice nucleation and leaf freezing damage (LT50 ) occurred at similar temperatures, typical of plant tissues that supercool. Higher leaf density and cell wall rigidity were observed during winter, consistent with a substantial acclimation to sub-zero temperatures. Larger supercooling capacity and lower LT50 were observed in cold-acclimated cultivars with higher osmotically active solute content, higher tissue elastic adjustments and lower apoplastic water. Irreversible leaf damage was only observed in laboratory experiments at very low temperatures, but not in the field. A comparative analysis of closely related plants avoids phylogenetic independence bias in a comparative study of adaptations to survive low temperatures. © 2015 John Wiley & Sons Ltd.
Introduction to the numerical solutions of Markov chains
Stewart, Williams J
1994-01-01
A cornerstone of applied probability, Markov chains can be used to help model how plants grow, chemicals react, and atoms diffuse - and applications are increasingly being found in such areas as engineering, computer science, economics, and education. To apply the techniques to real problems, however, it is necessary to understand how Markov chains can be solved numerically. In this book, the first to offer a systematic and detailed treatment of the numerical solution of Markov chains, William Stewart provides scientists on many levels with the power to put this theory to use in the actual world, where it has applications in areas as diverse as engineering, economics, and education. His efforts make for essential reading in a rapidly growing field. Here, Stewart explores all aspects of numerically computing solutions of Markov chains, especially when the state is huge. He provides extensive background to both discrete-time and continuous-time Markov chains and examines many different numerical computing metho...
Sonocrystallization of Interesterified Soybean Oil: Effect of Saturation Level and Supercooling.
Lee, Juhee; Claro da Silva, Roberta; Gibon, Veronique; Martini, Silvana
2018-04-01
The aim of this study was to investigate the effects of supercooling and degree of saturation on lipid sonocrystallization under similar driving force of crystallization. Samples consisting of 100%, 50%, and 20% interesterified soybean oil (IESBO) diluted in high-oleic sunflower oil (HOSFO) were crystallized with and without high-intensity ultrasound (HIU). Two power levels were used by changing the amplitude of vibration of the tip (24 μm and 108 μm of tip amplitude). HIU operating at a frequency of 20 kHz was applied for 10 s. Sonication induced crystallization in the 100% IESBO sample and sonication power did not affect the results. A greater induction in crystallization was observed when higher power levels were used in the 50% IESBO sample, while no effect was observed in the crystallization kinetics of the 20% IESBO samples. Changes in the crystallization kinetics affected physical properties of the material, influencing elasticity. For example, sonication increased the elasticity of the 100% IESBO sample for both tip amplitudes from 435.9 ± 173.3 Pa to 72735.0 ± 9547.9 Pa for the nonsonicated and sonicated samples using 108 μm of amplitude, respectively. However, sonication only increased the elasticity in the 50% sample when used at the higher power level of 108 μm from 564.2 ± 175.2 Pa to 21774.0 ± 5694.9 Pa, and it did not affect the elasticity of the 20% IESBO samples. These results show that the level of saturation and the degree of supercooling affect sonication efficiency. High-intensity ultrasound (HIU) has been used as a novel method for changing the crystallization behavior of fats. HIU can be used to improve the physical properties of trans-free fats that are low in saturated fatty acids. Although recent studies have proven the effectiveness of this method to induce crystallization, the process must still be optimized to the industrial setting. All process parameters should be considered during the application of HIU, as they directly
Aerodynamic levitator furnace for measuring thermophysical properties of refractory liquids.
Langstaff, D; Gunn, M; Greaves, G N; Marsing, A; Kargl, F
2013-12-01
The development of novel contactless aerodynamic laser heated levitation techniques is reported that enable thermophysical properties of refractory liquids to be measured in situ in the solid, liquid, and supercooled liquid state and demonstrated here for alumina. Starting with polished crystalline ruby spheres, we show how, by accurately measuring the changing radius, the known density in the solid state can be reproduced from room temperature to the melting point at 2323 K. Once molten, by coupling the floating liquid drop to acoustic oscillations via the levitating gas, the mechanical resonance and damping of the liquid can be measured precisely with high-speed high-resolution shadow cast imaging. The resonance frequency relates to the surface tension, the decay constant to the viscosity, and the ellipsoidal size and shape of the levitating drop to the density. This unique instrumentation enables these related thermophysical properties to be recorded in situ over the entire liquid and supercooled range of alumina, from the boiling point at 3240 K, until spontaneous crystallization occurs around 1860 K, almost 500 below the melting point. We believe that the utility that this unique instrumentation provides will be applicable to studying these important properties in many other high temperature liquids.
The Markov moment problem and extremal problems
Kreĭn, M G; Louvish, D
1977-01-01
In this book, an extensive circle of questions originating in the classical work of P. L. Chebyshev and A. A. Markov is considered from the more modern point of view. It is shown how results and methods of the generalized moment problem are interlaced with various questions of the geometry of convex bodies, algebra, and function theory. From this standpoint, the structure of convex and conical hulls of curves is studied in detail and isoperimetric inequalities for convex hulls are established; a theory of orthogonal and quasiorthogonal polynomials is constructed; problems on limiting values of integrals and on least deviating functions (in various metrics) are generalized and solved; problems in approximation theory and interpolation and extrapolation in various function classes (analytic, absolutely monotone, almost periodic, etc.) are solved, as well as certain problems in optimal control of linear objects.
Learning Markov Decision Processes for Model Checking
DEFF Research Database (Denmark)
Mao, Hua; Chen, Yingke; Jaeger, Manfred
2012-01-01
. The proposed learning algorithm is adapted from algorithms for learning deterministic probabilistic finite automata, and extended to include both probabilistic and nondeterministic transitions. The algorithm is empirically analyzed and evaluated by learning system models of slot machines. The evaluation......Constructing an accurate system model for formal model verification can be both resource demanding and time-consuming. To alleviate this shortcoming, algorithms have been proposed for automatically learning system models based on observed system behaviors. In this paper we extend the algorithm...... on learning probabilistic automata to reactive systems, where the observed system behavior is in the form of alternating sequences of inputs and outputs. We propose an algorithm for automatically learning a deterministic labeled Markov decision process model from the observed behavior of a reactive system...
Learning Markov models for stationary system behaviors
DEFF Research Database (Denmark)
Chen, Yingke; Mao, Hua; Jaeger, Manfred
2012-01-01
to a single long observation sequence, and in these situations existing automatic learning methods cannot be applied. In this paper, we adapt algorithms for learning variable order Markov chains from a single observation sequence of a target system, so that stationary system properties can be verified using......Establishing an accurate model for formal verification of an existing hardware or software system is often a manual process that is both time consuming and resource demanding. In order to ease the model construction phase, methods have recently been proposed for automatically learning accurate...... the learned model. Experiments demonstrate that system properties (formulated as stationary probabilities of LTL formulas) can be reliably identified using the learned model....
Neuroevolution Mechanism for Hidden Markov Model
Directory of Open Access Journals (Sweden)
Nabil M. Hewahi
2011-12-01
Full Text Available Hidden Markov Model (HMM is a statistical model based on probabilities. HMM is becoming one of the major models involved in many applications such as natural language
processing, handwritten recognition, image processing, prediction systems and many more. In this research we are concerned with finding out the best HMM for a certain application domain. We propose a neuroevolution process that is based first on converting the HMM to a neural network, then generating many neural networks at random where each represents a HMM. We proceed by
applying genetic operators to obtain new set of neural networks where each represents HMMs, and updating the population. Finally select the best neural network based on a fitness function.
Improved hidden Markov model for nosocomial infections.
Khader, Karim; Leecaster, Molly; Greene, Tom; Samore, Matthew; Thomas, Alun
2014-12-01
We propose a novel hidden Markov model (HMM) for parameter estimation in hospital transmission models, and show that commonly made simplifying assumptions can lead to severe model misspecification and poor parameter estimates. A standard HMM that embodies two commonly made simplifying assumptions, namely a fixed patient count and binomially distributed detections is compared with a new alternative HMM that does not require these simplifying assumptions. Using simulated data, we demonstrate how each of the simplifying assumptions used by the standard model leads to model misspecification, whereas the alternative model results in accurate parameter estimates. © The Authors 2013. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Estimation and uncertainty of reversible Markov models.
Trendelkamp-Schroer, Benjamin; Wu, Hao; Paul, Fabian; Noé, Frank
2015-11-07
Reversibility is a key concept in Markov models and master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model rely heavily on the reversibility property. The estimation of a reversible transition matrix from simulation data is, therefore, crucial to the successful application of the previously developed theory. In this work, we discuss methods for the maximum likelihood estimation of transition matrices from finite simulation data and present a new algorithm for the estimation if reversibility with respect to a given stationary vector is desired. We also develop new methods for the Bayesian posterior inference of reversible transition matrices with and without given stationary vector taking into account the need for a suitable prior distribution preserving the meta-stable features of the observed process during posterior inference. All algorithms here are implemented in the PyEMMA software--http://pyemma.org--as of version 2.0.
Monte Carlo simulation of Markov unreliability models
International Nuclear Information System (INIS)
Lewis, E.E.; Boehm, F.
1984-01-01
A Monte Carlo method is formulated for the evaluation of the unrealibility of complex systems with known component failure and repair rates. The formulation is in terms of a Markov process allowing dependences between components to be modeled and computational efficiencies to be achieved in the Monte Carlo simulation. Two variance reduction techniques, forced transition and failure biasing, are employed to increase computational efficiency of the random walk procedure. For an example problem these result in improved computational efficiency by more than three orders of magnitudes over analog Monte Carlo. The method is generalized to treat problems with distributed failure and repair rate data, and a batching technique is introduced and shown to result in substantial increases in computational efficiency for an example problem. A method for separating the variance due to the data uncertainty from that due to the finite number of random walks is presented. (orig.)
Recombination Processes and Nonlinear Markov Chains.
Pirogov, Sergey; Rybko, Alexander; Kalinina, Anastasia; Gelfand, Mikhail
2016-09-01
Bacteria are known to exchange genetic information by horizontal gene transfer. Since the frequency of homologous recombination depends on the similarity between the recombining segments, several studies examined whether this could lead to the emergence of subspecies. Most of them simulated fixed-size Wright-Fisher populations, in which the genetic drift should be taken into account. Here, we use nonlinear Markov processes to describe a bacterial population evolving under mutation and recombination. We consider a population structure as a probability measure on the space of genomes. This approach implies the infinite population size limit, and thus, the genetic drift is not assumed. We prove that under these conditions, the emergence of subspecies is impossible.
SHARP ENTRYWISE PERTURBATION BOUNDS FOR MARKOV CHAINS.
Thiede, Erik; VAN Koten, Brian; Weare, Jonathan
For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem in computational statistical physics. We have derived perturbation bounds on the relative error of the invariant distribution that reveal these variations in sensitivity. Our bounds are sharp, we do not impose any structural assumptions on the transition matrix or on the perturbation, and computing the bounds has the same complexity as computing the invariant distribution or computing other bounds in the literature. Moreover, our bounds have a simple interpretation in terms of hitting times, which can be used to draw intuitive but rigorous conclusions about the sensitivity of a chain to various types of perturbations.
