Supercooled liquids for pedestrians
Cavagna, Andrea
2009-06-01
When we lower the temperature of a liquid, at some point we meet a first order phase transition to the crystal. Yet, under certain conditions it is possible to keep the system in its metastable phase and to avoid crystallization. In this way the liquid enters in the supercooled phase. Supercooled liquids have a very rich phenomenology, which is still far from being completely understood. To begin with, there is the problem of how to prevent crystallization and how deeply the liquid can be supercooled before a metastability limit is hit. But by far the most interesting feature of supercooled liquids is the dynamic glass transition: when the temperature is decreased below a certain point, the relaxation time increases so much that a dramatic dynamical arrest intervenes and we are unable to equilibrate the system within reasonable experimental times. The glass transition is a phenomenon whose physical origin has stirred an enormous interest in the last hundred years. Why does it occur? Is it just a conventional reference point, or does it have a more profound physical meaning? Is it a purely dynamical event, or the manifestation of a true thermodynamic transition? What is the correlation length associated to the sharp increase of the relaxation time? Can we define a new kind of amorphous order? A shared theory of supercooled liquids and the glass transition does not yet exist and these questions are still largely open. Here, I will illustrate in the most elementary fashion the main phenomenological traits of supercooled liquids and discuss in a very partial way a few theoretical ideas on the subject.
Supercooled Liquids and Glasses
1999-01-01
In these lectures, which were presented at "Soft and Fragile Matter, Nonequilibrium Dynamics, Metastability and Flow" University of St. Andrews, 8 July - 22 July, 1999, I give an introduction to the physics of supercooled liquids and glasses and discuss some computer simulations done to investigate these systems.
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.
Entropy-driven liquid-liquid separation in supercooled water
Holten, V.; Anisimov, M.A.
2012-01-01
Twenty years ago Poole et al. (Nature 360, 324, 1992) suggested that the anomalous properties of supercooled water may be caused by a critical point that terminates a line of liquid-liquid separation of lower-density and higher-density water. Here we present an explicit thermodynamic model based on this hypothesis, which describes all available experimental data for supercooled water with better quality and with fewer adjustable parameters than any other model suggested so far. Liquid water a...
Entropy-driven liquid-liquid separation in supercooled water
Holten, V
2012-01-01
Twenty years ago Poole et al. (Nature 360, 324, 1992) suggested that the anomalous properties of supercooled water may be caused by a critical point that terminates a line of liquid-liquid separation of lower-density and higher-density water. Here we present an explicit thermodynamic model based on this hypothesis, which describes all available experimental data for supercooled water with better quality and with fewer adjustable parameters than any other model suggested so far. Liquid water at low temperatures is viewed as an 'athermal solution' of two molecular structures with different entropies and densities. Alternatively to popular models for water, in which the liquid-liquid separation is driven by energy, the phase separation in the athermal two-state water is driven by entropy upon increasing the pressure, while the critical temperature is defined by the 'reaction' equilibrium constant. In particular, the model predicts the location of density maxima at the locus of a near-constant fraction (about 0.1...
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
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
Hopping in a supercooled binary Lennard-Jones liquid
DEFF Research Database (Denmark)
Schrøder, Thomas; Dyre, Jeppe
1998-01-01
A binary LennardJones liquid has been investigated by molecular dynamics at equilibrium supercooled conditions. At the lowest temperature investigated, hopping is present in the system as indicated by a secondary peak in 4r2Gs(r,t), where Gs(r,t) is the van Hove self correlation function...
Entropy calculations for a supercooled liquid crystalline blue phase
Energy Technology Data Exchange (ETDEWEB)
Singh, U [Physics Department, University of the West Indies, PO Box 64, Bridgetown (Barbados)
2007-01-15
We observed, using polarized light microscopy, the supercooling of the blue phase (BPI) of cholesteryl proprionate and measured the corresponding liquid crystalline phase transition temperatures. From these temperatures and additional published data we have provided, for the benefit of undergraduate physics students, a nontraditional example involving entropy calculations for an irreversible transition.
On the potential energy landscape of supercooled liquids and glasses
DEFF Research Database (Denmark)
Rodney, D.; Schrøder, Thomas
2011-01-01
The activation-relaxation technique (ART), a saddle-point search method, is applied to determine the potential energy landscape around supercooled and glassy configurations of a three-dimensional binary Lennard-Jones system. We show a strong relation between the distribution of activation energies...... around a given glassy configuration and its history, in particular, the cooling rate used to produce the glass and whether or not the glass was plastically deformed prior to sampling. We also compare the thermally activated transitions found by ART around a supercooled configuration with the succession...... of transitions undergone by the same supercooled liquid during a time trajectory simulated by molecular dynamics. We find that ART is biased towards more heterogeneous transitions with higher activation energies and more broken bonds than the MD simulation....
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.
Shear-accelerated crystallization in a supercooled atomic liquid.
Shao, Zhen; Singer, Jonathan P; Liu, Yanhui; Liu, Ze; Li, Huiping; Gopinadhan, Manesh; O'Hern, Corey S; Schroers, Jan; Osuji, Chinedum O
2015-02-01
A bulk metallic glass forming alloy is subjected to shear flow in its supercooled state by compression of a short rod to produce a flat disk. The resulting material exhibits enhanced crystallization kinetics during isothermal annealing as reflected in the decrease of the crystallization time relative to the nondeformed case. The transition from quiescent to shear-accelerated crystallization is linked to strain accumulated during shear flow above a critical shear rate γ̇(c)≈0.3 s(-1) which corresponds to Péclet number, Pe∼O(1). The observation of shear-accelerated crystallization in an atomic system at modest shear rates is uncommon. It is made possible here by the substantial viscosity of the supercooled liquid which increases strongly with temperature in the approach to the glass transition. We may therefore anticipate the encounter of nontrivial shear-related effects during thermoplastic deformation of similar systems.
Hopping in a supercooled binary Lennard-Jones liquid
DEFF Research Database (Denmark)
Schrøder, Thomas; Dyre, Jeppe
1998-01-01
A binary LennardJones liquid has been investigated by molecular dynamics at equilibrium supercooled conditions. At the lowest temperature investigated, hopping is present in the system as indicated by a secondary peak in 4r2Gs(r,t), where Gs(r,t) is the van Hove self correlation function....... To examine the dynamics of the system, we consider transitions between the inherent structures (local minima in the potential energy) along the trajectory. We conclude that the plateau in the mean square displacement found at lower temperatures is indeed a result of particles being trapped in local "cages...
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.
Behavior of Supercooled Aqueous Solutions Stemming from Hidden Liquid-Liquid Transition in Water
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...
Electrostatic levitation studies of supercooled liquids and metastable solid phases
Rustan, Gustav Errol
A new laboratory has been developed at Iowa State University (ISU) to be used for the study of high temperature liquids and solids, with particular focus on the supercooling of liquids and their metastable solidification products. This new laboratory employs the electrostatic levitation (ESL) technique, in which a charged sample is suspended between a set of electrodes to achieve non-contact handling. Owing to the elimination of a crucible, high temperature processing of samples can be achieved with reduced levels of contamination and heterogeneous nucleation. Because of the reduction in heterogeneous nucleation, samples can be supercooled well below their equilibrium melting temperature, opening the door to a wide range of measurements on supercooled liquids. Measurements methods have been implemented for the characterization of thermophysical properties such as: volume/density, ratio of specific heat to total hemispherical emissivity, surface tension, viscosity, electrical resistivity, and magnetic susceptibility. For measurements of electrical resistivity and magnetic susceptibility, a new method has been developed at ISU based on the tunnel diode oscillator (TDO) technique. The TDO technique uses the negative differential resistance of a tunnel diode to drive an LC tank circuit into self-sustained oscillation at the resonant LC frequency. The LC tank is inductively coupled to the samples under study, and changes in the electrical resistivity or magnetic susceptibility of the sample are manifested as changes in the resonant frequency. By measuring the frequency shifts of the TDO, insights can be made into changes in the material's electrical and magnetic properties. This method has been validated by performing resistivity measurements on a sample of high purity Zr, and by performing measurements on the ferromagnetic transition in a low-carbon steel ball bearing. In addition to the development of the laboratory and its supporting instrumentation, an effort has
A phase space approach to supercooled liquids and a universal collapse of their viscosity
Weingartner, Nicholas B; Nogueira, Flavio S; Kelton, K F; Nussinov, Zohar
2016-01-01
A broad fundamental understanding of the mechanisms underlying the phenomenology of supercooled liquids has remained elusive, despite decades of intense exploration. When supercooled beneath its characteristic melting temperature, a liquid sees a sharp rise in its viscosity over a narrow temperature range, eventually becoming frozen on laboratory timescales. Explaining this immense increase in viscosity is one of the principle goals of condensed matter physicists. To that end, numerous theoretical frameworks have been proposed which explain and reproduce the temperature dependence of the viscosity of supercooled liquids. Each of these frameworks appears only applicable to specific classes of glassformers and each possess a number of variable parameters. Here we describe a classical framework for explaining the dynamical behavior of supercooled liquids based on statistical mechanical considerations, and possessing only a single variable parameter. This parameter varies weakly from liquid to liquid. Furthermore...
Dynamical Instability Causes the Demise of a Supercooled Tetrahedral Liquid
Gautam, Arvind Kumar; Pingua, Nandlal; Goyal, Aashish; Apte, Pankaj A.
2017-09-01
We investigate the relaxation mechanism of a supercooled tetrahedral liquid at its limit of stability using isothermal isobaric ( NPT) Monte Carlo simulations. In similarity with systems which are far from equilibrium but near the onset of jamming (O'Hern et al. in Phys Rev Lett 93:165702, 2004), we find that the relaxation is characterized by two time-scales: the decay of long-wavelength (slow) fluctuations of potential energy is controlled by the slope [partial (G/N)/partial φ ] of the Gibbs free energy ( G) at a unique value of per particle potential energy φ = φ _{{\\tiny mid}}. The short-wavelength (fast) fluctuations are controlled by the bath temperature T. The relaxation of the supercooled liquid is initiated with a dynamical crossover after which the potential energy fluctuations are biased towards values progressively lesser than φ _{{\\tiny mid}}. The dynamical crossover leads to the change of time-scale, i.e., the decay of long-wavelength potential energy fluctuations (intermediate stage of relaxation). Because of the condition [partial ^2 (G/N)/partial φ ^2 = 0] at φ = φ _{{\\tiny mid}}, the slope [partial (G/N)/partial φ ] has a unique value and governs the intermediate stage of relaxation, which ends just after the crossover. In the subsequent stage, there is a relatively rapid crystallization due to lack of long-wavelength fluctuations and the instability at φ _{{\\tiny mid}}, i.e., the condition that G decreases as configurations with potential energies lower than φ _{{\\tiny mid}} are accessed. The dynamical crossover point and the associated change in the time-scale of fluctuations is found to be consistent with the previous studies.
Spatiotemporal heterogeneity of local free volumes in highly supercooled liquid
Shiba, Hayato; Kawasaki, Takeshi
2013-11-01
We discuss the spatiotemporal behavior of local density and its relation to dynamical heterogeneity in a highly supercooled liquid by using molecular dynamics simulations of a binary mixture with different particle sizes in two dimensions. To trace voids heterogeneously existing with lower local densities, which move along with the structural relaxation, we employ the minimum local density for each particle in a time window whose width is set along with the structural relaxation time. Particles subject to free volumes correspond well to the configuration rearranging region of dynamical heterogeneity. While the correlation length for dynamical heterogeneity grows with temperature decrease, no growth in the correlation length of heterogeneity in the minimum local density distribution takes place. A comparison of these results with those of normal mode analysis reveals that superpositions of lower-frequency soft modes extending over the free volumes exhibit spatial correlation with the broken bonds. This observation suggests a possibility that long-ranged vibration modes facilitate the interactions between fragile regions represented by free volumes, to induce dynamical correlations at a large scale.
A phase space approach to supercooled liquids and a universal collapse of their viscosity
Directory of Open Access Journals (Sweden)
Nicholas Bryan Weingartner
2016-11-01
Full Text Available A broad fundamental understanding of the mechanisms underlying the phenomenology of supercooled liquids has remained elusive, despite decades of intense exploration. When supercooled beneath its characteristic melting temperature, a liquid sees a sharp rise in its viscosity over a narrow temperature range, eventually becoming frozen on laboratory timescales. Explaining this immense increase in viscosity is one of the principle goals of condensed matter physicists. To that end, numerous theoretical frameworks have been proposed which explain and reproduce the temperature dependence of the viscosity of supercooled liquids. Each of these frameworks appears only applicable to specific classes of glassformers and each possess a number of variable parameters. Here we describe a classical framework for explaining the dynamical behavior of supercooled liquids based on statistical mechanical considerations, and possessing only a single variable parameter. This parameter varies weakly from liquid to liquid. Furthermore, as predicted by this new classical theory and its earlier quantum counterpart, we find with the aid of a small dimensionless constant that varies in size from sim 0.05-0.12 , a universal (16 decade collapse of the viscosity data as a function of temperature. The collapse appears in all known types of glass forming supercooled liquids (silicates, metallic alloys, organic systems, chalcogenide, sugars, and water.
A phase space approach to supercooled liquids and a universal collapse of their viscosity
Weingartner, Nicholas; Nogueira, Flavio; Pueblo, Chris; Kelton, Kenneth; Nussinov, Zohar
2016-11-01
A broad fundamental understanding of the mechanisms underlying the phenomenology of supercooled liquids has remained elusive, despite decades of intense exploration. When supercooled beneath its characteristic melting temperature, a liquid sees a sharp rise in its viscosity over a narrow temperature range, eventually becoming frozen on laboratory timescales. Explaining this immense increase in viscosity is one of the principle goals of condensed matter physicists. To that end, numerous theoretical frameworks have been proposed which explain and reproduce the temperature dependence of the viscosity of supercooled liquids. Each of these frameworks appears only applicable to specific classes of glassformers and each possess a number of variable parameters. Here we describe a classical framework for explaining the dynamical behavior of supercooled liquids based on statistical mechanical considerations, and possessing only a single variable parameter. This parameter varies weakly from liquid to liquid. Furthermore, as predicted by this new classical theory and its earlier quantum counterpart, we find with the aid of a small dimensionless constant that varies in size from ˜ 0.05-0.12, a universal (16 decade) collapse of the viscosity data as a function of temperature. The collapse appears in all known types of glass forming supercooled liquids (silicates, metallic alloys, organic systems, chalcogenide, sugars, and water).