A Markov Chain Model for Contagion
Directory of Open Access Journals (Sweden)
Angelos Dassios
2014-11-01
Full Text Available We introduce a bivariate Markov chain counting process with contagion for modelling the clustering arrival of loss claims with delayed settlement for an insurance company. It is a general continuous-time model framework that also has the potential to be applicable to modelling the clustering arrival of events, such as jumps, bankruptcies, crises and catastrophes in finance, insurance and economics with both internal contagion risk and external common risk. Key distributional properties, such as the moments and probability generating functions, for this process are derived. Some special cases with explicit results and numerical examples and the motivation for further actuarial applications are also discussed. The model can be considered a generalisation of the dynamic contagion process introduced by Dassios and Zhao (2011.
Markov state models of protein misfolding
Sirur, Anshul; De Sancho, David; Best, Robert B.
2016-02-01
Markov state models (MSMs) are an extremely useful tool for understanding the conformational dynamics of macromolecules and for analyzing MD simulations in a quantitative fashion. They have been extensively used for peptide and protein folding, for small molecule binding, and for the study of native ensemble dynamics. Here, we adapt the MSM methodology to gain insight into the dynamics of misfolded states. To overcome possible flaws in root-mean-square deviation (RMSD)-based metrics, we introduce a novel discretization approach, based on coarse-grained contact maps. In addition, we extend the MSM methodology to include "sink" states in order to account for the irreversibility (on simulation time scales) of processes like protein misfolding. We apply this method to analyze the mechanism of misfolding of tandem repeats of titin domains, and how it is influenced by confinement in a chaperonin-like cavity.
Multivariate Markov chain modeling for stock markets
Maskawa, Jun-ichi
2003-06-01
We study a multivariate Markov chain model as a stochastic model of the price changes of portfolios in the framework of the mean field approximation. The time series of price changes are coded into the sequences of up and down spins according to their signs. We start with the discussion for small portfolios consisting of two stock issues. The generalization of our model to arbitrary size of portfolio is constructed by a recurrence relation. The resultant form of the joint probability of the stationary state coincides with Gibbs measure assigned to each configuration of spin glass model. Through the analysis of actual portfolios, it has been shown that the synchronization of the direction of the price changes is well described by the model.
Anatomy Ontology Matching Using Markov Logic Networks
Directory of Open Access Journals (Sweden)
Chunhua Li
2016-01-01
Full Text Available The anatomy of model species is described in ontologies, which are used to standardize the annotations of experimental data, such as gene expression patterns. To compare such data between species, we need to establish relationships between ontologies describing different species. Ontology matching is a kind of solutions to find semantic correspondences between entities of different ontologies. Markov logic networks which unify probabilistic graphical model and first-order logic provide an excellent framework for ontology matching. We combine several different matching strategies through first-order logic formulas according to the structure of anatomy ontologies. Experiments on the adult mouse anatomy and the human anatomy have demonstrated the effectiveness of proposed approach in terms of the quality of result alignment.
Hydrophobic Surfaces: Topography Effects on Wetting by Supercooled Water and Freezing Delay
DEFF Research Database (Denmark)
Heydari, Golrokh; Thormann, Esben; Järn, Mikael
2013-01-01
Hydrophobicity, and in particular superhydrophobicity, has been extensively considered to promote ice-phobicity. Dynamic contact angle measurements above 0 °C have been widely used to evaluate the water repellency. However, it is the wetting properties of supercooled water at subzero temperatures...... and the derived work of adhesion that are important for applications dealing with icing. In this work we address this issue by determining the temperature-dependent dynamic contact angle of microliter-sized water droplets on a smooth hydrophobic and a superhydrophobic surface with similar surface chemistry....... The data highlight how the work of adhesion of water in the temperature interval from about 25 °C to below −10 °C is affected by surface topography. A marked decrease in contact angle on the superhydrophobic surface is observed with decreasing temperature, and we attribute this to condensation below...
Study of magnetoresistance in the supercooled state of Dy-Y alloys
Jena, Rudra Prasad; Lakhani, Archana
2018-02-01
We report the magnetoresistance studies on Dy1-xYx (x ≤ 0.05) alloys across the first order helimagnetic to ferromagnetic phase transition. These alloys exhibit multiple magnetic phases on varying the temperature and magnetic field. The magnetoresistance studies in the hysteresis region shows irreversibility in forward and reverse field cycles. The resistivity values at zero field for these alloys after zero field cooling to the measurement temperatures, are different in both forward and reverse field cycles. The path dependence of magnetoresistance suggests the presence of helimagnetic phase as the supercooled metastable state which transforms to the stable ferromagnetic state on increasing the field. At high magnetic fields negative magnetoresistance following a linear dependence with field is observed which is attributed to the magnon scattering.
Crossing over...Markov meets Mendel.
Mneimneh, Saad
2012-01-01
Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them). From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics). However, other students may easily follow by omitting the
Crossing over...Markov meets Mendel.
Directory of Open Access Journals (Sweden)
Saad Mneimneh
Full Text Available Chromosomal crossover is a biological mechanism to combine parental traits. It is perhaps the first mechanism ever taught in any introductory biology class. The formulation of crossover, and resulting recombination, came about 100 years after Mendel's famous experiments. To a great extent, this formulation is consistent with the basic genetic findings of Mendel. More importantly, it provides a mathematical insight for his two laws (and corrects them. From a mathematical perspective, and while it retains similarities, genetic recombination guarantees diversity so that we do not rapidly converge to the same being. It is this diversity that made the study of biology possible. In particular, the problem of genetic mapping and linkage-one of the first efforts towards a computational approach to biology-relies heavily on the mathematical foundation of crossover and recombination. Nevertheless, as students we often overlook the mathematics of these phenomena. Emphasizing the mathematical aspect of Mendel's laws through crossover and recombination will prepare the students to make an early realization that biology, in addition to being experimental, IS a computational science. This can serve as a first step towards a broader curricular transformation in teaching biological sciences. I will show that a simple and modern treatment of Mendel's laws using a Markov chain will make this step possible, and it will only require basic college-level probability and calculus. My personal teaching experience confirms that students WANT to know Markov chains because they hear about them from bioinformaticists all the time. This entire exposition is based on three homework problems that I designed for a course in computational biology. A typical reader is, therefore, an instructional staff member or a student in a computational field (e.g., computer science, mathematics, statistics, computational biology, bioinformatics. However, other students may easily follow by
Bayesian tomography by interacting Markov chains
Romary, T.
2017-12-01
In seismic tomography, we seek to determine the velocity of the undergound from noisy first arrival travel time observations. In most situations, this is an ill posed inverse problem that admits several unperfect solutions. Given an a priori distribution over the parameters of the velocity model, the Bayesian formulation allows to state this problem as a probabilistic one, with a solution under the form of a posterior distribution. The posterior distribution is generally high dimensional and may exhibit multimodality. Moreover, as it is known only up to a constant, the only sensible way to addressthis problem is to try to generate simulations from the posterior. The natural tools to perform these simulations are Monte Carlo Markov chains (MCMC). Classical implementations of MCMC algorithms generally suffer from slow mixing: the generated states are slow to enter the stationary regime, that is to fit the observations, and when one mode of the posterior is eventually identified, it may become difficult to visit others. Using a varying temperature parameter relaxing the constraint on the data may help to enter the stationary regime. Besides, the sequential nature of MCMC makes them ill fitted toparallel implementation. Running a large number of chains in parallel may be suboptimal as the information gathered by each chain is not mutualized. Parallel tempering (PT) can be seen as a first attempt to make parallel chains at different temperatures communicate but only exchange information between current states. In this talk, I will show that PT actually belongs to a general class of interacting Markov chains algorithm. I will also show that this class enables to design interacting schemes that can take advantage of the whole history of the chain, by authorizing exchanges toward already visited states. The algorithms will be illustrated with toy examples and an application to first arrival traveltime tomography.
Ice-lens formation and geometrical supercooling in soils and other colloidal materials
Style, Robert W.
2011-10-14
We present a physically intuitive model of ice-lens formation and growth during the freezing of soils and other dense, particulate suspensions. Motivated by experimental evidence, we consider the growth of an ice-filled crack in a freezing soil. At low temperatures, ice in the crack exerts large pressures on the crack walls that will eventually cause the crack to split open. We show that the crack will then propagate across the soil to form a new lens. The process is controlled by two factors: the cohesion of the soil and the geometrical supercooling of the water in the soil, a new concept introduced to measure the energy available to form a new ice lens. When the supercooling exceeds a critical amount (proportional to the cohesive strength of the soil) a new ice lens forms. This condition for ice-lens formation and growth does not appeal to any ad hoc, empirical assumptions, and explains how periodic ice lenses can form with or without the presence of a frozen fringe. The proposed mechanism is in good agreement with experiments, in particular explaining ice-lens pattern formation and surges in heave rate associated with the growth of new lenses. Importantly for systems with no frozen fringe, ice-lens formation and frost heave can be predicted given only the unfrozen properties of the soil. We use our theory to estimate ice-lens growth temperatures obtaining quantitative agreement with the limited experimental data that are currently available. Finally we suggest experiments that might be performed in order to verify this theory in more detail. The theory is generalizable to complex natural-soil scenarios and should therefore be useful in the prediction of macroscopic frost-heave rates. © 2011 American Physical Society.
Modeling Uncertainty of Directed Movement via Markov Chains
Directory of Open Access Journals (Sweden)
YIN Zhangcai
2015-10-01
Full Text Available Probabilistic time geography (PTG is suggested as an extension of (classical time geography, in order to present the uncertainty of an agent located at the accessible position by probability. This may provide a quantitative basis for most likely finding an agent at a location. In recent years, PTG based on normal distribution or Brown bridge has been proposed, its variance, however, is irrelevant with the agent's speed or divergent with the increase of the speed; so they are difficult to take into account application pertinence and stability. In this paper, a new method is proposed to model PTG based on Markov chain. Firstly, a bidirectional conditions Markov chain is modeled, the limit of which, when the moving speed is large enough, can be regarded as the Brown bridge, thus has the characteristics of digital stability. Then, the directed movement is mapped to Markov chains. The essential part is to build step length, the state space and transfer matrix of Markov chain according to the space and time position of directional movement, movement speed information, to make sure the Markov chain related to the movement speed. Finally, calculating continuously the probability distribution of the directed movement at any time by the Markov chains, it can be get the possibility of an agent located at the accessible position. Experimental results show that, the variance based on Markov chains not only is related to speed, but also is tending towards stability with increasing the agent's maximum speed.
Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium
Kapfer, Sebastian C.; Krauth, Werner
2017-12-01
We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.