Behavior of supercooled aqueous solutions stemming from hidden liquid-liquid transition in water
Biddle, John W.; Holten, Vincent; Anisimov, Mikhail A.
2014-08-01
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, 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.
Liquid-liquid transition in supercooled water suggested by microsecond simulations.
Li, Yaping; Li, Jicun; Wang, Feng
2013-07-23
The putative liquid-liquid phase transition in supercooled water has been used to explain many anomalous behaviors of water. However, no direct experimental verification of such a phase transition has been accomplished, and theoretical studies from different simulations contradict each other. We investigated the putative liquid-liquid phase transition using the Water potential from Adaptive Force Matching for Ice and Liquid (WAIL). The simulation reveals a first-order phase transition in the supercooled regime with the critical point at ~207 K and 50 MPa. Normal water is high-density liquid (HDL). Low-density liquid (LDL) emerges at lower temperatures. The LDL phase has a density only slightly larger than that of the ice-Ih and shows more long-range order than HDL. However, the transformation from LDL to HDL is spontaneous across the first-order phase transition line, suggesting the LDL configuration is not poorly formed nanocrystalline ice. It has been demonstrated in the past that the WAIL potential provides reliable predictions of water properties such as melting temperature and temperature of maximum density. Compared with other simple water potentials, WAIL is not biased by fitting to experimental properties, and simulation with this potential reflects the prediction of a high-quality first-principle potential energy surface.
Indian Academy of Sciences (India)
Biman Jana; Biman Bagchi
2007-09-01
Recent optical kerr effect (OKE) studies have revealed that orientational relaxation of rodlike nematogens near the isotropic-nematic (I-N) phase boundary and also in the nematic phase exhibit temporal power law decay at intermediate times. Such behaviour has drawn an intriguing analogy with supercooled liquids. Here, we have investigated the single-particle and collective orientational dynamics of a family of model system of thermotropic liquid crystals using extensive computer simulations. Several remarkable features of glassy dynamics are on display including non-exponential relaxation, dynamical heterogeneity, and non-Arrhenius temperature dependence of the orientational relaxation time. Over a temperature range near the I-N phase boundary, the system behaves like a fragile glass-forming liquid. Using proper scaling, we construct the usual relaxation time versus inverse temperature plot and explicitly demonstrate that one can successfully define a density dependent fragility of liquid crystals. The fragility of liquid crystals shows a temperature and density dependence which is remarkably similar to the fragility of glass forming supercooled liquids. Energy landscape analysis of inherent structures shows that the breakdown of the Arrhenius temperature dependence of relaxation rate occurs at a temperature that marks the onset of the growth of the depth of the potential energy minima explored by the system.
Radiometric Observations of Supercooled Liquid Water within a Split Front over the Sierra Nevada.
Heggli, Mark F.; Reynolds, David W.
1985-11-01
A storm bearing close structural resemblance to a katafront was observed from the ground with microwave radiometry and a vertically pointing Ka-band radar over the Sierra Nevada of California. The onset and duration of supercooled liquid water was determined and matched to a split front model used to describe the synoptic features of a katafront. Results indicate that prior to the passage of the upper front no supercooled liquid water was observed. This portion of the storm provided the deepest cloud and coldest cloud tops. Supercooled liquid water was most prevalent after the upper front passage, and persisted until the suspected surface front passage. The duration of measured supercooled water was 16 hours.This information broadens the knowledge regarding the presence of supercooled liquid water, and thus possible seeding potential, within winter storms so that treatment can be confined to the period of storms amenable to cloud seeding. Future studies may well confirm the ease with which these periods can be predicted on an operational basis in the Sierra Nevada.
Toner, J.; Catling, D. C.; Light, B.
2013-12-01
The presence of liquid water on the cold and dry surface of Mars is possible where concentrated salt solutions lower the freezing point of water. The eutectic temperature is the maximum equilibrium freezing point depression possible for a given salt solution, which ranges from near 0°C for carbonates and sulfates, to as low as -75°C for perchlorates. Although eutectic temperatures suggest a lower temperature limit for liquid water on Mars, salt solutions will typically supercool below their eutectic before crystallization occurs. We report on results investigating the magnitude of supercooling and its variation with salt composition and concentration for pure salt solutions and saturated soil solutions of MgSO4, MgCl2, NaCl, NaClO4, Mg(ClO4)2, and Ca(ClO4)2. We measured supercooling by monitoring solution temperatures during slow cooling and warming experiments. Our results indicate that supercooling is pervasive. Slowly cooled MgSO4, MgCl2, NaCl, and NaClO4 solutions typically supercool 5-15°C below their eutectic temperature before crystallizing. The addition of soil to these salt solutions has a variable effect on supercooling. Relative to the pure salt solutions, supercooling decreases in MgSO4 soil solutions, increases in MgCl2 soil solutions, and is similar in NaCl and NaClO4 soil solutions. Supercooling in MgSO4, MgCl2, NaCl, and NaClO4 solutions could marginally extend the duration of liquid water during relatively warm daytime temperatures in the Martian summer. Remarkably, we found that Mg(ClO4)2 and Ca(ClO4)2 solutions never crystallize during slow cooling, but remain in a supercooled, liquid state until forming an amorphous glass near -120°C. Even if soil is added to the solutions, which will induce crystallization in most salt solutions, a glass still forms during cooling. The large supercooling effect in Mg(ClO4)2 and Ca(ClO4)2 solutions has the potential to prevent water from freezing over diurnal and possibly annual cycles on Mars. Glasses are
Lan, S.; Blodgett, M.; Kelton, K. F.; Ma, J. L.; Fan, J.; Wang, X.-L.
2016-05-01
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.
Liquid–liquid transition in supercooled water suggested by microsecond simulations
Li, Yaping; Li, Jicun; Wang, Feng
2013-01-01
The putative liquid–liquid phase transition in supercooled water has been used to explain many anomalous behaviors of water. However, no direct experimental verification of such a phase transition has been accomplished, and theoretical studies from different simulations contradict each other. We investigated the putative liquid–liquid phase transition using the Water potential from Adaptive Force Matching for Ice and Liquid (WAIL). The simulation reveals a first-order phase transition in the ...
DEFF Research Database (Denmark)
Jakobsen, Bo; Sanz, Alejandro; Niss, Kristine;
2016-01-01
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...
Energy Technology Data Exchange (ETDEWEB)
Xu, Yuntao [Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA; Dibble, Collin J. [Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA; Petrik, Nikolay G. [Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA; Smith, R. Scott [Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA; Joly, Alan G. [Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA; Tonkyn, Russell G. [Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA; Kay, Bruce D. [Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA; Kimmel, Greg A. [Physical Sciences Division, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA
2016-04-26
A pulsed laser heating system has been developed that enables investigations of the dynamics and kinetics of nanoscale liquid films and liquid/solid interfaces on the nanosecond timescale in ultrahigh vacuum (UHV). Details of the design, implementation and characterization of a nanosecond pulsed laser system for transiently heating nanoscale films are described. Nanosecond pulses from a Nd:YAG laser are used to rapidly heat thin films of adsorbed water or other volatile materials on a clean, well-characterized Pt(111) crystal in UHV. Heating rates of ~1010 K/s for temperature increases of ~100 – 200 K are obtained. Subsequent rapid cooling (~5 × 109 K/s) quenches the film, permitting in-situ, post-mortem analysis using a variety of surface science techniques. Lateral variations in the laser pulse energy are ~ ± 3% leading to a temperature uncertainty of ~ ± 5 K for a temperature jump of 200 K. Initial experiments with the apparatus demonstrate that crystalline ice films initially held at 90 K can be rapidly transformed into liquid water films with T > 273 K. No discernable recrystallization occurs during the rapid cooling back to cryogenic temperatures. In contrast, amorphous solid water films heated below the melting point rapidly crystallize. The nanosecond pulsed laser heating system can prepare nanoscale liquid and supercooled liquid films that persist for nanoseconds per heat pulse in an UHV environment, enabling experimental studies of a wide range of phenomena in liquids and at liquid/solid interfaces.
Mizuno, H; Yamamoto, R
2012-04-01
A steady shear flow can drive supercooled liquids into a non-equilibrium state. Using molecular dynamics simulations under steady shear flow superimposed with oscillatory shear strain for a probe, non-equilibrium mechanical responses are studied for a model supercooled liquid composed of binary soft spheres. We found that even in the strongly sheared situation, the supercooled liquid exhibits surprisingly isotropic responses to oscillating shear strains applied in three different components of the strain tensor. Based on this isotropic feature, we successfully constructed a simple two-mode Maxwell model that can capture the key features of the storage and loss moduli, even for highly non-equilibrium state. Furthermore, we examined the correlation functions of the shear stress fluctuations, which also exhibit isotropic relaxation behaviors in the sheared non-equilibrium situation. In contrast to the isotropic features, the supercooled liquid additionally demonstrates anisotropies in both its responses and its correlations to the shear stress fluctuations. Using the constitutive equation (a two-mode Maxwell model), we demonstrated that the anisotropic responses are caused by the coupling between the oscillating strain and the driving shear flow. Due to these anisotropic responses and fluctuations, the violation of the fluctuation-dissipation theorem (FDT) is distinct for different components. We measured the magnitude of this violation in terms of the effective temperature. It was demonstrated that the effective temperature is notably different between different components, which indicates that a simple scalar mapping, such as the concept of an effective temperature, oversimplifies the true nature of supercooled liquids under shear flow. An understanding of the mechanism of isotropies and anisotropies in the responses and fluctuations will lead to a better appreciation of these violations of the FDT, as well as certain consequent modifications to the concept of an
Liquid Supercoolability and Synthesis Kinetics of Quinary Refractory High-entropy Alloy
Wang, W. L.; Hu, L.; Yang, S. J.; Wang, A.; Wang, L.; Wei, B.
2016-11-01
The high-entropy configuration of equiatomic multicomponent alloys opens an effective access to the development of advanced materials. Here we report the synthesis of a new quinary refractory WMoTaNbZr high-entropy alloy under electrostatic levitation condition. It showed a high liquidus temperature of 2686 K and achieved a maximum supercooling of 640 K (0.24 TL) at molten state. The containerless measurements revealed a linear increasing tendency for both its liquid state density and the specific heat to emissivity ratio versus alloy supercooling. A high-entropy body-centered cubic (HEB) phase dominated its phase constitution despite the formation of a negligible amount of solid solution (Zr) phase. The dendritic growth of HEB phase always governed the crystallization process, attained a fastest growth velocity of 13.5 m/s and displayed a power function relation to alloy supercooling. The high speed videographic research of recalescence phenomenon indicated Johnson-Mehl-Avrami type transition kinetics for its rapid solidification process. As supercooling increases, the microstructures of primary HEB phase were refined conspicuously and exhibited an obvious solute trapping effect of the segregative Zr component. Meanwhile, the Vickers hardness of HEB phase displayed the rising tendency with supercooling.
Energy Technology Data Exchange (ETDEWEB)
Smith, R. Scott; Kay, Bruce D.
2012-03-15
Experimental measurements of the properties supercooled liquids at temperatures near their respective 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.
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)
Dmowski, W.; Gierlotka, S.; Wang, Z.; Yokoyama, Y.; Palosz, B.; Egami, T.
2017-07-26
Through high-energy x-ray diffraction and atomic pair density function analysis we find that Zr-based metallic alloy, heated to the supercooled liquid state under hydrostatic pressure and then quenched to room temperature, exhibits a distinct glassy structure. The PDF indicates that the Zr-Zr distances in this glass are significantly reduced compared to those quenched without pressure. Annealing at the glass transition temperature at ambient pressure reverses structural changes and the initial glassy state is recovered. This result suggests that pressure causes a liquid-to-liquid phase transition in this metallic alloy supercooled melt. Such a pressure induced transition is known for covalent liquids, but has not been observed for metallic liquids. The High Pressure Quenched glasses are stable in ambient conditions after decompression.
Boson peak, Ioffe-Regel Crossover, and Liquid-Liquid phase transition in Supercooled Water
Kumar, Pradeep
We have investigated the onset of Boson peak in a model of liquid water which exhibits a clear first-order phase transition between a low-density liquid phase and a high-density liquid phase of water at low temperature and high pressure. We find that the at low pressures, the onset of Boson peak coincides with the Widom-line of the system. At high pressures, the onset occurs at the transition temperature between the two liquids. Furthermore, we show that at both low and high pressure, the frequency of the Boson peak coincides with the Ioffe-Regel crossover of the transverse phonons, suggesting that the breakdown of Debye behavior is a general feature of Ioffe-Regel limit crossover in supercooled water. The frequency of the Boson peak is weakly pressure dependent and decreases with increasing pressure. Our work bridges gap between the experimental results on the Boson peak nanoconfined water and the behavior that one would expect from a bulk system.
Liquid-liquid coexistence and crystallization in supercooled ST2 water
Martelli, Fausto; Palmer, Jeremy; Debenedetti, Pablo; Car, Roberto
2014-03-01
We have computed the free energy landscape of ST2 water in the supercooled regime (228.6 K and 2.4 kbar) using several state-of-the-art computational techniques, including umbrella sampling and metadynamics. Such results conclusively demonstrate coexistence between two liquid phases, a high-density liquid (HDL) and a low-density liquid (HDL), which are metastable with respect to cubic ice. We show that the three phases have distinct structural features characterized by the local structure index and ring statistics. We also find that ice nucleation, should it occur, does so from the low-density liquid. Interestingly, we find that the number of 6-member rings increases monotonically along the path from HDL to LDL, while non-monotonic behavior is observed near the saddle point along the LDL-ice Ic path. This behavior indicates a complex re-arrangement of the H-bond network, followed by progressive crystallization. DOE: DE-SC0008626 (F. M. and R.C.)