Transitions through critical temperatures in nematic liquid crystals
Majumdar, Apala; Ockendon, John; Howell, Peter; Surovyatkina, Elena
2013-01-01
We obtain estimates for critical nematic liquid crystal (LC) temperatures under the action of a slowly varying temperature-dependent control variable. We show that biaxiality has a negligible effect within our model and that these delay estimates are well described by a purely uniaxial model. The static theory predicts two critical temperatures: the supercooling temperature below which the isotropic phase loses stability and the superheating temperature above which the ordered nematic states do not exist. In contrast to the static problem, the isotropic phase exhibits a memory effect below the supercooling temperature in the dynamic framework. This delayed loss of stability is independent of the rate of change of temperature and depends purely on the initial value of the temperature. We also show how our results can be used to improve estimates for LC material constants. © 2013 American Physical Society.
Transitions through critical temperatures in nematic liquid crystals
Majumdar, Apala
2013-08-06
We obtain estimates for critical nematic liquid crystal (LC) temperatures under the action of a slowly varying temperature-dependent control variable. We show that biaxiality has a negligible effect within our model and that these delay estimates are well described by a purely uniaxial model. The static theory predicts two critical temperatures: the supercooling temperature below which the isotropic phase loses stability and the superheating temperature above which the ordered nematic states do not exist. In contrast to the static problem, the isotropic phase exhibits a memory effect below the supercooling temperature in the dynamic framework. This delayed loss of stability is independent of the rate of change of temperature and depends purely on the initial value of the temperature. We also show how our results can be used to improve estimates for LC material constants. © 2013 American Physical Society.
Liquid Structures and Physical Properties -- Ground Based Studies for ISS Experiments
Kelton, K. F.; Bendert, J. C.; Mauro, N. A.
2012-01-01
Studies of electrostatically-levitated supercooled liquids have demonstrated strong short- and medium-range ordering in transition metal and alloy liquids, which can influence phase transitions like crystal nucleation and the glass transition. The structure is also related to the liquid properties. Planned ISS experiments will allow a deeper investigation of these results as well as the first investigations of a new type of coupling in crystal nucleation in primary crystallizing liquids, resulting from a linking of the stochastic processes of diffusion with interfacial-attachment. A brief description of the techniques used for ground-based studies and some results relevant to planned ISS investigations are discussed.
Markov processes from K. Ito's perspective (AM-155)
Stroock, Daniel W
2003-01-01
Kiyosi Itô''s greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô''s program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov''s approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed incremen
Sampling rare fluctuations of discrete-time Markov chains
Whitelam, Stephen
2018-03-01
We describe a simple method that can be used to sample the rare fluctuations of discrete-time Markov chains. We focus on the case of Markov chains with well-defined steady-state measures, and derive expressions for the large-deviation rate functions (and upper bounds on such functions) for dynamical quantities extensive in the length of the Markov chain. We illustrate the method using a series of simple examples, and use it to study the fluctuations of a lattice-based model of active matter that can undergo motility-induced phase separation.
Markov's theorem and algorithmically non-recognizable combinatorial manifolds
International Nuclear Information System (INIS)
Shtan'ko, M A
2004-01-01
We prove the theorem of Markov on the existence of an algorithmically non-recognizable combinatorial n-dimensional manifold for every n≥4. We construct for the first time a concrete manifold which is algorithmically non-recognizable. A strengthened form of Markov's theorem is proved using the combinatorial methods of regular neighbourhoods and handle theory. The proofs coincide for all n≥4. We use Borisov's group with insoluble word problem. It has two generators and twelve relations. The use of this group forms the base for proving the strengthened form of Markov's theorem
Variation along liquid isomorphs of the driving force for crystallization
DEFF Research Database (Denmark)
Pedersen, Ulf Rørbæk; Adrjanowicz, Karolina; Niss, Kristine
2017-01-01
at a reference temperature. More general analysis allows interpretation of experimental data for molecular liquids such as dimethyl phthalate and indomethacin, and suggests that the isomorph scaling exponent γ in these cases is an increasing function of density, although this cannot be seen in measurements......We investigate the variation of the driving force for crystallization of a supercooled liquid along isomorphs, curves along which structure and dynamics are invariant. The variation is weak, and can be predicted accurately for the Lennard-Jones fluid using a recently developed formalism and data...
International Nuclear Information System (INIS)
Mauro, N.A.; Vogt, Adam J.; Johnson, Mark L.; Bendert, James C.; Soklaski, Ryan; Yang, Li; Kelton, K.F.
2013-01-01
The results of high energy X-ray scattering studies of equilibrium and supercooled Cu 100−x Zr x (x = 46 and 54) and Cu x Hf 100−x (x = 55 and 60.8) liquids and the corresponding glasses are presented. The liquid data were obtained in a containerless environment using the beamline electrostatic levitation (BESL) technique. The total structure factor and total pair correlation functions were measured as a function of temperature for the liquids, and for the glasses at room temperature. A developing asymmetry in the peak of the first coordination shell in the total pair correlation function suggests chemical ordering in the liquids with cooling. This asymmetry takes the form of two prominent peaks, suggesting two prominent ordering length scales. When the magnitudes of these peaks are extrapolated to the glass transition temperature a discontinuity is observed, indicating that an abrupt increase in the magnitude is required to match the observed peak heights in the glass. This suggests that the structure of the supercooled liquid orders more rapidly near the glass transition temperature, a conclusion that is supported by molecular dynamics simulations. This observed structural evolution of the liquid indicates that the concept of fragility, typically defined from the behavior of viscosity with temperature, has a measurable structural signature as well, which can be observed in X-ray diffraction studies
Filtering of a Markov Jump Process with Counting Observations
International Nuclear Information System (INIS)
Ceci, C.; Gerardi, A.
2000-01-01
This paper concerns the filtering of an R d -valued Markov pure jump process when only the total number of jumps are observed. Strong and weak uniqueness for the solutions of the filtering equations are discussed
The Independence of Markov's Principle in Type Theory
DEFF Research Database (Denmark)
Coquand, Thierry; Mannaa, Bassel
2017-01-01
for the generic point of this model. Instead we design an extension of type theory, which intuitively extends type theory by the addition of a generic point of Cantor space. We then show the consistency of this extension by a normalization argument. Markov's principle does not hold in this extension......In this paper, we show that Markov's principle is not derivable in dependent type theory with natural numbers and one universe. One way to prove this would be to remark that Markov's principle does not hold in a sheaf model of type theory over Cantor space, since Markov's principle does not hold......, and it follows that it cannot be proved in type theory....
Classification of customer lifetime value models using Markov chain
Permana, Dony; Pasaribu, Udjianna S.; Indratno, Sapto W.; Suprayogi
2017-10-01
A firm’s potential reward in future time from a customer can be determined by customer lifetime value (CLV). There are some mathematic methods to calculate it. One method is using Markov chain stochastic model. Here, a customer is assumed through some states. Transition inter the states follow Markovian properties. If we are given some states for a customer and the relationships inter states, then we can make some Markov models to describe the properties of the customer. As Markov models, CLV is defined as a vector contains CLV for a customer in the first state. In this paper we make a classification of Markov Models to calculate CLV. Start from two states of customer model, we make develop in many states models. The development a model is based on weaknesses in previous model. Some last models can be expected to describe how real characters of customers in a firm.
Markov Chain: A Predictive Model for Manpower Planning ...
African Journals Online (AJOL)
ADOWIE PERE
Keywords: Markov Chain, Transition Probability Matrix, Manpower Planning, Recruitment, Promotion, .... movement of the workforce in Jordan productivity .... Planning periods, with T being the horizon, the value of t represents a session.
Continuous-time Markov decision processes theory and applications
Guo, Xianping
2009-01-01
This volume provides the first book entirely devoted to recent developments on the theory and applications of continuous-time Markov decision processes (MDPs). The MDPs presented here include most of the cases that arise in applications.
A simplified parsimonious higher order multivariate Markov chain model
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, a simplified parsimonious higher-order multivariate Markov chain model (SPHOMMCM) is presented. Moreover, parameter estimation method of TPHOMMCM is give. Numerical experiments shows the effectiveness of TPHOMMCM.
A tridiagonal parsimonious higher order multivariate Markov chain model
Wang, Chao; Yang, Chuan-sheng
2017-09-01
In this paper, we present a tridiagonal parsimonious higher-order multivariate Markov chain model (TPHOMMCM). Moreover, estimation method of the parameters in TPHOMMCM is give. Numerical experiments illustrate the effectiveness of TPHOMMCM.
Optimisation of Hidden Markov Model using Baum–Welch algorithm ...
Indian Academy of Sciences (India)
The present work is a part of development of Hidden Markov Model. (HMM) based ... the Himalaya. In this work, HMMs have been developed for forecasting of maximum and minimum ..... data collection teams of Snow and Avalanche Study.
Markov chain: a predictive model for manpower planning | Ezugwu ...
African Journals Online (AJOL)
In respect of organizational management, numerous previous studies have ... and to forecast the academic staff structure of the university in the next five years. ... Keywords: Markov Chain, Transition Probability Matrix, Manpower Planning, ...
A Novel Method for Decoding Any High-Order Hidden Markov Model
Directory of Open Access Journals (Sweden)
Fei Ye
2014-01-01
Full Text Available This paper proposes a novel method for decoding any high-order hidden Markov model. First, the high-order hidden Markov model is transformed into an equivalent first-order hidden Markov model by Hadar’s transformation. Next, the optimal state sequence of the equivalent first-order hidden Markov model is recognized by the existing Viterbi algorithm of the first-order hidden Markov model. Finally, the optimal state sequence of the high-order hidden Markov model is inferred from the optimal state sequence of the equivalent first-order hidden Markov model. This method provides a unified algorithm framework for decoding hidden Markov models including the first-order hidden Markov model and any high-order hidden Markov model.
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Valor, A.; Caleyo, F.; Alfonso, L.; Velázquez, J. C.; Hallen, J. M.
2013-01-01
The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure ...
On almost-periodic points of a topological Markov chain
International Nuclear Information System (INIS)
Bogatyi, Semeon A; Redkozubov, Vadim V
2012-01-01
We prove that a transitive topological Markov chain has almost-periodic points of all D-periods. Moreover, every D-period is realized by continuously many distinct minimal sets. We give a simple constructive proof of the result which asserts that any transitive topological Markov chain has periodic points of almost all periods, and study the structure of the finite set of positive integers that are not periods.
On mean reward variance in semi-Markov processes
Czech Academy of Sciences Publication Activity Database
Sladký, Karel
2005-01-01
Roč. 62, č. 3 (2005), s. 387-397 ISSN 1432-2994 R&D Projects: GA ČR(CZ) GA402/05/0115; GA ČR(CZ) GA402/04/1294 Institutional research plan: CEZ:AV0Z10750506 Keywords : Markov and semi-Markov processes with rewards * variance of cumulative reward * asymptotic behaviour Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 0.259, year: 2005
Reliability estimation of semi-Markov systems: a case study
International Nuclear Information System (INIS)
Ouhbi, Brahim; Limnios, Nikolaos
1997-01-01
In this article, we are concerned with the estimation of the reliability and the availability of a turbo-generator rotor using a set of data observed in a real engineering situation provided by Electricite De France (EDF). The rotor is modeled by a semi-Markov process, which is used to estimate the rotor's reliability and availability. To do this, we present a method for estimating the semi-Markov kernel from a censored data
Quantum tomography, phase-space observables and generalized Markov kernels
International Nuclear Information System (INIS)
Pellonpaeae, Juha-Pekka
2009-01-01
We construct a generalized Markov kernel which transforms the observable associated with the homodyne tomography into a covariant phase-space observable with a regular kernel state. Illustrative examples are given in the cases of a 'Schroedinger cat' kernel state and the Cahill-Glauber s-parametrized distributions. Also we consider an example of a kernel state when the generalized Markov kernel cannot be constructed.
Nandi, Prithwish K.; Burnham, Christian J.; English, Niall J.
2018-01-01
Understanding water solidification, especially in "No Man's Land" (NML) (150 K < T < 235 K) is crucially important (e.g., upper-troposphere cloud processes) and challenging. A rather neglected aspect of tropospheric ice-crystallite formation is inevitably present electromagnetic fields' role. Here, we employ non-equilibrium molecular dynamics of aggressively quenched supercooled water nano-droplets in the gas phase under NML conditions, in externally applied electromagnetic (e/m) fields, elucidating significant differences between effects of static and oscillating fields: although static fields induce "electro-freezing," e/m fields exhibit the contrary - solidification inhibition. This anti-freeze action extends not only to crystal-ice formation but also restricts amorphisation, i.e., suppression of low-density amorphous ice which forms otherwise in zero-field NML environments. E/m-field applications maintain water in the deeply supercooled state in an "entropic trap," which is ripe for industrial impacts in cryo-freezing, etc.
Yamaguchi, Akira; Namekawa, Manato; Itoh, Tetsuji; Teramae, Norio
2012-01-01
The fluorescence dynamics of rhodamine B (RhB) immobilized on the pore surface of aminopropyl (AP)-modified mesoporous silica (diameter of the silica framework, 3.1 nm) was examined at temperatures between 293 and 193 K to study the microviscosity of supercooled water confined inside the pores. The mesoporous silica specimen with a dense AP layer (2.1 molecules nm(-2)) was prepared, and RhB isothiocyanate was covalently bound to part of the surface AP groups. The fluorescence lifetime of the surface RhB increased with decreasing temperature from 293 to 223 K, indicating that freezing of the confined water did not occur in this temperature range. The microviscosity of the supercooled confined water was evaluated from an analysis of the lifetime data based on a frequency-dependent friction model.
McPhee, Miles G.; Stevens, Craig L.; Smith, Inga J.; Robinson, Natalie J.
2016-04-01
Late winter measurements of turbulent quantities in tidally modulated flow under land-fast sea ice near the Erebus Glacier Tongue, McMurdo Sound, Antarctica, identified processes that influence growth at the interface of an ice surface in contact with supercooled seawater. The data show that turbulent heat exchange at the ocean-ice boundary is characterized by the product of friction velocity and (negative) water temperature departure from freezing, analogous to similar results for moderate melting rates in seawater above freezing. Platelet ice growth appears to increase the hydraulic roughness (drag) of fast ice compared with undeformed fast ice without platelets. Platelet growth in supercooled water under thick ice appears to be rate-limited by turbulent heat transfer and that this is a significant factor to be considered in mass transfer at the underside of ice shelves and sea ice in the vicinity of ice shelves.
Hidden Markov models in automatic speech recognition
Wrzoskowicz, Adam
1993-11-01
This article describes a method for constructing an automatic speech recognition system based on hidden Markov models (HMMs). The author discusses the basic concepts of HMM theory and the application of these models to the analysis and recognition of speech signals. The author provides algorithms which make it possible to train the ASR system and recognize signals on the basis of distinct stochastic models of selected speech sound classes. The author describes the specific components of the system and the procedures used to model and recognize speech. The author discusses problems associated with the choice of optimal signal detection and parameterization characteristics and their effect on the performance of the system. The author presents different options for the choice of speech signal segments and their consequences for the ASR process. The author gives special attention to the use of lexical, syntactic, and semantic information for the purpose of improving the quality and efficiency of the system. The author also describes an ASR system developed by the Speech Acoustics Laboratory of the IBPT PAS. The author discusses the results of experiments on the effect of noise on the performance of the ASR system and describes methods of constructing HMM's designed to operate in a noisy environment. The author also describes a language for human-robot communications which was defined as a complex multilevel network from an HMM model of speech sounds geared towards Polish inflections. The author also added mandatory lexical and syntactic rules to the system for its communications vocabulary.
Hidden Markov Model for Stock Selection
Directory of Open Access Journals (Sweden)
Nguyet Nguyen
2015-10-01
Full Text Available The hidden Markov model (HMM is typically used to predict the hidden regimes of observation data. Therefore, this model finds applications in many different areas, such as speech recognition systems, computational molecular biology and financial market predictions. In this paper, we use HMM for stock selection. We first use HMM to make monthly regime predictions for the four macroeconomic variables: inflation (consumer price index (CPI, industrial production index (INDPRO, stock market index (S&P 500 and market volatility (VIX. At the end of each month, we calibrate HMM’s parameters for each of these economic variables and predict its regimes for the next month. We then look back into historical data to find the time periods for which the four variables had similar regimes with the forecasted regimes. Within those similar periods, we analyze all of the S&P 500 stocks to identify which stock characteristics have been well rewarded during the time periods and assign scores and corresponding weights for each of the stock characteristics. A composite score of each stock is calculated based on the scores and weights of its features. Based on this algorithm, we choose the 50 top ranking stocks to buy. We compare the performances of the portfolio with the benchmark index, S&P 500. With an initial investment of $100 in December 1999, over 15 years, in December 2014, our portfolio had an average gain per annum of 14.9% versus 2.3% for the S&P 500.
Stability and perturbations of countable Markov maps
Jordan, Thomas; Munday, Sara; Sahlsten, Tuomas
2018-04-01
Let T and , , be countable Markov maps such that the branches of converge pointwise to the branches of T, as . We study the stability of various quantities measuring the singularity (dimension, Hölder exponent etc) of the topological conjugacy between and T when . This is a well-understood problem for maps with finitely-many branches, and the quantities are stable for small ɛ, that is, they converge to their expected values if . For the infinite branch case their stability might be expected to fail, but we prove that even in the infinite branch case the quantity is stable under some natural regularity assumptions on and T (under which, for instance, the Hölder exponent of fails to be stable). Our assumptions apply for example in the case of Gauss map, various Lüroth maps and accelerated Manneville-Pomeau maps when varying the parameter α. For the proof we introduce a mass transportation method from the cusp that allows us to exploit thermodynamical ideas from the finite branch case. Dedicated to the memory of Bernd O Stratmann
Lectures from Markov processes to Brownian motion
Chung, Kai Lai
1982-01-01
This book evolved from several stacks of lecture notes written over a decade and given in classes at slightly varying levels. In transforming the over lapping material into a book, I aimed at presenting some of the best features of the subject with a minimum of prerequisities and technicalities. (Needless to say, one man's technicality is another's professionalism. ) But a text frozen in print does not allow for the latitude of the classroom; and the tendency to expand becomes harder to curb without the constraints of time and audience. The result is that this volume contains more topics and details than I had intended, but I hope the forest is still visible with the trees. The book begins at the beginning with the Markov property, followed quickly by the introduction of option al times and martingales. These three topics in the discrete parameter setting are fully discussed in my book A Course In Probability Theory (second edition, Academic Press, 1974). The latter will be referred to throughout this book ...
Markov branching in the vertex splitting model
International Nuclear Information System (INIS)
Stefánsson, Sigurdur Örn
2012-01-01
We study a special case of the vertex splitting model which is a recent model of randomly growing trees. For any finite maximum vertex degree D, we find a one parameter model, with parameter α element of [0,1] which has a so-called Markov branching property. When D=∞ we find a two parameter model with an additional parameter γ element of [0,1] which also has this feature. In the case D = 3, the model bears resemblance to Ford's α-model of phylogenetic trees and when D=∞ it is similar to its generalization, the αγ-model. For α = 0, the model reduces to the well known model of preferential attachment. In the case α > 0, we prove convergence of the finite volume probability measures, generated by the growth rules, to a measure on infinite trees which is concentrated on the set of trees with a single spine. We show that the annealed Hausdorff dimension with respect to the infinite volume measure is 1/α. When γ = 0 the model reduces to a model of growing caterpillar graphs in which case we prove that the Hausdorff dimension is almost surely 1/α and that the spectral dimension is almost surely 2/(1 + α). We comment briefly on the distribution of vertex degrees and correlations between degrees of neighbouring vertices
Bayesian posterior distributions without Markov chains.
Cole, Stephen R; Chu, Haitao; Greenland, Sander; Hamra, Ghassan; Richardson, David B
2012-03-01
Bayesian posterior parameter distributions are often simulated using Markov chain Monte Carlo (MCMC) methods. However, MCMC methods are not always necessary and do not help the uninitiated understand Bayesian inference. As a bridge to understanding Bayesian inference, the authors illustrate a transparent rejection sampling method. In example 1, they illustrate rejection sampling using 36 cases and 198 controls from a case-control study (1976-1983) assessing the relation between residential exposure to magnetic fields and the development of childhood cancer. Results from rejection sampling (odds ratio (OR) = 1.69, 95% posterior interval (PI): 0.57, 5.00) were similar to MCMC results (OR = 1.69, 95% PI: 0.58, 4.95) and approximations from data-augmentation priors (OR = 1.74, 95% PI: 0.60, 5.06). In example 2, the authors apply rejection sampling to a cohort study of 315 human immunodeficiency virus seroconverters (1984-1998) to assess the relation between viral load after infection and 5-year incidence of acquired immunodeficiency syndrome, adjusting for (continuous) age at seroconversion and race. In this more complex example, rejection sampling required a notably longer run time than MCMC sampling but remained feasible and again yielded similar results. The transparency of the proposed approach comes at a price of being less broadly applicable than MCMC.
Markov source model for printed music decoding
Kopec, Gary E.; Chou, Philip A.; Maltz, David A.
1995-03-01
This paper describes a Markov source model for a simple subset of printed music notation. The model is based on the Adobe Sonata music symbol set and a message language of our own design. Chord imaging is the most complex part of the model. Much of the complexity follows from a rule of music typography that requires the noteheads for adjacent pitches to be placed on opposite sides of the chord stem. This rule leads to a proliferation of cases for other typographic details such as dot placement. We describe the language of message strings accepted by the model and discuss some of the imaging issues associated with various aspects of the message language. We also point out some aspects of music notation that appear problematic for a finite-state representation. Development of the model was greatly facilitated by the duality between image synthesis and image decoding. Although our ultimate objective was a music image model for use in decoding, most of the development proceeded by using the evolving model for image synthesis, since it is computationally far less costly to image a message than to decode an image.