Xu, Yuntao; Dibble, Collin J; Petrik, Nikolay G; Smith, R Scott; Joly, Alan G; Tonkyn, Russell G; Kay, Bruce D; Kimmel, Greg A
2016-04-28
A pulsed laser heating system has been developed that enables investigations of the dynamics and kinetics of nanoscale liquid films and liquid/solid interfaces on the nanosecond time scale in ultrahigh vacuum (UHV). Details of the design, implementation, and characterization of a nanosecond pulsed laser system for transiently heating nanoscale films are described. Nanosecond pulses from a Nd:YAG laser are used to rapidly heat thin films of adsorbed water or other volatile materials on a clean, well-characterized Pt(111) crystal in UHV. Heating rates of ∼10(10) K/s for temperature increases of ∼100-200 K are obtained. Subsequent rapid cooling (∼5 × 10(9) K/s) quenches the film, permitting in-situ, post-heating analysis using a variety of surface science techniques. Lateral variations in the laser pulse energy are ∼±2.7% leading to a temperature uncertainty of ∼±4.4 K for a temperature jump of 200 K. Initial experiments with the apparatus demonstrate that crystalline ice films initially held at 90 K can be rapidly transformed into liquid water films with T > 273 K. No discernable recrystallization occurs during the rapid cooling back to cryogenic temperatures. In contrast, amorphous solid water films heated below the melting point rapidly crystallize. The nanosecond pulsed laser heating system can prepare nanoscale liquid and supercooled liquid films that persist for nanoseconds per heat pulse in an UHV environment, enabling experimental studies of a wide range of phenomena in liquids and at liquid/solid interfaces.
Xu, Yuntao; Dibble, Collin J.; Petrik, Nikolay G.; Smith, R. Scott; Joly, Alan G.; Tonkyn, Russell G.; Kay, Bruce D.; Kimmel, Greg A.
2016-04-01
A pulsed laser heating system has been developed that enables investigations of the dynamics and kinetics of nanoscale liquid films and liquid/solid interfaces on the nanosecond time scale in ultrahigh vacuum (UHV). Details of the design, implementation, and characterization of a nanosecond pulsed laser system for transiently heating nanoscale films are described. Nanosecond pulses from a Nd:YAG laser are used to rapidly heat thin films of adsorbed water or other volatile materials on a clean, well-characterized Pt(111) crystal in UHV. Heating rates of ˜1010 K/s for temperature increases of ˜100-200 K are obtained. Subsequent rapid cooling (˜5 × 109 K/s) quenches the film, permitting in-situ, post-heating analysis using a variety of surface science techniques. Lateral variations in the laser pulse energy are ˜±2.7% leading to a temperature uncertainty of ˜±4.4 K for a temperature jump of 200 K. Initial experiments with the apparatus demonstrate that crystalline ice films initially held at 90 K can be rapidly transformed into liquid water films with T > 273 K. No discernable recrystallization occurs during the rapid cooling back to cryogenic temperatures. In contrast, amorphous solid water films heated below the melting point rapidly crystallize. The nanosecond pulsed laser heating system can prepare nanoscale liquid and supercooled liquid films that persist for nanoseconds per heat pulse in an UHV environment, enabling experimental studies of a wide range of phenomena in liquids and at liquid/solid interfaces.
Real-time observation of the isothermal crystallization kinetics in a deeply supercooled liquid
Zanatta, M.; Cormier, L.; Hennet, L.; Petrillo, C.; Sacchetti, F.
2017-01-01
Below the melting temperature Tm, crystals are the stable phase of typical elemental or molecular systems. However, cooling down a liquid below Tm, crystallization is anything but inevitable. The liquid can be supercooled, eventually forming a glass below the glass transition temperature Tg. Despite their long lifetimes and the presence of strong barriers that produces an apparent stability, supercooled liquids and glasses remain intrinsically a metastable state and thermodynamically unstable towards the crystal. Here we investigated the isothermal crystallization kinetics of the prototypical strong glassformer GeO2 in the deep supercooled liquid at 1100 K, about half-way between Tm and Tg. The crystallization process has been observed through time-resolved neutron diffraction for about three days. Data show a continuous reorganization of the amorphous structure towards the alpha-quartz phase with the final material composed by crystalline domains plunged into a low-density, residual amorphous matrix. A quantitative analysis of the diffraction patterns allows determining the time evolution of the relative fractions of crystal and amorphous, that was interpreted through an empirical model for the crystallization kinetics. This approach provides a very good description of the experimental data and identifies a predator-prey-like mechanism between crystal and amorphous, where the density variation acts as a blocking barrier. PMID:28255173
Evidence of the existence of the low-density liquid phase in supercooled, confined water
Mallamace, Francesco; Broccio, Matteo; Corsaro, Carmelo; Faraone, Antonio; Majolino, Domenico; Venuti, Valentina; Liu, Li; Mou, Chung-Yuan; Chen, Sow-Hsin
2006-01-01
By confining water in a nanoporous structure so narrow that the liquid could not freeze, it is possible to study properties of this previously undescribed system well below its homogeneous nucleation temperature TH = 231 K. Using this trick, we were able to study, by means of a Fourier transform infrared spectroscopy, vibrational spectra (HOH bending and OH-stretching modes) of deeply supercooled water in the temperature range 183 < T < 273 K. We observed, upon decreasing temperature, the bui...
Direct measurement of the surface dynamics of supercooled liquid-glycerol by optical scanning a film
Institute of Scientific and Technical Information of China (English)
Zhang Fang; Zhang Guo-Feng; Dong Shuang-Li; Sun Jian-Hu; Chen Rui-Yun; Xiao Lian-Tuan; Jia Suo-Tang
2009-01-01
The surface dynamics of supercooled liquid-glycerol is studied by scanning the thickness of the glycerol film with single photon detection. Measurements are performed at room temperature well above the glycerol's glass transition temperature. It is shown that the surface dynamics of the glycerol film is very sensitive to the temperature. The linear relationship between the thickness of the film and the viscosity predicted by the Vogel-Fulcher-Tammann-Hesse (VFTH) law is also presented experimentally.
In-situ High-energy X-ray Diffraction Study of the Local Structure of Supercooled Liquid Si
Lee, G. W.; Kim, T. H.; Sieve, B.; Gangopadhyay, A. K.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.; Robinson, D. S.; Kelton, K. F.; Goldman, A. I.
2005-01-01
While changes in the coordination number for liquid silicon upon supercooling, signaling an underlying liquid-liquid phase transition, have been predicted, x-ray and neutron measurements have produced conflicting reports. In particular some studies have found an increase in the first shell coordination as temperature decreases in the supercooled regime, while others have reported increases in the coordination number with decreasing temperature. Employing the technique of electrostatic levitation coupled with high energy x-ray diffraction (125 keV), and rapid data acquisition (100ms collection times) using an area detector, we have obtained high quality structural data more deeply into the supercooled regime than has been possible before. No change in coordination number is observed in this temperature region, calling into question previous experimental claims of structural evidence for the existence of a liquid-liquid phase transition.
Evidence of the existence of the low-density liquid phase in supercooled, confined water.
Mallamace, Francesco; Broccio, Matteo; Corsaro, Carmelo; Faraone, Antonio; Majolino, Domenico; Venuti, Valentina; Liu, Li; Mou, Chung-Yuan; Chen, Sow-Hsin
2007-01-09
By confining water in a nanoporous structure so narrow that the liquid could not freeze, it is possible to study properties of this previously undescribed system well below its homogeneous nucleation temperature TH = 231 K. Using this trick, we were able to study, by means of a Fourier transform infrared spectroscopy, vibrational spectra (HOH bending and OH-stretching modes) of deeply supercooled water in the temperature range 183 < T < 273 K. We observed, upon decreasing temperature, the building up of a new population of hydrogen-bonded oscillators centered around 3,120 cm(-1), the contribution of which progressively dominates the spectra as one enters into the deeply supercooled regime. We determined that the fractional weight of this spectral component reaches 50% just at the temperature, TL approximately 225 K, where the confined water shows a fragile-to-strong dynamic cross-over phenomenon [Ito, K., Moynihan, C. T., Angell, C. A. (1999) Nature 398:492-494]. Furthermore, the fact that the corresponding OH stretching spectral peak position of the low-density-amorphous solid water occurs exactly at 3,120 cm(-1) [Sivakumar, T. C., Rice, S. A., Sceats, M. G. (1978) J. Chem. Phys. 69:3468-3476.] strongly suggests that these oscillators originate from existence of the low-density-liquid phase derived from the occurrence of the first-order liquid-liquid (LL) phase transition and the associated LL critical point in supercooled water proposed earlier by a computer molecular dynamics simulation [Poole, P. H., Sciortino, F., Essmann, U., Stanley, H. E. (1992) Nature 360:324-328].
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.
Stable glass transformation to supercooled liquid via surface-initiated growth front.
Swallen, Stephen F; Traynor, Katherine; McMahon, Robert J; Ediger, M D; Mates, Thomas E
2009-02-13
Highly stable glasses of tris-naphthylbenzene transform into a liquid when annealed above the glass transition temperature T_{g}. In contrast to the predictions of standard models, the observed transformation is spatially inhomogeneous. Secondary ion mass spectrometry experiments on isotopically labeled multilayer films show that the liquid grows into the stable glass with sharp growth fronts initiated at the free surface and at the interface with the substrate. For the free surface, the growth velocity is constant in time and has the same temperature dependence as self-diffusion in the equilibrium supercooled liquid. These stable glasses are packed so efficiently that surfaces and interfaces are required to initiate the transformation to the liquid even well above T_{g}.
Optical Kerr effect of liquid and supercooled water: The experimental and data analysis perspective
Taschin, A.; Bartolini, P.; Eramo, R.; Righini, R.; Torre, R.
2014-08-01
The time-resolved optical Kerr effect spectroscopy (OKE) is a powerful experimental tool enabling accurate investigations of the dynamic phenomena in molecular liquids. We introduced innovative experimental and fitting procedures, that enable a safe deconvolution of sample response function from the instrumental function. This is a critical issue in order to measure the dynamics of liquid water. We report OKE data on water measuring intermolecular vibrations and the structural relaxation processes in an extended temperature range, inclusive of the supercooled states. The unpreceded data quality makes possible a solid comparison with few theoretical models: the multi-mode Brownian oscillator model, the Kubo's discrete random jump model, and the schematic mode-coupling model. All these models produce reasonable good fits of the OKE data of stable liquid water, i.e., over the freezing point. The features of water dynamics in the OKE data becomes unambiguous only at lower temperatures, i.e., for water in the metastable supercooled phase. We found that the schematic mode-coupling model provides the more rigorous and complete model for water dynamics, even if its intrinsic hydrodynamic approach does not give a direct access to the molecular information.
Toner, J. D.; Catling, D. C.; Light, B.
2014-05-01
Salt solutions on Mars can stabilize liquid water at low temperatures by lowering the freezing point of water. The maximum equilibrium freezing-point depression possible, known as the eutectic temperature, suggests a lower temperature limit for liquid water on Mars; however, salt solutions can supercool below their eutectic before crystallization occurs. To investigate the magnitude of supercooling and its variation with salt composition and concentration, we performed slow cooling and warming experiments on pure salt solutions and saturated soil-solutions of MgSO4, MgCl2, NaCl, NaClO4, Mg(ClO4)2, and Ca(ClO4)2. By monitoring solution temperatures, we identified exothermic crystallization events and determined the composition of precipitated phases from the eutectic melting temperature. Our results indicate that supercooling is pervasive. In general, supercooling is greater in more concentrated solutions and with salts of Ca and Mg. Slowly cooled MgSO4, MgCl2, NaCl, and NaClO4 solutions investigated in this study typically supercool 5-15 °C below their eutectic temperature before crystallizing. The addition of soil to these salt solutions has a variable effect on supercooling. Relative to the pure salt solutions, supercooling decreases in MgSO4 soil-solutions, increases in MgCl2 soil-solutions, and is similar in NaCl and NaClO4 soil-solutions. Supercooling in MgSO4, MgCl2, NaCl, and NaClO4 solutions could marginally extend the duration of liquid water during relatively warm daytime temperatures in the martian summer. In contrast, we find that Mg(ClO4)2 and Ca(ClO4)2 solutions do not crystallize during slow cooling, but remain in a supercooled, liquid state until forming an amorphous glass near -120 °C. Even if soil is added to the solutions, a glass still forms during cooling. The large supercooling effect in Mg(ClO4)2 and Ca(ClO4)2 solutions has the potential to prevent water from freezing over diurnal and possibly annual cycles on Mars. Glasses are also
Using Peltier cells to study solid-liquid-vapour transitions and supercooling
Energy Technology Data Exchange (ETDEWEB)
Torzo, Giacomo [ICIS-CNR and Physics Department of Padova University, Padova (Italy); Soletta, Isabella [Liceo Scientifico Fermi, Alghero (Italy); Branca, Mario [Chemical Department of Sassari University, Sassari (Italy)
2007-05-15
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.
Using Peltier cells to study solid liquid vapour transitions and supercooling
Torzo, Giacomo; Soletta, Isabella; Branca, Mario
2007-05-01
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.
A maximum-entropy approach to the adiabatic freezing of a supercooled liquid.
Prestipino, Santi
2013-04-28
I employ the van der Waals theory of Baus and co-workers to analyze the fast, adiabatic decay of a supercooled liquid in a closed vessel with which the solidification process usually starts. By imposing a further constraint on either the system volume or pressure, I use the maximum-entropy method to quantify the fraction of liquid that is transformed into solid as a function of undercooling and of the amount of a foreign gas that could possibly be also present in the test tube. Upon looking at the implications of thermal and mechanical insulation for the energy cost of forming a solid droplet within the liquid, I identify one situation where the onset of solidification inevitably occurs near the wall in contact with the bath.
The glass crossover from mean-field Spin-Glasses to supercooled liquids
Rizzo, Tommaso
2016-03-01
Stochastic-Beta-Relaxation provides a characterisation of the glass crossover in discontinuous Spin-Glasses and supercoooled liquid. Notably it can be derived through a rigorous computation from a dynamical Landau theory. In this paper, I will discuss the precise meaning of this connection in a language that does not require familiarity with statistical field theory. I will discuss finite-size corrections in mean-field Spin-Glass models and loop corrections in finite-dimensional models that are both described by the dynamical Landau theory considered. Then I will argue that the same Landau theory can be associated to supercooled liquid described by Mode-Coupling Theory invoking a physical principle of time-scale invariance.
Measuring ice and liquid water content in moderately supercooled clouds with Cloudnet
Bühl, Johannes; Seifert, Patric; Myagkov, Alexander; Albert, Ansmann
2016-04-01
The interaction between ice nuclei and clouds is an important topic in weather and climate research. Recent laboratory experiments and field in-situ field campaigns present more and more detailed measurements of ice nucleating particles (INP) at temperatures close to 0°C. This brings moderately supercooled mixed-phase clouds into the focus of current cloud research. One current example is the European Union BACCHUS project. A major goal of BACCHUS is the analysis of the anthropogenic impact on ice nucleation. Within this project, we use the Leipzig Aerosol Cloud Remote Observations System (LACROS) and the Cloudnet framework in order to get quantitative insight into the formation of ice in mixed-phase layered clouds with cloud top temperature (CTT) from -40 to 0°C. Depolarization measurements from lidar and radar show a clear dependence between particle shape and the temperature under which the particles have been formed. The special focus of this work is on the CTT range from -10 to 0°C. An algorithm is presented to decide between ice and liquid water precipitation falling from the clouds showing that between 10% and 30% of all layered clouds show ice precipitation with CTT between -5 and 0°C. For these slightly supercooled clouds an average ice-water-content between 10e-7 and 10e-8 [kg per cubic meter] is found.
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 L...
Local structure of equilibrium and supercooled Ti-Zr-Ni liquids
Energy Technology Data Exchange (ETDEWEB)
Lee, G. W.; Gangopadhyay, A.; Hyers, R.; Rathz, T.; Rogers, J.; Robinson, D.; Goldman, A.; Kelton, K.
2008-05-01
Recently, we reported the results of experimental in situ high-energy x-ray diffraction studies of electrostatically levitated equilibrium and supercooled metallic elements and alloy liquids, showing evidence for icosahedral short-range ordering (ISRO). In this paper, these studies are extended to binary Ti-Zr and ternary Ti-Zr-Ni alloys. From a cluster-based analysis of the x-ray structure factors, it is concluded that ISRO in the binary alloys becomes progressively more dominant, and the coherence length of the order becomes longer, with the addition of Ni, especially near the concentration of 21 at. % Ni. The effect of chemical interactions among Ti/Zr-Ni and the atomic size on the stabilization of the ISRO is discussed.
He, Li; Zhang, Pei; Besser, Matthew F; Kramer, Matthew Joseph; Voyles, Paul M
2015-08-01
Electron correlation microscopy (ECM) is a new technique that utilizes time-resolved coherent electron nanodiffraction to study dynamic atomic rearrangements in materials. It is the electron scattering equivalent of photon correlation spectroscopy with the added advantage of nanometer-scale spatial resolution. We have applied ECM to a Pd40Ni40P20 metallic glass, heated inside a scanning transmission electron microscope into a supercooled liquid to measure the structural relaxation time τ between the glass transition temperature T g and the crystallization temperature, T x . τ determined from the mean diffraction intensity autocorrelation function g 2(t) decreases with temperature following an Arrhenius relationship between T g and T g +25 K, and then increases as temperature approaches T x . The distribution of τ determined from the g 2(t) of single speckles is broad and changes significantly with temperature.
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.
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
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...... 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...
Energy Technology Data Exchange (ETDEWEB)
Choi, Seo-Woo; Kim, Soree; Jung, YounJoon, E-mail: yjjung@snu.ac.kr [Department of Chemistry, Seoul National University, Seoul 151-747 (Korea, Republic of)
2015-06-28
Kinetically constrained models have gained much interest as models that assign the origins of interesting dynamic properties of supercooled liquids to dynamical facilitation mechanisms that have been revealed in many experiments and numerical simulations. In this work, we investigate the dynamic heterogeneity in the fragile-to-strong liquid via Monte Carlo method using the model that linearly interpolates between the strong liquid-like behavior and the fragile liquid-like behavior by an asymmetry parameter b. When the asymmetry parameter is sufficiently small, smooth fragile-to-strong transition is observed both in the relaxation time and the diffusion constant. Using these physical quantities, we investigate fractional Stokes-Einstein relations observed in this model. When b is fixed, the system shows constant power law exponent under the temperature change, and the exponent has the value between that of the Frederickson-Andersen model and the East model. Furthermore, we investigate the dynamic length scale of our systems and also find the crossover relation between the relaxation time. We ascribe the competition between energetically favored symmetric relaxation mechanism and entropically favored asymmetric relaxation mechanism to the fragile-to-strong crossover behavior.
Pabst, Florian; Gabriel, Jan; Weigl, Peter; Blochowicz, Thomas
2017-09-01
We investigate molecular dynamics of two supercooled room temperature ionic liquids (RTILs) above of their glass transition temperature by means of dynamic light scattering and broadband dielectric spectroscopy from nanoseconds up to ≈105s . We show that a direct comparison of the raw data of these two techniques allows us to identify the reorientation of ions in the dielectric data, giving experimental evidence to a very recently proposed model of Gainaru et al. [1], stating that the conductivity process in ionic liquids takes place through a reorientational step of ions escaping their cage formed by surrounding counterions. Within this approach we can also understand the apparent decoupling of time constants from dielectric spectroscopy and light scattering, often found in ionic liquids, in a very natural way. Furthermore, as a consequence of knowing the reorientational part of the dielectric spectrum, we are able to show that two more processes contribute to these spectra, which are due to electrode polarization effects. The relative position of all three contributions vary among the systems and may overshadow each other, thus complicating the data analysis and favor misinterpretations.
Energy Technology Data Exchange (ETDEWEB)
Smith, R. Scott; Matthiesen, Jesper; Kay, Bruce D.
2010-03-28
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 near (100-115 K) the glass transition temperature, Tg (103 K). Layered films, consisting of CH3OH and CD3OH, are deposited ontop 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.
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.
NOH, Y. J.; Miller, S. D.; Heidinger, A. K.
2015-12-01
Many studies have demonstrated the utility of multispectral information from satellite passive radiometers for detecting and retrieving the properties of cloud globally, which conventionally utilizes shortwave- and thermal-infrared bands. However, the satellite-derived cloud information comes mainly from cloud top or represents a vertically integrated property. This can produce a large bias in determining cloud phase characteristics, in particular for mixed-phase clouds which are often observed to have supercooled liquid water at cloud top but a predominantly ice phase residing below. The current satellite retrieval algorithms may report these clouds simply as supercooled liquid without any further information regarding the presence of a sub-cloud-top ice phase. More accurate characterization of these clouds is very important for climate models and aviation applications. In this study, we present a physical basis and preliminary results for the algorithm development of supercooled liquid-topped mixed-phase cloud detection using satellite radiometer observations. The detection algorithm is based on differential absorption properties between liquid and ice particles in the shortwave-infrared bands. Solar reflectance data in narrow bands at 1.6 μm and 2.25 μm are used to optically probe below clouds for distinction between supercooled liquid-topped clouds with and without an underlying mixed phase component. Varying solar/sensor geometry and cloud optical properties are also considered. The spectral band combination utilized for the algorithm is currently available on Suomi NPP Visible/Infrared Imaging Radiometer Suite (VIIRS), Himawari-8 Advanced Himawari Imager (AHI), and the future GOES-R Advance Baseline Imager (ABI). When tested on simulated cloud fields from WRF model and synthetic ABI data, favorable results were shown with reasonable threat scores (0.6-0.8) and false alarm rates (0.1-0.2). An ARM/NSA case study applied to VIIRS data also indicated promising
Directory of Open Access Journals (Sweden)
Vinš Václav
2016-01-01
Full Text Available An experimental apparatus with a horizontal capillary tube for measurement of the surface tension of supercooled liquids, i.e. liquids in a metastable state below the equilibrium freezing point, was designed and tested in the previous study [V. Vinš et al., EPJ Web Conf. 92, 02108 (2015]. In this work, recent modifications of both the experimental setup and the measurement analysis are described. The main aim is to improve the accuracy and the reproducibility of measured surface tension and to achieve higher degrees of supercooling. Temperature probes measuring the temperature of cooling medium near the horizontal capillary tube were calibrated in the relevant temperature range from – 31 °C to + 45 °C. An additional pressure transducer was installed in the helium distribution setup at the position close to the capillary tube. The optical setup observing the liquid meniscus at the open end of the horizontal capillary tube together with the video analysis were thoroughly revised. The red laser illuminating the liquid meniscus, used at the original apparatus, was replaced by a fiber optic light source, which significantly improved the quality of the meniscus image. The modified apparatus was used for the measurement of surface tension of supercooled water at temperatures down to – 11 °C. The new data have a lower scatter compared to the previous horizontal measurements and show a good agreement with the other data obtained with a different measurement technique based on the modified capillary rise method.
Directory of Open Access Journals (Sweden)
Carlos Alejandro De Luna Ortega
2006-01-01
Full Text Available En este artículo se aborda el diseño de un reconocedor de voz, con el idioma español mexicano, del estado de Aguascalientes, de palabras aisladas, con dependencia del hablante y vocabulario pequeño, empleando Redes Neuronales Artificiales (ANN por sus siglas en inglés, Alineamiento Dinámico del Tiempo (DTW por sus siglas en inglés y Modelos Ocultos de Markov (HMM por sus siglas en inglés para la realización del algoritmo de reconocimiento.
Energy Technology Data Exchange (ETDEWEB)
Schroer, Carsten F. E., E-mail: c.schroer@uni-muenster.de [Institut für Physikalische Chemie, Westfälische Wilhelms-Universität Münster, Corrensstraße 28/30, 48149 Münster (Germany); NRW Graduate School of Chemistry, Wilhelm-Klemm-Straße 10, 48149 Münster (Germany); Heuer, Andreas, E-mail: andheuer@uni-muenster.de [Institut für Physikalische Chemie, Westfälische Wilhelms-Universität Münster, Corrensstraße 28/30, 48149 Münster (Germany); Center of Nonlinear Science, Corresstraße 2, 48149 Münster (Germany); Center for Multiscale Theory and Computation, Corrensstraße 40, 48149 Münster (Germany)
2015-12-14
In active microrheology, the mechanical properties of a material are tested by adding probe particles which are pulled by an external force. In case of supercooled liquids, strong forcing leads to a thinning of the host material which becomes more pronounced as the system approaches the glass transition. In this work, we provide a quantitative theoretical description of this thinning behavior based on the properties of the Potential Energy Landscape (PEL) of a model glass-former. A key role plays the trap-like nature of the PEL. We find that the mechanical properties in the strongly driven system behave the same as in a quiescent system at an enhanced temperature, giving rise to a well-characterized effective temperature. Furthermore, this effective temperature turns out to be independent of the chosen observable and individually shows up in the thermodynamic and dynamic properties of the system. Based on this underlying theoretical understanding, we can estimate its dependence on temperature and force by the PEL-properties of the quiescent system. We furthermore critically discuss the relevance of effective temperatures obtained by scaling relations for the description of out-of-equilibrium situations.
Hard rhenium–boron–cobalt amorphous alloys with a wide supercooled liquid region
Energy Technology Data Exchange (ETDEWEB)
Wang, Jianfeng, E-mail: jfwang316@zzu.edu.cn [School of Materials Science and Engineering, Zhengzhou University, Zhengzhou 450001 (China); Zhu, Shijie; Wang, Liguo; Guan, Shaokang [School of Materials Science and Engineering, Zhengzhou University, Zhengzhou 450001 (China); Li, Ran; Zhang, Tao [School of Materials Science and Engineering, Beihang University, Beijing 100191 (China)
2015-10-01
Novel Re–B–Co amorphous alloys with compositions of Re{sub 65−x}B{sub 35}Co{sub x} (at%, x=25, 30, 35, 40, 45, and 50) were fabricated by single-roller melt spinning. These alloys were found to exhibit a clear glass transition phenomenon. The width of supercooled liquid region (ΔT{sub x}) is in the range of 52–71 K. Such a large ΔT{sub x} allows us to produce amorphous alloy bulks by thermoplastic forming. The Vickers hardness is up to 19.10 GPa for the Re{sub 40}B{sub 35}Co{sub 25} alloy, which is close to that reported for some hard covalent crystals. Thus, the present alloys with a combination of large ΔT{sub x} and high hardness are expected to be used as a new type of structural materials. Furthermore, the relationships of hardness with glass transition temperature and Young's modulus were also discussed.
Schroer, Carsten F. E.; Heuer, Andreas
2015-12-01
In active microrheology, the mechanical properties of a material are tested by adding probe particles which are pulled by an external force. In case of supercooled liquids, strong forcing leads to a thinning of the host material which becomes more pronounced as the system approaches the glass transition. In this work, we provide a quantitative theoretical description of this thinning behavior based on the properties of the Potential Energy Landscape (PEL) of a model glass-former. A key role plays the trap-like nature of the PEL. We find that the mechanical properties in the strongly driven system behave the same as in a quiescent system at an enhanced temperature, giving rise to a well-characterized effective temperature. Furthermore, this effective temperature turns out to be independent of the chosen observable and individually shows up in the thermodynamic and dynamic properties of the system. Based on this underlying theoretical understanding, we can estimate its dependence on temperature and force by the PEL-properties of the quiescent system. We furthermore critically discuss the relevance of effective temperatures obtained by scaling relations for the description of out-of-equilibrium situations.