NonMarkov Ito Processes with 1- state memory
McCauley, Joseph L.
2010-08-01
A Markov process, by definition, cannot depend on any previous state other than the last observed state. An Ito process implies the Fokker-Planck and Kolmogorov backward time partial differential eqns. for transition densities, which in turn imply the Chapman-Kolmogorov eqn., but without requiring the Markov condition. We present a class of Ito process superficially resembling Markov processes, but with 1-state memory. In finance, such processes would obey the efficient market hypothesis up through the level of pair correlations. These stochastic processes have been mislabeled in recent literature as 'nonlinear Markov processes'. Inspired by Doob and Feller, who pointed out that the ChapmanKolmogorov eqn. is not restricted to Markov processes, we exhibit a Gaussian Ito transition density with 1-state memory in the drift coefficient that satisfies both of Kolmogorov's partial differential eqns. and also the Chapman-Kolmogorov eqn. In addition, we show that three of the examples from McKean's seminal 1966 paper are also nonMarkov Ito processes. Last, we show that the transition density of the generalized Black-Scholes type partial differential eqn. describes a martingale, and satisfies the ChapmanKolmogorov eqn. This leads to the shortest-known proof that the Green function of the Black-Scholes eqn. with variable diffusion coefficient provides the so-called martingale measure of option pricing.
Switching Markov chains for a holistic modeling of SIS unavailability
International Nuclear Information System (INIS)
Mechri, Walid; Simon, Christophe; BenOthman, Kamel
2015-01-01
This paper proposes a holistic approach to model the Safety Instrumented Systems (SIS). The model is based on Switching Markov Chain and integrates several parameters like Common Cause Failure, Imperfect Proof testing, partial proof testing, etc. The basic concepts of Switching Markov Chain applied to reliability analysis are introduced and a model to compute the unavailability for a case study is presented. The proposed Switching Markov Chain allows us to assess the effect of each parameter on the SIS performance. The proposed method ensures the relevance of the results. - Highlights: • A holistic approach to model the unavailability safety systems using Switching Markov chains. • The model integrates several parameters like probability of failure due to the test, the probability of not detecting a failure in a test. • The basic concepts of the Switching Markov Chains are introduced and applied to compute the unavailability for safety systems. • The proposed Switching Markov Chain allows assessing the effect of each parameter on the chemical reactor performance
Prognostics for Steam Generator Tube Rupture using Markov Chain model
International Nuclear Information System (INIS)
Kim, Gibeom; Heo, Gyunyoung; Kim, Hyeonmin
2016-01-01
This paper will describe the prognostics method for evaluating and forecasting the ageing effect and demonstrate the procedure of prognostics for the Steam Generator Tube Rupture (SGTR) accident. Authors will propose the data-driven method so called MCMC (Markov Chain Monte Carlo) which is preferred to the physical-model method in terms of flexibility and availability. Degradation data is represented as growth of burst probability over time. Markov chain model is performed based on transition probability of state. And the state must be discrete variable. Therefore, burst probability that is continuous variable have to be changed into discrete variable to apply Markov chain model to the degradation data. The Markov chain model which is one of prognostics methods was described and the pilot demonstration for a SGTR accident was performed as a case study. The Markov chain model is strong since it is possible to be performed without physical models as long as enough data are available. However, in the case of the discrete Markov chain used in this study, there must be loss of information while the given data is discretized and assigned to the finite number of states. In this process, original information might not be reflected on prediction sufficiently. This should be noted as the limitation of discrete models. Now we will be studying on other prognostics methods such as GPM (General Path Model) which is also data-driven method as well as the particle filer which belongs to physical-model method and conducting comparison analysis
Probability distributions for Markov chain based quantum walks
Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.
2018-01-01
We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.
Quintas, M. A. C.; Fundo, J. F.; Silva, C. L. M.
2010-01-01
Sucrose is probably one of the most studied molecules by food scientists, since it plays an important role as an ingredient or preserving agent in many formulations and technological processes. When sucrose is present in a product with a concentration near or greater than the saturation point—i.e. in the supercooled state—it possesses high potentialities for the food industry in areas as different as pastry industry, dairy and frozen desserts or films and coatings production. This paper prese...
DEFF Research Database (Denmark)
Johansen, Jakob Berg; Dannemand, Mark; Kong, Weiqiang
2015-01-01
. The graphite powder was stabilized using carboxymetyl cellulose and successfully tested in heating and supercooling cycles with no loss of performance. Thermal conductivity enhancing properties of graphite powder was shown in samples. Since the experiments were conducted in small scale, at 200 g per sample......, large scale experiments are required to validate graphite as a thermo conductivity enhancing agent, suitable for use in seasonal heat storage applications utilizing SAT....
Inhibition of ice nucleation by slippery liquid-infused porous surfaces (SLIPS).
Wilson, Peter W; Lu, Weizhe; Xu, Haojun; Kim, Philseok; Kreder, Michael J; Alvarenga, Jack; Aizenberg, Joanna
2013-01-14
Ice repellent coatings have been studied and keenly sought after for many years, where any advances in the durability of such coatings will result in huge energy savings across many fields. Progress in creating anti-ice and anti-frost surfaces has been particularly rapid since the discovery and development of slippery, liquid infused porous surfaces (SLIPS). Here we use SLIPS-coated differential scanning calorimeter (DSC) pans to investigate the effects of the surface modification on the nucleation of supercooled water. This investigation is inherently different from previous studies which looked at the adhesion of ice to SLIPS surfaces, or the formation of ice under high humidity conditions. Given the stochastic nature of nucleation of ice from supercooled water, multiple runs on the same sample are needed to determine if a given surface coating has a real and statistically significant effect on the nucleation temperature. We have cycled supercooling to freezing and then thawing of deionized water in hydrophilic (untreated aluminum), hydrophobic, superhydrophobic, and SLIPS-treated DSC pans multiple times to determine the effects of surface treatment on the nucleation and subsequent growth of ice. We find that SLIPS coatings lower the nucleation temperature of supercooled water in contact with statistical significance and show no deterioration or change in the coating performance even after 150 freeze-thaw cycles.
Sebastian, Tunny; Jeyaseelan, Visalakshi; Jeyaseelan, Lakshmanan; Anandan, Shalini; George, Sebastian; Bangdiwala, Shrikant I
2018-01-01
Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.
Experimental Observation of Bulk Liquid Water Structure in ``No Man's Land''
Sellberg, Jonas; McQueen, Trevor; Huang, Congcong; Loh, Duane; Laksmono, Hartawan; Sierra, Raymond; Hampton, Christina; Starodub, Dmitri; Deponte, Daniel; Martin, Andrew; Barty, Anton; Wikfeldt, Thor; Schlesinger, Daniel; Pettersson, Lars; Beye, Martin; Nordlund, Dennis; Weiss, Thomas; Feldkamp, Jan; Caronna, Chiara; Seibert, Marvin; Messerschmidt, Marc; Williams, Garth; Boutet, Sebastien; Bogan, Michael; Nilsson, Anders
2013-03-01
Experiments on pure bulk water below about 235 K have so far been difficult: water crystallization occurs very rapidly below the homogeneous nucleation temperature of 232 K and above 160 K, leading to a ``no man's land'' devoid of experimental results regarding the structure. Here, we demonstrate a new, general experimental approach to study the structure of liquid states at supercooled conditions below their limit of homogeneous nucleation. We use femtosecond x-ray pulses generated by the LCLS x-ray laser to probe evaporatively cooled droplets of supercooled bulk water and find experimental evidence for the existence of metastable bulk liquid water down to temperatures of 223 K in the previously largely unexplored ``no man's land''. We acknoweledge NSF (CHE-0809324), Office of Basic Energy Sciences, and the Swedish Research Council for financial support.
Rowlinson, J S; Baldwin, J E; Buckingham, A D; Danishefsky, S
2013-01-01
Liquids and Liquid Mixtures, Third Edition explores the equilibrium properties of liquids and liquid mixtures and relates them to the properties of the constituent molecules using the methods of statistical thermodynamics. Topics covered include the critical state, fluid mixtures at high pressures, and the statistical thermodynamics of fluids and mixtures. This book consists of eight chapters and begins with an overview of the liquid state and the thermodynamic properties of liquids and liquid mixtures, including vapor pressure and heat capacities. The discussion then turns to the thermodynami
Maximally reliable Markov chains under energy constraints.
Escola, Sean; Eisele, Michael; Miller, Kenneth; Paninski, Liam
2009-07-01
Signal-to-noise ratios in physical systems can be significantly degraded if the outputs of the systems are highly variable. Biological processes for which highly stereotyped signal generations are necessary features appear to have reduced their signal variabilities by employing multiple processing steps. To better understand why this multistep cascade structure might be desirable, we prove that the reliability of a signal generated by a multistate system with no memory (i.e., a Markov chain) is maximal if and only if the system topology is such that the process steps irreversibly through each state, with transition rates chosen such that an equal fraction of the total signal is generated in each state. Furthermore, our result indicates that by increasing the number of states, it is possible to arbitrarily increase the reliability of the system. In a physical system, however, an energy cost is associated with maintaining irreversible transitions, and this cost increases with the number of such transitions (i.e., the number of states). Thus, an infinite-length chain, which would be perfectly reliable, is infeasible. To model the effects of energy demands on the maximally reliable solution, we numerically optimize the topology under two distinct energy functions that penalize either irreversible transitions or incommunicability between states, respectively. In both cases, the solutions are essentially irreversible linear chains, but with upper bounds on the number of states set by the amount of available energy. We therefore conclude that a physical system for which signal reliability is important should employ a linear architecture, with the number of states (and thus the reliability) determined by the intrinsic energy constraints of the system.
Energy Technology Data Exchange (ETDEWEB)
Kobakhidze, Archil; Lagger, Cyril; Manning, Adrian [University of Sydney, ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, Sydney, NSW (Australia); Yue, Jason [National Taiwan Normal University, Department of Physics, Taipei (China)
2017-08-15
We investigate the properties of a stochastic gravitational wave background produced by a first-order electroweak phase transition in the regime of extreme supercooling. We study a scenario whereby the percolation temperature that signifies the completion of the transition, T{sub p}, is as low as a few MeV (nucleosynthesis temperature), while most of the true vacuum bubbles are formed much earlier at the nucleation temperature, T{sub n} ∝ 50 GeV. This implies that the gravitational wave spectrum is mainly produced by the collisions of large bubbles and characterised by a large amplitude and a peak frequency as low as f ∝ 10{sup -9}-10{sup -7} Hz. We show that such a scenario can occur in (but not limited to) a model based on a non-linear realisation of the electroweak gauge group, so that the Higgs vacuum configuration is altered by a cubic coupling. In order to carefully quantify the evolution of the phase transition of this model over such a wide temperature range we go beyond the usual fast transition approximation, taking into account the expansion of the Universe as well as the behaviour of the nucleation probability at low temperatures. Our computation shows that there exists a range of parameters for which the gravitational wave spectrum lies at the edge between the exclusion limits of current pulsar timing array experiments and the detection band of the future Square Kilometre Array observatory. (orig.)
DEFF Research Database (Denmark)
Furbo, Simon; Dragsted, Janne; Fan, Jianhua
2011-01-01
to transfer heat to and from the module have been tested. Further, a solidification start method, based on a strong cooling of a small part of the salt water mixture in the module by boiling CO2 in a small brass tank in good thermal contact to the outer side of the module wall, has been tested. Tests......Laboratory tests of a 230 l seasonal heat storage module with a sodium acetate water mixture have been carried out. The aim of the tests is to elucidate how best to design a seasonal heat storage based on the salt water mixture, which supercools in a stable way. The module can be a part...... of a seasonal heat storage, that will be suitable for solar heating systems which can fully cover the yearly heat demand of Danish low energy buildings. The tested module has approximately the dimensions 2020 mm x 1285 mm x 80 mm. The module material is steel and the wall thickness is 2 mm. Different methods...
Super-cool paints: optimizing composition with a modified four-flux model
Gali, Marc A.; Arnold, Matthew D.; Gentle, Angus R.; Smith, Geoffrey B.
2017-09-01
The scope for maximizing the albedo of a painted surface to produce low cost new and retro-fitted super-cool roofing is explored systematically. The aim is easy to apply, low cost paint formulations yielding albedos in the range 0.90 to 0.95. This requires raising the near-infrared (NIR) spectral reflectance into this range, while not reducing the more easily obtained high visible reflectance values. Our modified version of the four-flux method has enabled results on more complex composites. Key parameters to be optimized include; fill factors, particle size and material, using more than one mean size, thickness, substrate and binder materials. The model used is a variation of the classical four-flux method that solves the energy transfer problem through four balance differential equations. We use a different approach to the characteristic parameters to define the absorptance and scattering of the complete composite. This generalization allows extension to inclusion of size dispersion of the pigment particle and various binder resins, including those most commonly in use based on acrylics. Thus, the pigment scattering model has to take account of the matrix having loss in the NIR. A paint ranking index aimed specifically at separating paints with albedo above 0.80 is introduced representing the fraction of time at a sub-ambient temperature.
The effect of the melt thermal gradient on the size of the constitutionally supercooled zone
International Nuclear Information System (INIS)
Prasad, A; StJohn, D; Yuan, L; Lee, P D; Easton, M
2016-01-01
Recent verification of the analytical Interdependence model by a numerical solidification model (µMatIC) confirmed the critical role of constitutional supercooling (CS) in achieving sufficient undercooling to trigger successful nucleation events. The location of the maximum amount of CS (ΔT CSmax ) is some distance from the interface of the previously growing grain and this distance contributes to the final as-cast grain size. The effect of the thermal gradient, G, on the size of the CS zone (CSZ) was neglected in that work. However, G is expected to affect the size of the CSZ (i.e. the length of the CSZ, x’ CSZ , and the location of ΔTCSmax, x’ CSmax ). This investigation assesses the effect of G on x’csz and x' CSmax . A range of G values is introduced into both the analytical and the numerical models to obtain a correlation between the value of G and the dimensions of the CSZ. The result of a test case from the analytical model shows that x’ CSmax initially decreases rapidly and then decreases gradually approaching zero at very high values of G. Independent of the analytical model, the results from the numerical model replicate the trend obtained from the analytical model. (paper)
In-Situ Phase Transition Control in the Supercooled State for Robust Active Glass Fiber.
Lv, Shichao; Cao, Maoqing; Li, Chaoyu; Li, Jiang; Qiu, Jianrong; Zhou, Shifeng
2017-06-21
The construction of a dopant-activated photonic composite is of great technological importance for various applications, including smart lighting, optical amplification, laser, and optical detection. The bonding arrangement around the introduced dopants largely determines the properties, yet it remains a daunting challenge to manipulate the local state of the matrix (i.e., phase) inside the transparent composite in a controllable manner. Here we demonstrate that the relaxation of the supercooled state enables in-situ phase transition control in glass. Benefiting from the unique local atom arrangement manner, the strategy offers the possibility for simultaneously tuning the chemical environment of the incorporated dopant and engineering the dopant-host interaction. This allows us to effectively activate the dopant with high efficiency (calculated as ∼100%) and profoundly enhance the dopant-host energy-exchange interaction. Our results highlight that the in-situ phase transition control in glass may provide new opportunities for fabrication of unusual photonic materials with intense broadband emission at ∼1100 nm and development of the robust optical detection unit with high compactness and broadband photon-harvesting capability (from X-ray to ultraviolet light).
Long range stress correlations in the inherent structures of liquids at rest
Energy Technology Data Exchange (ETDEWEB)
Chowdhury, Sadrul; Abraham, Sneha; Hudson, Toby; Harrowell, Peter [School of Chemistry, University of Sydney, Sydney, NSW 2006 (Australia)
2016-03-28
Simulation studies of the atomic shear stress in the local potential energy minima (inherent structures) are reported for binary liquid mixtures in 2D and 3D. These inherent structure stresses are fundamental to slow stress relaxation and high viscosity in supercooled liquids. We find that the atomic shear stress in the inherent structures (IS’s) of both liquids at rest exhibits slowly decaying anisotropic correlations. We show that the stress correlations contribute significantly to the variance of the total shear stress of the IS configurations and consider the origins of the anisotropy and spatial extent of the stress correlations.
Acoustic and thermal anomalies in a liquid-glass transition of racemic S(+)-R(-) ketoprofen
Shibata, Tomohiko; Takayama, Haruki; Kim, Tae Hyun; Kojima, Seiji
2014-01-01
Acoustic and thermal properties of pharmaceutical racemic S(+)-R(-) ketoprofen were investigated in wide temperature range including glassy, supercooled liquid and liquid states by Brillouin scattering and temperature modulated DSC. Sound velocity and acoustic attenuation exhibited clear changes at 265 K indicating a liquid-glass transition and showed the typical structural relaxation above Tg. The high value of the fragility index m = 71 was determined by the dispersion of the complex heat capacity. New relaxation map was suggested in combination with previous study of dielectric measurement.
DEFF Research Database (Denmark)
Hecksher, Tina; Olsen, Niels Boye; Dyre, Jeppe C.
2017-01-01
represented by a “Cole-Cole retardation element” defined as a series connection of a capacitor and a constant-phase element, resulting in the Cole-Cole compliance function well-known from dielectrics. The model, which assumes that the high-frequency decay of the alpha shear compliance loss varies...
Afzal, Aboothahir; Shahin Thayyil, M.; Sulaiman, M. K.; Kulkarni, A. R.
2018-05-01
Brucine has good anti-tumor effects, on both liver cancer and breast cancer. It has bioavailability of 40.83%. Since the bioavailability of the drug is low, an alternative method to increase its bioavailability and solubility is by changing the drug into glassy form. We used Differential Scanning Calorimetry (DSC) for studying the glass forming ability of the drug. Brucine was found to be a very good glass former glass transition temperature 365 K. Based on the DSC analysis we have used broadband dielectric spectroscopy (BDS) for studying the drug in the super cooled and glassy state. BDS is an effective tool to probe the molecular dynamics in the super cooled and glassy state. Molecular mobility is found to be present even in the glassy state of this active pharmaceutical ingredient (API) which is responsible for the instability. Our aim is to study the factors responsible for instability of this API in amorphous form. Cooling curves for dielectric permittivity and dielectric loss revealed the presence of structural (α) and secondary relaxations (β and γ). Temperature dependence of relaxation time is fitted by Vogel-Fulcher-Tammann equation and found the values of activation energy of the α relaxation, fragility and glass transition temperature. Paluch's anti correlation is also verified, that the width of the α-loss peak at or near the glass transition temperature Tg is strongly anticorrelated with the polarity of the molecule. The larger the dielectric relaxation strength Δɛ (Tg) of the system, the narrower is the α-loss peak (higher value of βKWW).
Markov Chain Models for the Stochastic Modeling of Pitting Corrosion
Directory of Open Access Journals (Sweden)
A. Valor
2013-01-01
Full Text Available The stochastic nature of pitting corrosion of metallic structures has been widely recognized. It is assumed that this kind of deterioration retains no memory of the past, so only the current state of the damage influences its future development. This characteristic allows pitting corrosion to be categorized as a Markov process. In this paper, two different models of pitting corrosion, developed using Markov chains, are presented. Firstly, a continuous-time, nonhomogeneous linear growth (pure birth Markov process is used to model external pitting corrosion in underground pipelines. A closed-form solution of the system of Kolmogorov's forward equations is used to describe the transition probability function in a discrete pit depth space. The transition probability function is identified by correlating the stochastic pit depth mean with the empirical deterministic mean. In the second model, the distribution of maximum pit depths in a pitting experiment is successfully modeled after the combination of two stochastic processes: pit initiation and pit growth. Pit generation is modeled as a nonhomogeneous Poisson process, in which induction time is simulated as the realization of a Weibull process. Pit growth is simulated using a nonhomogeneous Markov process. An analytical solution of Kolmogorov's system of equations is also found for the transition probabilities from the first Markov state. Extreme value statistics is employed to find the distribution of maximum pit depths.
Prediction of inspection intervals using the Markov analysis
International Nuclear Information System (INIS)
Rea, R.; Arellano, J.
2005-01-01
To solve the unmanageable number of states of Markov of systems that have a great number of components, it is intends a modification to the method of Markov, denominated Markov truncated analysis, in which is assumed that it is worthless the dependence among faults of components. With it the number of states is increased in a lineal way (not exponential) with the number of components of the system, simplifying the analysis vastly. As example, the proposed method was applied to the system HPCS of the CLV considering its 18 main components. It thinks about that each component can take three states: operational, with hidden fault and with revealed fault. Additionally, it takes into account the configuration of the system HPCS by means of a block diagram of dependability to estimate their unavailability at level system. The results of the model here proposed are compared with other methods and approaches used to simplify the Markov analysis. It also intends the modification of the intervals of inspection of three components of the system HPCS. This finishes with base in the developed Markov model and in the maximum time allowed by the code ASME (NUREG-1482) to inspect components of systems that are in reservation in nuclear power plants. (Author)
Benchmarking of a Markov multizone model of contaminant transport.
Jones, Rachael M; Nicas, Mark
2014-10-01
A Markov chain model previously applied to the simulation of advection and diffusion process of gaseous contaminants is extended to three-dimensional transport of particulates in indoor environments. The model framework and assumptions are described. The performance of the Markov model is benchmarked against simple conventional models of contaminant transport. The Markov model is able to replicate elutriation predictions of particle deposition with distance from a point source, and the stirred settling of respirable particles. Comparisons with turbulent eddy diffusion models indicate that the Markov model exhibits numerical diffusion in the first seconds after release, but over time accurately predicts mean lateral dispersion. The Markov model exhibits some instability with grid length aspect when turbulence is incorporated by way of the turbulent diffusion coefficient, and advection is present. However, the magnitude of prediction error may be tolerable for some applications and can be avoided by incorporating turbulence by way of fluctuating velocity (e.g. turbulence intensity). © The Author 2014. Published by Oxford University Press on behalf of the British Occupational Hygiene Society.