Heterogeneous nucleation from a supercooled ionic liquid on a carbon surface
He, Xiaoxia; Shen, Yan; Hung, Francisco R.; Santiso, Erik E.
2016-12-01
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 × 1011 cm-3 s-1) is about one order of magnitude faster than the homogeneous rate (˜6.6 × 1010 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 glasses).
Klameth, F; Henritzi, P; Vogel, M
2014-04-14
We perform molecular dynamics simulations to study static and dynamic length scales in molecular supercooled liquids, in particular, water. For a determination of these scales, we use equilibrium configurations and pin appropriate subsets of molecules so as to obtain random matrices, cylindrical pores, and slit confinements. Static length scales ξ(s) are determined by analyzing overlap correlation functions for various fractions of pinned molecules or distances to the confining walls. For water in all confinements and for propylene oxide trimers in random geometry, a linear increase of ξ(s) with inverse temperature is found. Dynamic length scales ξ(d) are determined by analogous analysis of fraction-dependent or position-resolved correlation times of structural relaxation. While ξ(d) continuously grows upon cooling in the cylindrical and slit confinements, we find no evidence for a temperature dependence in random matrices, implying that molecular dynamics in parsed volumes is qualitatively different from that in bulk liquids. Finally, we study possible connections between the growth of the static and dynamic length scales and the slowdown of the structural relaxation of the supercooled bulk liquids. For water, we observe a linear relation between ln τ(α) and ξ(s)²/T in the whole accessible range down to the critical temperature of mode-coupling theory, T(c). In the weakly supercooled regime, the same relation holds also for ξ(d), as obtained from cylindrical and slit confinements, but deviations from this behavior are observed near T(c). The results are discussed in connection with random first-order theory and experimental studies of liquid dynamics in nanoscopic confinements and binary mixtures.
Volume of supercooled water under pressure and the liquid-liquid critical point.
Mishima, Osamu
2010-10-14
The volume of water (H(2)O) was obtained at about 200-275 K and 40-400 MPa by using emulsified water. The plot of volume against temperature showed slightly concave-downward curvature at pressures higher than ≈200 MPa. This is compatible with the liquid-liquid critical-point hypothesis, but hardly with the singularity-free scenario. When the critical point is assumed to exist at ≈50 MPa and ≈223 K, the experimental volume and the derived compressibility are qualitatively described by the modified Fuentevilla-Anisimov scaling equation.
Elemental and cooperative diffusion in a liquid, supercooled liquid and glass resolved
Cassar, Daniel R.; Lancelotti, Ricardo F.; Nuernberg, Rafael; Nascimento, Marcio L. F.; Rodrigues, Alisson M.; Diz, Luiza T.; Zanotto, Edgar D.
2017-07-01
The diffusion mechanisms controlling viscous flow, structural relaxation, liquid-liquid phase separation, crystal nucleation, and crystal growth in multicomponent glass-forming liquids are of great interest and relevance in physics, chemistry, materials, and glass science. However, the diffusing entities that control each of these important dynamic processes are still unknown. The main objective of this work is to shed some light on this mystery, advancing the knowledge on this phenomenon. For that matter, we measured the crystal growth rates, the viscosity, and lead diffusivities in PbSiO3 liquid and glass in a wide temperature range. We compared our measured values with published data covering 16 orders of magnitude. We suggest that above a certain temperature range Td (1.2Tg-1.3Tg), crystal growth and viscous flow are controlled by the diffusion of silicon and lead. Below this temperature, crystal growth and viscous flow are more sluggish than the diffusion of silicon and lead. Therefore, Td marks the temperature where decoupling between the (measured) cationic diffusivity and the effective diffusivities calculated from viscosity and crystal growth rates occurs. We reasonably propose that the nature or size of the diffusional entities controlling viscous flow and crystal growth below Td is quite different; the slowest is the one controlling viscous flow, but both processes require cooperative movements of some larger structural units rather than jumps of only one or a few isolated atoms.
Nature of the anomalies in the supercooled liquid state of the mW model of water
Holten, Vincent; Molinero, Valeria; Anisimov, Mikhail A
2013-01-01
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 particular 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 fitting the power laws implied by weak crystallization theory is found not to be physically meaningful. 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 e...
Predicting How Nanoconfinement Changes the Relaxation Time of a Supercooled Liquid
DEFF Research Database (Denmark)
Ingebrigtsen, Trond; Errington, Jeff; Truskett, Tom;
2013-01-01
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...
Chua, Y. Z.; Young-Gonzales, A. R.; Richert, R.; Ediger, M. D.; Schick, C.
2017-07-01
Physical vapor deposition has been used to prepare glasses of ethanol. Upon heating, the glasses transformed into the supercooled liquid phase and then crystallized into the plastic crystal phase. The dynamic glass transition of the supercooled liquid is successfully measured by AC nanocalorimetry, and preliminary results for the plastic crystal are obtained. The frequency dependences of these dynamic glass transitions observed by AC nanocalorimetry are in disagreement with conclusions from previously published dielectric spectra of ethanol. Existing dielectric loss spectra have been carefully re-evaluated considering a Debye peak, which is a typical feature in the dielectric loss spectra of monohydroxy alcohols. The re-evaluated dielectric fits reveal a prominent dielectric Debye peak, a smaller and asymmetrically broadened peak, which is identified as the signature of the structural α-relaxation and a Johari-Goldstein secondary relaxation process. This new assignment of the dielectric processes is supported by the observation that the AC nanocalorimetry dynamic glass transition temperature, Tα, coincides with the dielectric structural α-relaxation process rather than the Debye process. The combined results from dielectric spectroscopy and AC nanocalorimetry on the plastic crystal of ethanol suggest the occurrence of a Debye process also in the plastic crystal phase.
Possible Evidence for a New Form of Liquid Buried in the Surface Tension of Supercooled Water
Rogers, T. Ryan; Leong, Kai-Yang; Wang, Feng
2016-09-01
Contrary to the historical data, several recent experiments indicate that the surface tension of supercooled water follows a smooth extrapolation of the IAPWS equation in the supercooled regime. It can be seen, however, that a small deviation from the IAPWS equation is present in the recent experimental measurements. It is shown with simulations using the WAIL water potential that the small deviation in the experimental data is consistent with the tail of an exponential growth in surface tension as temperature decreases. The emergence temperature, Te, of a substantial deviation from the IAPWS equation is shown to be 227 K for the WAIL water and 235 K for real water. Since the 227 K Te is close to the Widom line in WAIL water, we argue that real water at 235 K approaches a similar crossover line at one atmospheric pressure.
Energy Technology Data Exchange (ETDEWEB)
Lesher, Charles E.; Wang, Yanbin; Gaudio, Sarah; Clark, Alisha; Nishiyama, Nori; Rivers, Mark; (UCD); (UC)
2009-06-01
The volumetric properties of silicate glasses and supercooled liquid are examined at high pressures and temperatures using X-ray computed tomography (CT) and absorption. The high pressure X-ray microtomography (HPXMT) system at the Advanced Photon Source, Argonne National Laboratory (GeoSoilEnvironCARS 13-BM-D beamline) consists of two opposing anvils compressed within an X-ray-transparent containment ring supported by thrust bearings and loaded using a 250-ton hydraulic press. This system permits the pressure cell to rotate under the load, while collecting radiographs through at least 180{sup o} of rotation. The 13-BM-D beamline permits convenient switching between monochromatic radiation required for radiography and polychromatic radiation for pressure determination by energy dispersive diffraction. We report initial results on several refractory magnesium silicate glasses synthesized by levitation laser heating. Volume changes during room temperature compression of Mg-silicate glasses with 33 mol% and 38 mol% SiO2 up to 11.5 GPa give an isothermal bulk moduli of 93--100 GPa for a K' of 1. These values are consistent with ultrasonic measurements of more silica-rich glasses. The volumetric properties of amorphous MgSiO{sub 3} at 2 GPa were examined during annealing up to 1000 C. We consider the consequences of heating through the glass transition and the implications for thermal expansivity of supercooled liquids at high pressure. Our results illustrate the capabilities of HPXMT for studies of refractory glasses and liquids at high pressure and offer strategies for future studies of liquid densities within the melting interval for magmas in planet interiors.
Directory of Open Access Journals (Sweden)
Vinš Václav
2015-01-01
Full Text Available 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....
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....
Woutersen, Sander; Zhao, Zuofeng; Angell, C Austen
2016-01-01
The striking anomalies in physical properties of supercooled water that were discovered in the 1960-70s, remain incompletely understood and so provide both a source of controversy amongst theoreticians, and a stimulus to experimentalists and simulators to find new ways of penetrating the "crystallization curtain" that effectively shields the problem from solution. Recently a new door on the problem was opened by showing that, in ideal solutions, made using ionic liquid solutes, water anomalies are not destroyed as earlier found for common salt and most molecular solutes, but instead are enhanced to the point of precipitating an apparently first order liquid-liquid transition. The evidence was a spike in apparent heat capacity during cooling that could be fully reversed during reheating before any sign of ice crystallization appeared. Here, we use decoupled-oscillator infrared spectroscopy to define the structural character of this phenomenon using similar down and upscan rates as in the calorimetric study. Th...
Deformation behavior of Zr-based bulk metallic glass and composite in the supercooled liquid region
Institute of Scientific and Technical Information of China (English)
2008-01-01
A Zr-based bulk metallic glass (BMG) with a composition of (Zr75Cu25)78.5Ta4Ni10Al7.5 and a bulk metallic glass matrix composite (BMGC) with a composition of (Zr75Cu25)74.5Ta8Ni10Al7.5 have been prepared by copper-mold casting. The compres-sive deformation behavior of the BMG and BMGC was investigated in the super-cooled region at different temperatures and various strain rates ranging from 8×10-4s-1 to 8×10-2s-1. It was found that both the strain rate and test temperature signifi-cantly affect the deformation behavior of the two alloys. The deformation follows Newtonian flow at low strain rates but non-Newtonian flow at high strain rates. The deformation mechanism for the two kinds of alloys was discussed in terms of the transition state theory.
Energy Technology Data Exchange (ETDEWEB)
Li, M.; Wang, C. Z.; Mandelev, M.; Ho, K. M.
2008-05-13
Molecular dynamics simulations are performed to study the structure and dynamical heterogeneity in the liquid and glass states of Al using a frequently employed embedded atom potential. While the pair correlation function of the glass and liquid states displays only minor differences, the icosahedral short-range order (ISRO) and the dynamics of the two states are very different. The ISRO is much stronger in the glass than in the liquid. It is also found that both the most mobile and the most immobile atoms in the glass state tend to form clusters, and the clusters formed by the immobile atoms are more compact. In order to investigate the local environment of each atom in the liquid and glass states, a local density is defined to characterize the local atomic packing. There is a strong correlation between the local packing density and the mobility of the atoms. These results indicate that dynamical heterogeneity in glasses is directly correlated to the local structure. We also analyze the diffusion mechanisms of atoms in the liquid and glass states. It is found that for the mobile atoms in the glass state, initially they are confined in the cages formed by their nearest neighbors and vibrating. On the time scale of {beta} relaxation, the mobile atoms try to break up the cage confinement and hop into new cages. In the supercooled liquid states, however, atoms continuously diffuse. Furthermore, it is found that on the time scale of {beta} relaxation, some of the mobile atoms in the glass state cooperatively hop, which is facilitated by the stringlike cluster structures. On the longer time scale, it is found that a certain fraction of atoms can simultaneously hop, although they are not nearest neighbors. Further analysis shows that these hopping atoms form big and more compact clusters than the characterized most mobile atoms. The cooperative rearrangement of these big compact clusters might facilitate the simultaneous hopping of atoms in the glass states on the long
Energy Technology Data Exchange (ETDEWEB)
Kawamura, Y.; Shibata, T.; Inoue, A.; Masumoto, T. [Tohoku Univ., Sendai (Japan). Inst. for Materials Research
1997-12-19
The workability of the supercooled liquid in metallic glass has been examined through the extrusion of a Zr{sub 6.5}Al{sub 10}Ni{sub 10}Cu{sub 15} at.% bulk glassy alloy with a wide supercooled liquid region. The metallic glass exhibited superplastic-like deformation behavior at high strain rates, resulting in an excellent workability. The working throughout a wide range of extrusion conditions was compatible with retaining the glass phase and the original strength. The extrusion maps and the expression between extrusion temperature, pressure and ram-speed have been established. Moreover, the features of working such as the Barus effect and the advantage of a small stepwise increase in strain rate have been revealed.
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.
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…
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
Directory of Open Access Journals (Sweden)
Felix Köhler
2014-09-01
Full Text Available Supercooled liquid water (SLW in the atmosphere is responsible for aircraft icing which can cause severe accidents. To date, the microphysics scheme in the model of the Deutscher Wetterdienst (DWD for the European scale (COSMO-EU; due to be replaced by ICON-EU in 2015 has been optimised to forecast precipitation on the ground but not the water phase in the atmosphere. As a consequence, prediction of SLW is rather poor, as was shown in a series of case studies by the Aeronautical Meteorology department at DWD. ADWICE – the tool used by the DWD to predict aircraft icing – therefore does not rely on COSMO model SLW output, but predicts SLW by itself using a simple parcel method. In an effort to improve ADWICE it has been found that this algorithm has its limits and that it should be replaced by SLW prediction from a 3D weather prediction model. To this end it is necessary to improve the SLW prediction in the COSMO model. In this paper we analyse the microphysics scheme of COSMO-EU with respect to SLW production and depletion and present modifications that greatly improve SLW prediction. As reference for two case studies we use radar-lidar-radiometer products from the Meteorological Observatory Lindenberg to verify the change in SLW prediction.