Automated generation of partial Markov chain from high level descriptions
International Nuclear Information System (INIS)
Brameret, P.-A.; Rauzy, A.; Roussel, J.-M.
2015-01-01
We propose an algorithm to generate partial Markov chains from high level implicit descriptions, namely AltaRica models. This algorithm relies on two components. First, a variation on Dijkstra's algorithm to compute shortest paths in a graph. Second, the definition of a notion of distance to select which states must be kept and which can be safely discarded. The proposed method solves two problems at once. First, it avoids a manual construction of Markov chains, which is both tedious and error prone. Second, up the price of acceptable approximations, it makes it possible to push back dramatically the exponential blow-up of the size of the resulting chains. We report experimental results that show the efficiency of the proposed approach. - Highlights: • We generate Markov chains from a higher level safety modeling language (AltaRica). • We use a variation on Dijkstra's algorithm to generate partial Markov chains. • Hence we solve two problems: the first problem is the tedious manual construction of Markov chains. • The second problem is the blow-up of the size of the chains, at the cost of decent approximations. • The experimental results highlight the efficiency of the method
Xu, Xiaoxiao; Dong, Zhijun; Memon, Shazim Ali; Bao, Xiaohua; Cui, Hongzhi
2017-06-23
Salt hydrates have issues of supercooling when they are utilized as phase change materials (PCMs). In this research, a new method was adopted to prepare a salt hydrate PCM (based on a mixture of calcium chloride dihydrate and calcium chloride anhydrous) as a novel PCM system to reduce the supercooling phenomenon existing in CaCl₂·6H₂O. Six samples with different compositions of CaCl₂ were prepared. The relationship between the performance and the proportion of calcium chloride dihydrate (CaCl₂·2H₂O) and calcium chloride anhydrous (CaCl₂) was also investigated. The supercooling degree of the final PCM reduced with the increase in volume of CaCl₂·2H₂O during its preparation. The PCM obtained with 66.21 wt % CaCl₂·2H₂O reduced the supercooling degree by about 96.8%. All six samples, whose ratio of CaCl₂·2H₂O to (CaCl₂ plus CaCl₂·2H₂O) was 0%, 34.03%, 53.82%, 76.56%, 90.74%, and 100% respectively, showed relatively higher enthalpy (greater than 155.29 J/g), and have the possibility to be applied in buildings for thermal energy storage purposes. Hence, CaCl₂·2H₂O plays an important role in reducing supercooling and it can be helpful in adjusting the solidification enthalpy. Thereafter, the influence of adding different percentages of Nano-SiO₂ (0.1 wt %, 0.3 wt %, 0.5 wt %) in reducing the supercooling degree of some PCM samples was investigated. The test results showed that the supercooling of the salt hydrate PCM in Samples 6 and 5 reduced to 0.2 °C and 0.4 °C respectively. Finally, the effect of the different cooling conditions, including frozen storage (-20 °C) and cold storage (5 °C), that were used to prepare the salt hydrate PCM was considered. It was found that both cooling conditions are effective in reducing the supercooling degree of the salt hydrate PCM. With the synergistic action of the two materials, the performance and properties of the newly developed PCM systems were better especially in terms of reducing
Markov chain modelling of pitting corrosion in underground pipelines
Energy Technology Data Exchange (ETDEWEB)
Caleyo, F. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)], E-mail: fcaleyo@gmail.com; Velazquez, J.C. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico); Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400 La Habana (Cuba); Hallen, J.M. [Departamento de Ingenieri' a Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, Mexico D. F. 07738 (Mexico)
2009-09-15
A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.
Influence of credit scoring on the dynamics of Markov chain
Galina, Timofeeva
2015-11-01
Markov processes are widely used to model the dynamics of a credit portfolio and forecast the portfolio risk and profitability. In the Markov chain model the loan portfolio is divided into several groups with different quality, which determined by presence of indebtedness and its terms. It is proposed that dynamics of portfolio shares is described by a multistage controlled system. The article outlines mathematical formalization of controls which reflect the actions of the bank's management in order to improve the loan portfolio quality. The most important control is the organization of approval procedure of loan applications. The credit scoring is studied as a control affecting to the dynamic system. Different formalizations of "good" and "bad" consumers are proposed in connection with the Markov chain model.
Markov chain modelling of pitting corrosion in underground pipelines
International Nuclear Information System (INIS)
Caleyo, F.; Velazquez, J.C.; Valor, A.; Hallen, J.M.
2009-01-01
A continuous-time, non-homogenous linear growth (pure birth) Markov process has been used to model external pitting corrosion in underground pipelines. The closed form solution of Kolmogorov's forward equations for this type of Markov process is used to describe the transition probability function in a discrete pit depth space. The identification of the transition probability function can be achieved by correlating the stochastic pit depth mean with the deterministic mean obtained experimentally. Monte-Carlo simulations previously reported have been used to predict the time evolution of the mean value of the pit depth distribution for different soil textural classes. The simulated distributions have been used to create an empirical Markov chain-based stochastic model for predicting the evolution of pitting corrosion depth and rate distributions from the observed properties of the soil. The proposed model has also been applied to pitting corrosion data from pipeline repeated in-line inspections and laboratory immersion experiments.
Markov chain solution of photon multiple scattering through turbid slabs.
Lin, Ying; Northrop, William F; Li, Xuesong
2016-11-14
This work introduces a Markov Chain solution to model photon multiple scattering through turbid slabs via anisotropic scattering process, i.e., Mie scattering. Results show that the proposed Markov Chain model agree with commonly used Monte Carlo simulation for various mediums such as medium with non-uniform phase functions and absorbing medium. The proposed Markov Chain solution method successfully converts the complex multiple scattering problem with practical phase functions into a matrix form and solves transmitted/reflected photon angular distributions by matrix multiplications. Such characteristics would potentially allow practical inversions by matrix manipulation or stochastic algorithms where widely applied stochastic methods such as Monte Carlo simulations usually fail, and thus enable practical diagnostics reconstructions such as medical diagnosis, spray analysis, and atmosphere sciences.
The spectral method and ergodic theorems for general Markov chains
International Nuclear Information System (INIS)
Nagaev, S V
2015-01-01
We study the ergodic properties of Markov chains with an arbitrary state space and prove a geometric ergodic theorem. The method of the proof is new: it may be described as an operator method. Our main result is an ergodic theorem for Harris-Markov chains in the case when the return time to some fixed set has finite expectation. Our conditions for the transition function are more general than those used by Athreya-Ney and Nummelin. Unlike them, we impose restrictions not on the original transition function but on the transition function of an embedded Markov chain constructed from the return times to the fixed set mentioned above. The proof uses the spectral theory of linear operators on a Banach space
An Application of Graph Theory in Markov Chains Reliability Analysis
Directory of Open Access Journals (Sweden)
Pavel Skalny
2014-01-01
Full Text Available The paper presents reliability analysis which was realized for an industrial company. The aim of the paper is to present the usage of discrete time Markov chains and the flow in network approach. Discrete Markov chains a well-known method of stochastic modelling describes the issue. The method is suitable for many systems occurring in practice where we can easily distinguish various amount of states. Markov chains are used to describe transitions between the states of the process. The industrial process is described as a graph network. The maximal flow in the network corresponds to the production. The Ford-Fulkerson algorithm is used to quantify the production for each state. The combination of both methods are utilized to quantify the expected value of the amount of manufactured products for the given time period.
Prediction of pipeline corrosion rate based on grey Markov models
International Nuclear Information System (INIS)
Chen Yonghong; Zhang Dafa; Peng Guichu; Wang Yuemin
2009-01-01
Based on the model that combined by grey model and Markov model, the prediction of corrosion rate of nuclear power pipeline was studied. Works were done to improve the grey model, and the optimization unbiased grey model was obtained. This new model was used to predict the tendency of corrosion rate, and the Markov model was used to predict the residual errors. In order to improve the prediction precision, rolling operation method was used in these prediction processes. The results indicate that the improvement to the grey model is effective and the prediction precision of the new model combined by the optimization unbiased grey model and Markov model is better, and the use of rolling operation method may improve the prediction precision further. (authors)
Energy Technology Data Exchange (ETDEWEB)
Rea, R.; Arellano, J. [IIE, Calle Reforma 113, Col. Palmira, Cuernavaca, Morelos (Mexico)]. e-mail: rrea@iie.org.mx
2005-07-01
To solve the unmanageable number of states of Markov of systems that have a great number of components, it is intends a modification to the method of Markov, denominated Markov truncated analysis, in which is assumed that it is worthless the dependence among faults of components. With it the number of states is increased in a lineal way (not exponential) with the number of components of the system, simplifying the analysis vastly. As example, the proposed method was applied to the system HPCS of the CLV considering its 18 main components. It thinks about that each component can take three states: operational, with hidden fault and with revealed fault. Additionally, it takes into account the configuration of the system HPCS by means of a block diagram of dependability to estimate their unavailability at level system. The results of the model here proposed are compared with other methods and approaches used to simplify the Markov analysis. It also intends the modification of the intervals of inspection of three components of the system HPCS. This finishes with base in the developed Markov model and in the maximum time allowed by the code ASME (NUREG-1482) to inspect components of systems that are in reservation in nuclear power plants. (Author)
Analyzing the profit-loss sharing contracts with Markov model
Directory of Open Access Journals (Sweden)
Imam Wahyudi
2016-12-01
Full Text Available The purpose of this paper is to examine how to use first order Markov chain to build a reliable monitoring system for the profit-loss sharing based contracts (PLS as the mode of financing contracts in Islamic bank with censored continuous-time observations. The paper adopts the longitudinal analysis with the first order Markov chain framework. Laplace transform was used with homogenous continuous time assumption, from discretized generator matrix, to generate the transition matrix. Various metrics, i.e.: eigenvalue and eigenvector were used to test the first order Markov chain assumption. Cox semi parametric model was used also to analyze the momentum and waiting time effect as non-Markov behavior. The result shows that first order Markov chain is powerful as a monitoring tool for Islamic banks. We find that waiting time negatively affected present rating downgrade (upgrade significantly. Likewise, momentum covariate showed negative effect. Finally, the result confirms that different origin rating have different movement behavior. The paper explores the potential of Markov chain framework as a risk management tool for Islamic banks. It provides valuable insight and integrative model for banks to manage their borrower accounts. This model can be developed to be a powerful early warning system to identify which borrower needs to be monitored intensively. Ultimately, this model could potentially increase the efficiency, productivity and competitiveness of Islamic banks in Indonesia. The analysis used only rating data. Further study should be able to give additional information about the determinant factors of rating movement of the borrowers by incorporating various factors such as contract-related factors, bank-related factors, borrower-related factors and macroeconomic factors.