Banerjee, Atreyee; Nandi, Manoj Kumar; Sastry, Srikanth; Bhattacharyya, Sarika Maitra
2016-07-01
In this paper, we present a study of supercooled liquids interacting with the Lennard Jones potential and the corresponding purely repulsive (Weeks-Chandler-Andersen) potential, over a range of densities and temperatures, in order to understand the origin of their different dynamics in spite of their structures being similar. Using the configurational entropy as the thermodynamic marker via the Adam Gibbs relation, we show that the difference in the dynamics of these two systems at low temperatures can be explained from thermodynamics. At higher densities both the thermodynamical and dynamical difference between these model systems decrease, which is quantitatively demonstrated in this paper by calculating different parameters. The study also reveals the origin of the difference in pair entropy despite the similarity in the structure. Although the maximum difference in structure is obtained in the partial radial distribution function of the B type of particles, the rdf of AA pairs and AB pairs gives rise to the differences in the entropy and dynamics. This work supports the observation made in an earlier study [A. Banerjee et al., Phys. Rev. Lett. 113, 225701 (2014)] and shows that they are generic in nature, independent of density.
Directory of Open Access Journals (Sweden)
Jiao Long
2015-01-01
Full Text Available The quantitative structure property relationship (QSPR for supercooled liquid vapour pressures (PL of PBDEs was investigated. Molecular distance-edge vector (MDEV index was used as the structural descriptor. The quantitative relationship between the MDEV index and lgPL was modeled by using multivariate linear regression (MLR and artificial neural network (ANN respectively. Leave-one-out cross validation and k-fold cross validation were carried out to assess the prediction ability of the developed models. For the MLR method, the prediction root mean square relative error (RMSRE of leave-one-out cross validation and k-fold cross validation is 9.95 and 9.05 respectively. For the ANN method, the prediction RMSRE of leave-one-out cross validation and k-fold cross validation is 8.75 and 8.31 respectively. It is demonstrated the established models are practicable for predicting the lgPL of PBDEs. The MDEV index is quantitatively related to the lgPL of PBDEs. MLR and L-ANN are practicable for modeling this relationship. Compared with MLR, ANN shows slightly higher prediction accuracy. Subsequently, an MLR model, which regression equation is lgPL = 0.2868 M11 - 0.8449 M12 - 0.0605, and an ANN model, which is a two inputs linear network, were developed. The two models can be used to predict the lgPL of each PBDE.
Energy Technology Data Exchange (ETDEWEB)
Louzguine-Luzgin, D. V.; Inoue, A. [WPI Advanced Institute for Materials Research, Tohoku University, Aoba-Ku, Sendai 980-8577 (Japan); Belosludov, R.; Kawazoe, Y. [Institute for Materials Research, Tohoku University, Aoba-Ku, Sendai 980-8577 (Japan); Yavari, A. R. [WPI Advanced Institute for Materials Research, Tohoku University, Aoba-Ku, Sendai 980-8577 (Japan); SIMAP-LTPCM, Institut National Polytechnique de Grenoble, St-Martin-d' Heres Campus, Grenoble, BP 75, 38402 (France); European Synchrotron Radiation Facility, 38042, Grenoble (France); Georgarakis, K. [WPI Advanced Institute for Materials Research, Tohoku University, Aoba-Ku, Sendai 980-8577 (Japan); SIMAP-LTPCM, Institut National Polytechnique de Grenoble, St-Martin-d' Heres Campus, Grenoble, BP 75, 38402 (France); Vaughan, G. [European Synchrotron Radiation Facility, 38042, Grenoble (France); Egami, T. [Joint Institute for Neutron Sciences, Department of Materials Science and Engineering and Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996 (United States); Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States); WPI Advanced Institute for Materials Research, Tohoku University, Aoba-Ku, Sendai 980-8577 (Japan)
2011-08-15
Metallic melts above the liquidus temperature exhibit nearly Arrhenius-type temperature dependence of viscosity. On cooling below the equilibrium liquidus temperature metallic melts exhibit a non-Arrhenius temperature dependence of viscosity characterized by liquid fragility phenomenon which origin is still not well understood. Structural changes and vitrification of the Pd{sub 42.5}Cu{sub 30}Ni{sub 7.5}P{sub 20} liquid alloy on cooling from above the equilibrium liquidus temperature are studied by synchrotron radiation X-ray diffraction and compared with the results of first-principles calculations. Subsequent analysis of the atomic and electronic structure of the alloy in liquid and glassy states reveals formation of chemical short-range order in the temperature range corresponding to such a non-Arrhenius behavior. The first-principles calculations were applied to confirm the experimental findings.
Directory of Open Access Journals (Sweden)
Robert F. Tournier
2014-08-01
Full Text Available A few experiments have detected icosahedral superclusters in undercooled liquids. These superclusters survive above the crystal melting temperature Tm because all their surface atoms have the same fusion heat as their core atoms, and are melted by liquid homogeneous and heterogeneous nucleation in their core, depending on superheating time and temperature. They act as heterogeneous growth nuclei of crystallized phase at a temperature Tc of the undercooled melt. They contribute to the critical barrier reduction, which becomes smaller than that of crystals containing the same atom number n. After strong superheating, the undercooling rate is still limited because the nucleation of 13-atom superclusters always reduces this barrier, and increases Tc above a homogeneous nucleation temperature equal to Tm/3 in liquid elements. After weak superheating, the most stable superclusters containing n = 13, 55, 147, 309 and 561 atoms survive or melt and determine Tc during undercooling, depending on n and sample volume. The experimental nucleation temperatures Tc of 32 liquid elements and the supercluster melting temperatures are predicted with sample volumes varying by 18 orders of magnitude. The classical Gibbs free energy change is used, adding an enthalpy saving related to the Laplace pressure change associated with supercluster formation, which is quantified for n = 13 and 55.
Metal-organic frameworks as host materials of confined supercooled liquids.
Fischer, J K H; Sippel, P; Denysenko, D; Lunkenheimer, P; Volkmer, D; Loidl, A
2015-10-21
In this work, we examine the use of metal-organic framework (MOF) systems as host materials for the investigation of glassy dynamics in confined geometry. We investigate the confinement of the molecular glass former glycerol in three MFU-type MOFs with different pore sizes (MFU stands for "Metal-Organic Framework Ulm-University") and study the dynamics of the confined liquid via dielectric spectroscopy. In accord with previous reports on confined glass formers, we find different degrees of deviations from bulk behavior depending on pore size, demonstrating that MOFs are well-suited host systems for confinement investigations.
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.
Thermodynamic geometry of supercooled water
May, Helge-Otmar; Mausbach, Peter; Ruppeiner, George
2015-03-01
The thermodynamic curvature scalar R is evaluated for supercooled water with a two-state equation of state correlated with the most recent available experimental data. This model assumes a liquid-liquid critical point. Our investigation extends the understanding of the thermodynamic behavior of R considerably. We show that R diverges to -∞ when approaching the assumed liquid-liquid critical point. This limit is consistent with all of the fluid critical point models known so far. In addition, we demonstrate a sign change of R along the liquid-liquid line from negative near the critical point to positive on moving away from the critical point in the low density "ice-like" liquid phase. We also trace out the Widom line in phase space. In addition, we investigate increasing correlation length in supercooled water and compare our results with recent published small angle x-ray scattering measurements.
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.
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.
Mauro, N A; Kelton, K F
2011-03-01
High-energy x-ray diffraction studies of metallic liquids provide valuable information about structural evolution on the atomic length scale, leading to insights into the origin of the nucleation barrier and the processes of supercooling and glass formation. The containerless processing of the beamline electrostatic levitation (BESL) facility allows coordinated thermophysical and structural studies of equilibrium and supercooled liquids to be made in a contamination-free, high-vacuum (∼10(-8) Torr) environment. To date, the incorporation of electrostatic levitation facilities into synchrotron beamlines has been difficult due to the large footprint of the apparatus and the difficulties associated with its transportation and implementation. Here, we describe a modular levitation facility that is optimized for diffraction studies of high-temperature liquids at high-energy synchrotron beamlines. The modular approach used in the apparatus design allows it to be easily transported and quickly setup. Unlike most previous electrostatic levitation facilities, BESL can be operated by a single user instead of a user team.
Hirsikko, Anne; Brus, David; O'Connor, Ewan J.; Filioglou, Maria; Komppula, Mika; Romakkaniemi, Sami
2017-04-01
In the high and mid latitudes super-cooled liquid water layers are frequently observed on top of clouds. These layers are difficult to forecast with numerical weather prediction models, even though, they have strong influence on atmospheric radiative properties, cloud microphysical properties, and subsequently, precipitation. This work investigates properties of super-cooled liquid water layer topped sub-arctic clouds and precipitation observed with ground-based in-situ (cloud probes) and remote-sensing (a cloud radar, Doppler and multi-wavelength lidars) instrumentation during two-month long Pallas Cloud Experiment (PaCE 2015) in autumn 2015. Analysis is based on standard Cloudnet scheme supplemented with new retrieval products of the specific clouds and their properties. Combination of two scales of observation provides new information on properties of clouds and precipitation in the sub-arctic Pallas region. Current status of results will be presented during the conference. The authors acknowledge financial support by the Academy of Finland (Centre of Excellence Programme, grant no 272041; and ICINA project, grant no 285068), the ACTRIS2 - European Union's Horizon 2020 research and innovation programme under grant agreement No 654109, the KONE foundation, and the EU FP7 project BACCHUS (grant no 603445).
Ishikawa, Takehiko; Yoda, Shinichi; Paradis, Paul-Francois; 石川 毅彦; 依田 真一
2005-01-01
The use of an hybrid pressurized electrostatic-aerodynamic levitation furnace and procedures developed by the Japan Aerospace Exploration Agency overcame the contamination problems associated with the processing of ceramics under extreme temperature conditions. This made possible property measurements over wide temperature ranges that cover the superheated as well as the supercooled states. In this study, samples of various ceramics were levitated and their densities were found as a function ...
Mohammadi, Morteza; Tembely, Moussa; Dolatabadi, Ali
2017-02-28
Dynamical analysis of an impacting liquid drop on superhydrophobic surfaces is mostly carried out by evaluating the droplet contact time and maximum spreading diameter. In this study, we present a general transient model of the droplet spreading diameter developed from the previously defined mass-spring model for bouncing drops. The effect of viscosity was also considered in the model by definition of a dash-pot term extracted from experiments on various viscous liquid droplets on a superhydrophobic surface. Furthermore, the resultant shear force of the stagnation air flow was also considered with the help of the classical Homann flow approach. It was clearly shown that the proposed model predicts the maximum spreading diameter and droplet contact time very well. On the other hand, where stagnation air flow is present in contradiction to the theoretical model, the droplet contact time was reduced as a function of both droplet Weber numbers and incoming air velocities. Indeed, the reduction in the droplet contact time (e.g., 35% at a droplet Weber number of up to 140) was justified by the presence of a formed thin air layer underneath the impacting drop on the superhydrophobic surface (i.e., full slip condition). Finally, the droplet wetting model was also further developed to account for low temperature through the incorporation of classical nucleation theory. Homogeneous ice nucleation was integrated into the model through the concept of the reduction of the supercooled water drop surface tension as a function of the gas-liquid interface temperature, which was directly correlated with the Nusselt number of incoming air flow. It was shown that the experimental results was qualitatively predicted by the proposed model under all supercooling conditions (i.e., from -10 to -30 °C).
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.
What am I? Supercooled droplet or ice?
Antonini, Carlo; Maitra, Tanmoy; Tiwari, Manish K; Poulikakos, Dimos
2013-01-01
In this fluid dynamics video we show the trick played by a supercooled liquid water drop against a superhydrophobic surface. The water drop shows a double personality, impacting onto the surface the first time while still in the liquid state, and then re-impacting as a frozen ice crystal.
Ni, Yicun; Skinner, J. L.
2016-06-01
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.
Ni, Yicun; Skinner, J L
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.
Energy Technology Data Exchange (ETDEWEB)
Fan, Jiwen; Leung, L. Ruby; Rosenfeld, Daniel; DeMott, Paul J.
2017-01-01
How orographic mixed-phase clouds respond to the change in cloud condensation nuclei (CCN) and ice nucleating particles (INPs) are highly uncertain. The main snow production mechanism in warm and cold mixed-phase orographic clouds (referred to as WMOCs and CMOCs, respectively, distinguished here as those having cloud tops warmer and colder than -20°C) could be very different. We quantify the CCN and INP impacts on supercooled water content, cloud phases, and precipitation for a WMOC case and a CMOC case, with sensitivity tests using the same CCN and INP concentrations between the WMOC and CMOC cases. It was found that deposition plays a more important role than riming for forming snow in the CMOC case, while the role of riming is dominant in the WMOC case. As expected, adding CCN suppresses precipitation, especially in WMOCs and low INPs. However, this reverses strongly for CCN of 1000 cm^{-3} and larger. We found a new mechanism through which CCN can invigorate mixed-phase clouds over the Sierra Nevada and drastically intensify snow precipitation when CCN concentrations are high (1000 cm^{-3} or higher). In this situation, more widespread shallow clouds with a greater amount of cloud water form in the Central Valley and foothills west of the mountain range. The increased latent heat release associated with the formation of these clouds strengthens the local transport of moisture to the windward slope, invigorating mixed-phase clouds over the mountains, and thereby producing higher amounts of snow precipitation. Under all CCN conditions, increasing the INPs leads to decreased riming and mixed-phase fraction in the CMOC as a result of liquid-limited conditions, but has the opposite effects in the WMOC as a result of ice-limited conditions. However, precipitation in both cases is increased by increasing INPs due to an increase in deposition for the CMOC but enhanced riming and deposition in the WMOC. Increasing the INPs dramatically reduces
Energy Technology Data Exchange (ETDEWEB)
Shaw, Milton Sam [Los Alamos National Laboratory; Coe, Joshua D [Los Alamos National Laboratory; Sewell, Thomas D [UNIV OF MISSOURI-COLUMBIA
2009-01-01
An optimized version of the Nested Markov Chain Monte Carlo sampling method is applied to the calculation of the Hugoniot for liquid nitrogen. The 'full' system of interest is calculated using density functional theory (DFT) with a 6-31 G* basis set for the configurational energies. The 'reference' system is given by a model potential fit to the anisotropic pair interaction of two nitrogen molecules from DFT calculations. The EOS is sampled in the isobaric-isothermal (NPT) ensemble with a trial move constructed from many Monte Carlo steps in the reference system. The trial move is then accepted with a probability chosen to give the full system distribution. The P's and T's of the reference and full systems are chosen separately to optimize the computational time required to produce the full system EOS. The method is numerically very efficient and predicts a Hugoniot in excellent agreement with experimental data.