Application of Hidden Markov Models in Biomolecular Simulations.
Shukla, Saurabh; Shamsi, Zahra; Moffett, Alexander S; Selvam, Balaji; Shukla, Diwakar
2017-01-01
Hidden Markov models (HMMs) provide a framework to analyze large trajectories of biomolecular simulation datasets. HMMs decompose the conformational space of a biological molecule into finite number of states that interconvert among each other with certain rates. HMMs simplify long timescale trajectories for human comprehension, and allow comparison of simulations with experimental data. In this chapter, we provide an overview of building HMMs for analyzing bimolecular simulation datasets. We demonstrate the procedure for building a Hidden Markov model for Met-enkephalin peptide simulation dataset and compare the timescales of the process.
Hidden Markov processes theory and applications to biology
Vidyasagar, M
2014-01-01
This book explores important aspects of Markov and hidden Markov processes and the applications of these ideas to various problems in computational biology. The book starts from first principles, so that no previous knowledge of probability is necessary. However, the work is rigorous and mathematical, making it useful to engineers and mathematicians, even those not interested in biological applications. A range of exercises is provided, including drills to familiarize the reader with concepts and more advanced problems that require deep thinking about the theory. Biological applications are t
Transportation and concentration inequalities for bifurcating Markov chains
DEFF Research Database (Denmark)
Penda, S. Valère Bitseki; Escobar-Bach, Mikael; Guillin, Arnaud
2017-01-01
We investigate the transportation inequality for bifurcating Markov chains which are a class of processes indexed by a regular binary tree. Fitting well models like cell growth when each individual gives birth to exactly two offsprings, we use transportation inequalities to provide useful...... concentration inequalities.We also study deviation inequalities for the empirical means under relaxed assumptions on the Wasserstein contraction for the Markov kernels. Applications to bifurcating nonlinear autoregressive processes are considered for point-wise estimates of the non-linear autoregressive...
Martingales and Markov chains solved exercises and elements of theory
Baldi, Paolo; Priouret, Pierre
2002-01-01
CONDITIONAL EXPECTATIONSIntroductionDefinition and First PropertiesConditional Expectations and Conditional LawsExercisesSolutionsSTOCHASTIC PROCESSESGeneral FactsStopping TimesExercisesSolutionsMARTINGALESFirst DefinitionsFirst PropertiesThe Stopping TheoremMaximal InequalitiesSquare Integral MartingalesConvergence TheoremsRegular MartingalesExercisesProblemsSolutionsMARKOV CHAINSTransition Matrices, Markov ChainsConstruction and ExistenceComputations on the Canonical ChainPotential OperatorsPassage ProblemsRecurrence, TransienceRecurrent Irreducible ChainsPeriodicityExercisesProblemsSolution
Dynamic modeling of presence of occupants using inhomogeneous Markov chains
DEFF Research Database (Denmark)
Andersen, Philip Hvidthøft Delff; Iversen, Anne; Madsen, Henrik
2014-01-01
on time of day, and by use of a filter of the observations it is able to capture per-employee sequence dynamics. Simulations using this method are compared with simulations using homogeneous Markov chains and show far better ability to reproduce key properties of the data. The method is based...... on inhomogeneous Markov chains with where the transition probabilities are estimated using generalized linear models with polynomials, B-splines, and a filter of passed observations as inputs. For treating the dispersion of the data series, a hierarchical model structure is used where one model is for low presence...
Markov chain analysis of single spin flip Ising simulations
International Nuclear Information System (INIS)
Hennecke, M.
1997-01-01
The Markov processes defined by random and loop-based schemes for single spin flip attempts in Monte Carlo simulations of the 2D Ising model are investigated, by explicitly constructing their transition matrices. Their analysis reveals that loops over all lattice sites using a Metropolis-type single spin flip probability often do not define ergodic Markov chains, and have distorted dynamical properties even if they are ergodic. The transition matrices also enable a comparison of the dynamics of random versus loop spin selection and Glauber versus Metropolis probabilities
Hierarchical Multiple Markov Chain Model for Unsupervised Texture Segmentation
Czech Academy of Sciences Publication Activity Database
Scarpa, G.; Gaetano, R.; Haindl, Michal; Zerubia, J.
2009-01-01
Roč. 18, č. 8 (2009), s. 1830-1843 ISSN 1057-7149 R&D Projects: GA ČR GA102/08/0593 EU Projects: European Commission(XE) 507752 - MUSCLE Institutional research plan: CEZ:AV0Z10750506 Keywords : Classification * texture analysis * segmentation * hierarchical image models * Markov process Subject RIV: BD - Theory of Information Impact factor: 2.848, year: 2009 http://library.utia.cas.cz/separaty/2009/RO/haindl-hierarchical multiple markov chain model for unsupervised texture segmentation.pdf
Quantum Markov processes and applications in many-body systems
International Nuclear Information System (INIS)
Temme, P. K.
2010-01-01
This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but
Bisimulation on Markov Processes over Arbitrary Measurable Spaces
DEFF Research Database (Denmark)
Bacci, Giorgio; Bacci, Giovanni; Larsen, Kim Guldstrand
2014-01-01
We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates with a mea......We introduce a notion of bisimulation on labelled Markov Processes over generic measurable spaces in terms of arbitrary binary relations. Our notion of bisimulation is proven to coincide with the coalgebraic definition of Aczel and Mendler in terms of the Giry functor, which associates...
Detecting Faults By Use Of Hidden Markov Models
Smyth, Padhraic J.
1995-01-01
Frequency of false alarms reduced. Faults in complicated dynamic system (e.g., antenna-aiming system, telecommunication network, or human heart) detected automatically by method of automated, continuous monitoring. Obtains time-series data by sampling multiple sensor outputs at discrete intervals of t and processes data via algorithm determining whether system in normal or faulty state. Algorithm implements, among other things, hidden first-order temporal Markov model of states of system. Mathematical model of dynamics of system not needed. Present method is "prior" method mentioned in "Improved Hidden-Markov-Model Method of Detecting Faults" (NPO-18982).
On a Markov chain roulette-type game
International Nuclear Information System (INIS)
El-Shehawey, M A; El-Shreef, Gh A
2009-01-01
A Markov chain on non-negative integers which arises in a roulette-type game is discussed. The transition probabilities are p 01 = ρ, p Nj = δ Nj , p i,i+W = q, p i,i-1 = p = 1 - q, 1 ≤ W < N, 0 ≤ ρ ≤ 1, N - W < j ≤ N and i = 1, 2, ..., N - W. Using formulae for the determinant of a partitioned matrix, a closed form expression for the solution of the Markov chain roulette-type game is deduced. The present analysis is supported by two mathematical models from tumor growth and war with bargaining
Study on the Evolution of Weights on the Market of Competitive Products using Markov Chains
Directory of Open Access Journals (Sweden)
Daniel Mihai Amariei
2016-10-01
Full Text Available In this paper aims the application through the Markov Process mode, within the software product WinQSB, Markov chain in the establishment of the development on the market of five brands of athletic shoes.
International Nuclear Information System (INIS)
Adamczyk, J.; Opiela, M.
1998-01-01
Effect of plastic deformation at austenizing temperature was investigated on phase transformations, structure and hardness of the supercooled austenite transformation products of the Cr-Mo constructional steel with Nb, Ti and B microadditions. Basing on the analysis of the phase transformation plots of the supercooled undeformed austenite and of the supercooled and plastically deformed one, it was found out that direct cooling of specimens after completing their plastic deformation in the above mentioned conditions, results in significant acceleration of the α→β, and ferritic and pearlitic transformations, and in the decrease of transformation products hardness. These phenomena are of great importance for working out of the thermo-mechanical treatment of products made from the heat-treated microalloyed steel. (author)
Zhang, Damao; Wang, Zhien; Luo, Tao; Yin, Yan; Flynn, Connor
2017-03-01
Ice particle formation in slightly supercooled stratiform clouds is not well documented or understood. In this study, 4 years of combined lidar depolarization and radar reflectivity (Ze) measurements are analyzed to distinguish between cold drizzle and ice crystal formations in slightly supercooled Arctic stratiform clouds over the Atmospheric Radiation Measurement Program Climate Research Facility North Slope of Alaska Utqiaġvik ("Barrow") site. Ice particles are detected and statistically shown to be responsible for the strong precipitation in slightly supercooled Arctic stratiform clouds at cloud top temperatures as high as -4°C. For ice precipitating Arctic stratiform clouds, the lidar particulate linear depolarization ratio (δpar_lin) correlates well with radar Ze at each temperature range, but the δpar_lin-Ze relationship varies with temperature ranges. In addition, lidar depolarization and radar Ze observations of ice generation characteristics in Arctic stratiform clouds are consistent with laboratory-measured temperature-dependent ice growth habits.
The explicit form of the rate function for semi-Markov processes and its contractions
Sughiyama, Yuki; Kobayashi, Testuya J.
2018-03-01
We derive the explicit form of the rate function for semi-Markov processes. Here, the ‘random time change trick’ plays an essential role. Also, by exploiting the contraction principle of large deviation theory to the explicit form, we show that the fluctuation theorem (Gallavotti-Cohen symmetry) holds for semi-Markov cases. Furthermore, we elucidate that our rate function is an extension of the level 2.5 rate function for Markov processes to semi-Markov cases.
International Nuclear Information System (INIS)
Kawasaki, Takeshi; Tanaka, Hajime
2009-01-01
Here we study the relation between the mobility and the translational diffusion in supercooled two-dimensional polydisperse colloidal liquids, using numerical simulations. We find an apparent violation of the Einstein-Smoluchowski (ES) relation D=k B Tμ (D: diffusion constant; μ: mobility; k B ; Boltzmann's constant; T: temperature). The violation is a direct consequence of the fact that it is difficult for a driven particle to enter a jammed region with high order due to its yield stress. The degree of this apparent ES violation is controlled solely by the characteristic size of slow jammed regions, ξ. Our finding implies that the characteristic time of this problem is not the structural relaxation time τ α but the lifetime of dynamic heterogeneity, τ ξ . A supercooled liquid can be regarded to be ergodic only over τ ξ , which may be the slowest intrinsic time scale of the system.
Berman-Konsowa principle for reversible Markov jump processes
Hollander, den W.Th.F.; Jansen, S.
2013-01-01
In this paper we prove a version of the Berman-Konsowa principle for reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle provides a variational formula for the capacity of a pair of disjoint measurable sets. There are two versions, one involving a class of probability
Evaluating The Markov Assumption For Web Usage Mining
DEFF Research Database (Denmark)
Jespersen, S.; Pedersen, Torben Bach; Thorhauge, J.
2003-01-01
) model~\\cite{borges99data}. These techniques typically rely on the \\textit{Markov assumption with history depth} $n$, i.e., it is assumed that the next requested page is only dependent on the last $n$ pages visited. This is not always valid, i.e. false browsing patterns may be discovered. However, to our...