Peculiar thermodynamics of the second critical point in supercooled water.
Bertrand, C E; Anisimov, M A
2011-12-08
On the basis of the principle of critical-point universality, we examine the peculiar thermodynamics of the liquid-liquid critical point in supercooled water. We show that the liquid-liquid criticality in water represents a special kind of critical behavior in fluids, intermediate between two limiting cases: the lattice gas, commonly used to model liquid-vapor transitions, and the lattice liquid, a weakly compressible liquid with an entropy-driven phase separation. While the ordering field in the lattice gas is associated with the chemical potential and the order parameter with the density, in the lattice liquid the ordering field is the temperature and the order parameter is the entropy. The behavior of supercooled water is much closer to lattice-liquid behavior than to lattice-gas behavior. Using new experimental data recently obtained by Mishima [J. Chem. Phys. 2010, 133, 144503], we have revised the parametric scaled equation of state, previously suggested by Fuentevilla and Anisimov [Phys. Rev. Lett. 2006, 97, 195702], and obtain a consistent description of the thermodynamic anomalies of supercooled water by adjusting linear backgrounds, one critical amplitude, and the critical pressure. We also show how the lattice-liquid description affects the finite-size scaling description of supercooled water in confined media.
Mechanism of supercooled droplet freezing on surfaces
Jung, Stefan; Tiwari, Manish K.; Doan, N. Vuong; Poulikakos, Dimos
2012-01-01
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.
Transport properties of supercooled confined water
Mallamace, F.; Branca, C.; Broccio, M.; Corsaro, C.; Gonzalez-Segredo, N.; Spooren, J.; Stanley, H. E.; Chen, S.-H.
2008-07-01
This article presents an overview of recent experiments performed on transport properties of water in the deeply supercooled region, a temperature region of fundamental importance in the science of water. We report data of nuclear magnetic resonance, quasi-elastic neutron scattering, Fourier-transform infrared spectroscopy, and Raman spectroscopy, studying water confined in nanometer-scale environments. When contained within small pores, water does not crystallise, and can be supercooled well below its homogeneous nucleation temperature Th. On this basis it is possible to carry out a careful analysis of the well known thermodynamical 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, water in the liquid state is a mixture of two different local structures, characterised by different densities, namely the low density liquid (LDL) and the high-density liquid (HDL). The LLPT line should terminate at a special transition point: a low-T liquid-liquid critical point. We discuss the following experimental findings on liquid water: (i) a crossover from non-Arrhenius behaviour at high T to Arrhenius behaviour at low T in transport parameters; (ii) a breakdown of the Stokes-Einstein relation; (iii) the existence of a Widom line, which is the locus of points corresponding to maximum correlation length in the p-T phase diagram and which ends in the liquid-liquid critical point; (iv) the direct observation of the LDL phase; (v) a minimum in the density at approximately 70 K below the temperature of the density maximum. In our opinion these results represent the experimental proofs of the validity of the LLPT hypothesis.
Markov Chains and Markov Processes
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...
Supercooled smectic nanoparticles
DEFF Research Database (Denmark)
Kuntsche, Judith; Koch, Michel H J; Fahr, Alfred
2009-01-01
, 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...... in the bulk was studied by polarizing light microscopy, differential scanning calorimetry (DSC) and small angle X-ray scattering (SAXS). Colloidal dispersions with pure and mixed cholesterol ester matrices were prepared by high-pressure melt homogenization and characterized by photon correlation spectroscopy...... administration of lipophilic drugs, the cytotoxicity of selected formulations was compared with that of a clinically used colloidal fat emulsion (Lipofundin MCT) in the murine fibroblast cell line L929 using the sulforhodamine B assay. The supercooled smectic nanoparticle formulations display a good overall cell...
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.
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.
Fragile to strong crossover at the Widom line in supercooled aqueous solutions of NaCl.
Gallo, P; Corradini, D; Rovere, M
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.
Odabasi, Mustafa; Cetin, Eylem; Sofuoglu, Aysun
Octanol-air partition coefficients ( KOA) for 14 polycyclic aromatic hydrocarbons (PAHs) were determined as a function of temperature using the gas chromatographic retention time method. log KOA values at 25° ranged over six orders of magnitude, between 6.34 (acenaphthylene) and 12.59 (dibenz[ a,h]anthracene). The determined KOA values were within factor of 0.7 (dibenz[ a,h]anthracene) to 15.1 (benz[ a]anthracene) of values calculated as the ratio of octanol-water partition coefficient to dimensionless Henry's law constant. Supercooled liquid vapor pressures ( PL) of 13 PAHs were also determined using the gas chromatographic retention time technique. Activity coefficients in octanol calculated using KOA and PL ranged between 3.2 and 6.2 indicating near-ideal solution behavior. Atmospheric concentrations measured in this study in Izmir, Turkey were used to investigate the partitioning of PAHs between particle and gas-phases. Experimental gas-particle partition coefficients ( Kp) were compared to the predictions of KOA absorption and KSA (soot-air partition coefficient) models. Octanol-based absorptive partitioning model predicted lower partition coefficients especially for relatively volatile PAHs. Ratios of measured/modeled partition coefficients ranged between 1.1 and 15.5 (4.5±6.0, average±SD) for KOA model. KSA model predictions were relatively better and measured to modeled ratios ranged between 0.6 and 5.6 (2.3±2.7, average±SD).
Graphs: Associated Markov Chains
2012-01-01
In this research paper, weighted / unweighted, directed / undirected graphs are associated with interesting Discrete Time Markov Chains (DTMCs) as well as Continuous Time Markov Chains (CTMCs). The equilibrium / transient behaviour of such Markov chains is studied. Also entropy dynamics (Shannon entropy) of certain structured Markov chains is investigated. Finally certain structured graphs and the associated Markov chains are studied.
Revuz, D
1984-01-01
This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail. The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.
Institute of Scientific and Technical Information of China (English)
郑志镇; 成蛟; 王新云; 李建军
2009-01-01
The friction behavior of Zr_(55) Al_(10)Ni_5Cu_(30) bulk metallic glass in the supercooled liquid region was investigated. The influence of forming temperature and velocity on friction factor was established by double cup extrusion test. The calibration curves of friction factor were evaluated by FE simulation and Kawamura's constitutive equation was adopted. Constant parameters in the constitutive equation were acquired by fitting the data from compression test. The results indicate that the friction factor of bulk metallic glass forming in the supercooled liquid region is between 0. 2 and 0. 7. With the temperature rising, the friction factor decreases in general under a low forming velocity. However, the friction factor increases slightly and then decreases abruptly under a high forming velocity. In low temperature area of supercooled liquid region, the friction factor increases abruptly with increasing of the forming velocity. While in high temperature area of supercooled liquid region, the friction factor decreases slightly with increasing of the forming velocity. The friction mechanism of bulk metallic glass forming in supercooled liquid region was analyzed by modern tribology theory. Adhesion is the dominant factor contributing to the friction of bulk metallic glass.%采用双杯挤压方法研究了成形温度、应变速率等工艺参数对Zr_(55) Al_(10) Ni_5 Cu_(30)块体非晶合金在过冷液相区塑性成形时模具和零件之间的摩擦行为的影响.采用有限元模拟方法获得大块非晶合金双杯挤压的摩擦因数标定曲线,有限元模拟中非晶合金的变形采用Kawamura的本构模型,将高温压缩实验的数据拟合,获得本构模型中的参数,结果表明非晶合金在过冷液相区内变形的摩擦因数在0.2～0.7之间.当应变速率较低时,随着温度的升高,摩擦因数总体上降低;而当应变速率较高时,随着温度的升高,摩擦因数先略有上升,然后急剧下降.当温度较低
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...
Fluctuations and Linear Response in Supercooled Liquids
DEFF Research Database (Denmark)
Nielsen, Johannes K.
Fluctuation dissipation theorems are derived for thermodynamic properties like frequency dependent specific heat and compressibility. First the case where a systems dynamics are restricted by constant volume and energy is considered. The dynamic linear response to a heat pulse and a volume change...... at time zero is calculated, under assumption of energy conservation. Then the case of isothermal isobaric conditions are treated by a slight modification of ordinary linear response theory. In both cases the perturbation cannot be stated through the Hamiltonian, but has to be imposed by variation...... of the external thermodynamic system parameters. In thermodynamic response theory equivalence between ensembles is broken, but time correlation functions sampled in different ensembles are connected through the Maxwell relations of thermodynamics generalized to the frequency domain. Different applications...
Decomposition mechanism in supercooled liquid alloys.
Energy Technology Data Exchange (ETDEWEB)
Johnson, W. L.; Loffler, J. F.; Thiyagarajan, P.
1999-07-12
The authors performed small-angle neutron scattering experiments on the bulk amorphous alloy Zr{sub 41.2}Ti{sub 13.8}Cu{sub 12.5}Ni{sub 10}Be{sub 22.5} (Vit1{reg_sign}) and on further alloys, where the ZrTi and CuBe content have been changed, following the tie-line in the direction of Zr{sub 46.8}Ti{sub 8.2}Cu{sub 7.5}Ni{sub 10}Be{sub 27.5} (Vit4{reg_sign}). The SANS data of the samples, preannealed at temperatures between 330 C and 390 C, show interference peaks giving evidence for spatially correlated arrangements of inhomogeneities. The Q values of the interference peaks, Q{sub max}, decrease with increasing annealing temperature T{sub a} and, at a given annealing temperature, with composition following the tie-line from Vit1 to Vit4. They find that, in two distinguished regimes, the data follow a relation 1/L{sup 2} {proportional_to} T{sub a} as predicted by Cahn's theory (L = 2{pi}/Q{sub max} is the wavelength of the decomposition), with a crossover at the glass transition temperature T{sub g} = 350 C. The authors explain the crossover by different diffusion mechanisms below and above T{sub g}.
Slow dynamics of supercooled water confined in nanoporous silica materials
Energy Technology Data Exchange (ETDEWEB)
Liu, L [Department of Nuclear Engineering, 24-209 MIT, Cambridge, MA 02139 (United States); Faraone, A [Department of Nuclear Engineering, 24-209 MIT, Cambridge, MA 02139 (United States); Mou, C-Y [Department of Chemistry, National Taiwan University, Taipei, 106, Taiwan (China); Yen, C-W [Department of Chemistry, National Taiwan University, Taipei, 106, Taiwan (China); Chen, S-H [Department of Nuclear Engineering, 24-209 MIT, Cambridge, MA 02139 (United States)
2004-11-17
We review our incoherent quasielastic neutron scattering (QENS) studies of the dynamics of supercooled water confined in nanoporous silica materials. QENS data were analysed by using the relaxing cage model (RCM) previously developed by us. We first use molecular dynamics (MD) simulation of the extended simple point charge model (SPC/E) for bulk supercooled water to establish the validity of the RCM, which applies to both the translational and rotational motion of water molecules. We then assume that the dynamics of water molecules in the vicinity of a hydrophilic surface is similar to a bulk water at an equivalent lower supercooled temperature. This analogy was experimentally demonstrated in previous investigations of water in Vycor glasses and near hydrophilic protein surfaces. Studies were made of supercooled water in MCM-41-S (pore sizes 25, 18, and 14 A) and MCM-48-S (pore size 22 A) using three QENS spectrometers of respective energy resolutions 1, 30, and 60 {mu}eV, covering the temperature range from 325 to 200 K. Five quantities are extracted from the analysis: they are {beta}, the stretch exponent characterizing the {alpha}-relaxation; {beta}{gamma}, the exponent determining the power-law dependence of the relaxation time on Q; <{tau}{sub 0}>, the Q-independent pre-factor for the average translational relaxation time; <{tau}{sub R{sub 1}}>, the relaxation time for the first-order rotational correlation function; and <{tau}{sub R{sub 3}}>, the relaxation time for the second-order rotational correlation function. We discuss the temperature dependence of these parameters and note that, in particular, the dynamics is rapidly slowing down at temperature around 220 K, signalling the onset of a structural arrest transition of liquid water into an amorphous solid water.
Dynamics of hydrogen bonds in water and consequences for the unusual behaviour of supercooled water
Indian Academy of Sciences (India)
José Teixeira
2008-10-01
The dynamics of liquid water is evaluated by the coherent quasi-elastic scattering at two different momentum transfers, in order to discriminate hydrogen bond life-time from molecular dynamics. The results indicate a possible issue for the puzzle of the behaviour of supercooled water.
Compressive Deformation Induced Nanocrystallization of a Supercooled Zr-Based Bulk Metallic Glass
Institute of Scientific and Technical Information of China (English)
GUO Xiao-Lin; SHAN De-Bin; MA Ming-Zhen; GUO Bin
2008-01-01
The nanocrystallization behaviour of a bulk Zr-based metallic glass subjected to compressive stress is investigated in the supercooled liquid region. Compared with annealing treatments without compressive stress, compressive deformation promotes the development of nucleation and suppresses the coarsening of nanocrystallites at high ternperatures.
Quantum Markov fields on graphs
2009-01-01
We introduce generalized quantum Markov states and generalized d-Markov chains which extend the notion quantum Markov chains on spin systems to that on $C^*$-algebras defined by general graphs. As examples of generalized d-Markov chains, we construct the entangled Markov fields on tree graphs. The concrete examples of generalized d-Markov chains on Cayley trees are also investigated.
Institute of Scientific and Technical Information of China (English)
周丽丽; 刘让苏; 田泽安; 刘海蓉; 侯兆阳; 朱轩民; 刘全慧
2011-01-01
The formation and evolution characteristics of bcc phase during the isothermal relaxation processes for supercooled-liquid and amorphous Pb were investigated by molecular dynamics simulation and cluster-type index method (CTIM). It is found that during the relaxation process,the formation and evolution of bcc phase are closely dependent on the initial temperature and structure.During the simulation time scale,when the initial temperature is in the range of supercooled liquid region,the bcc phase can be formed and kept a long time; while it is in the range of glassy region,the bcc phase can be formed at first and then partially transformed into hcp phase; when it decreases to the lower one,the hcp and fcc phases can be directly transformed from the glassy structure without undergoing the metastable bcc phase. The Ostwald's "step rule" is impactful during the isothermal relaxation process of the supercooled and glassy Pb,and the metastable bcc phase plays an important role in the precursor of crystallization.%采用分子动力学模拟方法和团簇类型指数法,对过冷液态和非晶态金属Pb在等温驰豫过程中bcc相的形成和演变特性进行研究.结果表明:bcc相的形成和演变密切依赖等温驰豫过程的初始温度和初始结构,在过冷液态区,bcc相很容易形成并在模拟时间范围内保持稳定;而在非晶态区,bcc相先形成并随后部分转变为hcp相,当驰豫的初始温度在较低的153 K和113 K时,hcp和fcc相不经历亚稳bcc相而直接在非晶态结构中形成;这说明Ostwald的"步进原则"在过冷液态和非晶态Pb等温驰豫过程中是有效的,并且,亚稳bcc相起到重要的晶化前驱的作用.
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 suffer from phase separation which is the phenomenon where anhydrous salt settles to the bottom over time. This happens especially in supercooled state. The heat released from the crystallization of supercooled sodium acetate trihydrate with phase separation will be lower than the heat released from...... sodium acetate trihydrate without phase separation. Possible ways of avoiding or reducing the problem of phase separation were investigated. A wide variety of composites of sodium acetate trihydrate with additives including extra water, thickening agents, solid and liquid polymers have been...
Markov stochasticity coordinates
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.
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.
Thermodynamics and dynamics of supercooled water
Mazza, Marco G.
This thesis employs methods of statistical mechanics and numerical simulations to study some aspects of the thermodynamic and dynamic behavior of liquid water. As liquid water is cooled down into the supercooled state, some regions of the sample show correlated molecular motion. Previously, only the translational motion has been the object of investigation. Given the importance of orientational dynamics for water, a question that naturally arises is whether the rotational molecular motion also shows heterogeneous dynamics. We show that the most rotationally mobile molecules tend to form clusters, "rotational heterogeneities", and we study their dependence upon observation time and temperature. Further, we show evidence that molecules belonging to dynamic heterogeneities are involved in bifurcated bonds. Since the presence of dynamic heterogeneities is increasingly important as the temperature is lowered, one would expect a signature of this phenomenon in dynamical quantities. We study the effect of dynamic heterogeneities on the origin of the breakdown of the Stokes--- Einstein and Stokes---Einstein---Debye relations for water. These relations link the diffusivity to temperature and viscosity. We study the separation of time scales of dynamic heterogeneities and the diffusive regime. We also consider different sets of mobility, slowest and fastest, for both translational and rotational heterogeneities. A long-standing problem in biology is the seemingly universal loss of biological activity of all biomolecules, a phenomenon termed the "protein glass transition". We explore the connection between the hypothesized liquid-liquid phase transition of water, and the protein glass transition. We find that the protein glass transition coincides with the crossing of the Widom line of hydration water. Many different scenarios have been proposed to rationalize water's thermodynamic anomalies. We study a tell model for water using the Wolff' cluster algorithm, which permits
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......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...... of pure enantiomers and their 50–50 equimolar mixture in the metastable supercooled liquid state. Crystallization kinetic studies revealed that at the same isochronal conditions the behavior of the S-enantiomer and R,S-racemic mixture of ketoprofen is entirely different. This was examined in the context...
Partridge, D.G.; Vrugt, J.A.; Tunved, P.; Ekman, A.M.L.; Struthers, H.; Sooroshian, A.
2012-01-01
This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov chain Monte Carlo (MCMC) algorithm to an adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools t
Fragile-to-strong crossover in supercooled water: A comparison between TIP4P and TIP4P/2005 models
De Marzio, M.; Camisasca, G.; Rovere, M.; Gallo, P.
2016-05-01
We present recent simulation results on the dynamics of supercooled water with the TIP4P/2005 potential. We find that the dynamical behaviour of the translational motion of the molecules is well interpreted in terms of the Mode Coupling Theory, as it was found for supercooled TIP4P water. We compare the results of the two models and in particular we find also in TIP4P/2005 a crossover from a fragile to a strong regime. We connect this crossover to the crossing of the Widom line emanating from the liquid-liquid critical point.
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
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....
Abdulla, Parosh Aziz; 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 particular, this holds for probabilistic lossy channel systems (PLCS). Furthermore, all globally coarse Markov chains are decisive. This class includes probabilistic vector addition systems (PVASS) and probabilistic noisy Turing machines (PNTM). We consider both safety and liveness problems for decisive Markov chains, i.e., the probabilities that a given set of states F is eventually reached or reached infinitely often, respectively. 1. We express the qualitative problems in abstract terms for decisive Markov chains, and show...
Ristad, E S; Ristad, Eric Sven; Thomas, Robert G.
1996-01-01
A statistical language model assigns probability to strings of arbitrary length. Unfortunately, it is not possible to gather reliable statistics on strings of arbitrary length from a finite corpus. Therefore, a statistical language model must decide that each symbol in a string depends on at most a small, finite number of other symbols in the string. In this report we propose a new way to model conditional independence in Markov models. The central feature of our nonuniform Markov model is that it makes predictions of varying lengths using contexts of varying lengths. Experiments on the Wall Street Journal reveal that the nonuniform model performs slightly better than the classic interpolated Markov model. This result is somewhat remarkable because both models contain identical numbers of parameters whose values are estimated in a similar manner. The only difference between the two models is how they combine the statistics of longer and shorter strings. Keywords: nonuniform Markov model, interpolated Markov m...
Gonzalez-Lopez, Jesus E Garcia Veronica A
2010-01-01
In this work we introduce a new and richer class of finite order Markov chain models and address the following model selection problem: find the Markov model with the minimal set of parameters (minimal Markov model) which is necessary to represent a source as a Markov chain of finite order. Let us call $M$ the order of the chain and $A$ the finite alphabet, to determine the minimal Markov model, we define an equivalence relation on the state space $A^{M}$, such that all the sequences of size $M$ with the same transition probabilities are put in the same category. In this way we have one set of $(|A|-1)$ transition probabilities for each category, obtaining a model with a minimal number of parameters. We show that the model can be selected consistently using the Bayesian information criterion.
Dynamics of deeply supercooled interfacial water.
Swenson, Jan; Cerveny, Silvina
2015-01-28
In this review we discuss the relaxation dynamics of glassy and deeply supercooled water in different types of systems. We compare the dynamics of such interfacial water in ordinary aqueous solutions, hard confinements and biological soft materials. In all these types of systems the dielectric relaxation time of the main water process exhibits a dynamic crossover from a high-temperature non-Arrhenius temperature dependence to a low-temperature Arrhenius behavior. Moreover, at large enough water content the low-temperature process is universal and exhibits the same temperature behavior in all types of systems. However, the physical nature of the dynamic crossover is somewhat different for the different types of systems. In ordinary aqueous solutions it is not even a proper dynamic crossover, since the water relaxation decouples from the cooperative α-relaxation of the solution slightly above the glass transition in the same way as all secondary (β) relaxations of glass-forming materials. In hard confinements, the physical origin of the dynamic crossover is not fully clear, but it seems to occur when the cooperative main relaxation of water at high temperatures reaches a temperature where the volume required for its cooperative motion exceeds the size of the geometrically-confined water cluster. Due to this confinement effect the α-like main relaxation of the confined water seems to transform to a more local β-relaxation with decreasing temperature. Since this low-temperature β-relaxation is universal for all systems at high water content it is possible that it can be considered as an intrinsic β-relaxation of supercooled water, including supercooled bulk water. This possibility, together with other findings for deeply supercooled interfacial water, suggests that the most accepted relaxation scenarios for supercooled bulk water have to be altered.
Solidification of supercooled water in the vicinity of a solid wall
Schremb, Markus; Tropea, Cameron
2016-11-01
An experimental approach utilizing a Hele-Shaw cell for the investigation of the solidification of a supercooled liquid in contact with a solid wall is presented. The setup is based on an idea presented by Marín et al. [A. G. Marín et al., Phys. Rev. Lett. 113, 054301 (2014), 10.1103/PhysRevLett.113.054301], who investigated the planar freezing of a sessile drop without supercooling. This apparatus overcomes optical distortions present when observing the freezing of sessile drops, arising due to reflections and refraction of light on the drop surface. The facility is used to investigate the freezing process of water drops, supercooled down to -20∘C , and to qualitatively demonstrate that the growth behavior is uninfluenced by the use of the Hele-Shaw cell. Different features during freezing, which are known for sessile water drops, are also observed with the Hele-Shaw cell. The growth morphology within the first phase of solidification is categorized according to the initial drop supercooling. Furthermore, freezing velocities within this phase are related to data available in the literature for the growth of single ice dendrites.
Metastable Demixing of Supercooled Cu-Co and Cu-Fe Alloys in an Oxide Flux
Li, D.; Robinson, M. B.; Rathz, T. J.; Williams, G.
1998-01-01
A systematic study on the liquid separation in supercooled Cu-Co and Cu-Fe alloys was performed using a melt fluxing which permits high supercooling to be achieved. Moreover, this method renders it possible to directly measure binodal temperatures and establish metastable liquid miscibility gap (LMG). All phase-separated samples at compositions ranging from 10 to 80 wt pct Co or to 83 wt pct Fe were found to exhibit droplet-shaped morphologies, in spite of various droplet distributions. Uniformly dispersed microstructures were obtained as the minority component was less than 20 vol.%; while beyond this percentage, serious coarsening was brought about. Calculations of the miscibility gap in the Cu-Co system and Stokes movement velocity of Co and Fe droplets in Cu matrix were made to analyze the experimental results.
Fuzzy Markov chains: uncertain probabilities
2002-01-01
We consider finite Markov chains where there are uncertainties in some of the transition probabilities. These uncertainties are modeled by fuzzy numbers. Using a restricted fuzzy matrix multiplication we investigate the properties of regular, and absorbing, fuzzy Markov chains and show that the basic properties of these classical Markov chains generalize to fuzzy Markov chains.
Massey, J. L.
1975-01-01
A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.
Massey, J. L.
1975-01-01
A regular Markov source is defined as the output of a deterministic, but noisy, channel driven by the state sequence of a regular finite-state Markov chain. The rate of such a source is the per letter uncertainty of its digits. The well-known result that the rate of a unifilar regular Markov source is easily calculable is demonstrated, where unifilarity means that the present state of the Markov chain and the next output of the deterministic channel uniquely determine the next state. At present, there is no known method to calculate the rate of a nonunifilar source. Two tentative approaches to this unsolved problem are given, namely source identical twins and the master-slave source, which appear to shed some light on the question of rate calculation for a nonunifilar source.
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.
Buhariwalla, Connor R C; Bowles, Richard K; Saika-Voivod, Ivan; Sciortino, Francesco; Poole, Peter H
2015-05-01
The ST2 interaction potential has been used in a large number of simulation studies to explore the possibility of a liquid-liquid phase transition (LLPT) in supercooled water. Using umbrella sampling Monte Carlo simulations of ST2 water, we evaluate the free energy of formation of small ice nuclei in the supercooled liquid in the vicinity of the Widom line, the region above the critical temperature of the LLPT where a number of thermodynamic anomalies occur. Our results show that in this region there is a substantial free-energy cost for the formation of small ice nuclei, demonstrating that the thermodynamic anomalies associated with the Widom line in ST2 water occur in a well-defined metastable liquid phase. On passing through the Widom line, we identify changes in the free energy to form small ice nuclei that illustrate how the thermodynamic anomalies associated with the LLPT may influence the ice nucleation process.
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…
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.
Biddle, John W.; Singh, Rakesh S.; Sparano, Evan M.; Ricci, Francesco; González, Miguel A.; Valeriani, Chantal; Abascal, José L. F.; Debenedetti, Pablo G.; Anisimov, Mikhail A.; Caupin, Frédéric
2017-01-01
One of the most promising frameworks for understanding the anomalies of cold and supercooled water postulates the existence of two competing, interconvertible local structures. If the non-ideality in the Gibbs energy of mixing overcomes the ideal entropy of mixing of these two structures, a liquid-liquid phase transition, terminated at a liquid-liquid critical point, is predicted. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data for metastable, deeply supercooled water and simulations of molecular water models. However, existing TSEOSs were not designed to describe the negative pressure region and do not account for the stability limit of the liquid state with respect to the vapor. While experimental data on supercooled water at negative pressures may shed additional light on the source of the anomalies of water, such data are very limited. To fill this gap, we have analyzed simulation results for TIP4P/2005, one of the most accurate classical water models available. We have used recently published simulation data, and performed additional simulations, over a broad range of positive and negative pressures, from ambient temperature to deeply supercooled conditions. We show that, by explicitly incorporating the liquid-vapor spinodal into a TSEOS, we are able to match the simulation data for TIP4P/2005 with remarkable accuracy. In particular, this equation of state quantitatively reproduces the lines of extrema in density, isothermal compressibility, and isobaric heat capacity. Contrary to an explanation of the thermodynamic anomalies of water based on a "retracing spinodal," the liquid-vapor spinodal in the present TSEOS continues monotonically to lower pressures upon cooling, influencing but not giving rise to density extrema and other thermodynamic anomalies.
Thermodynamic scaling of molecular dynamics in supercooled ibuprofen.
Adrjanowicz, K; Wojnarowska, Z; Paluch, M; Pionteck, J
2011-04-28
It was shown recently that ibuprofen revealed a strong tendency to form hydrogen bonded aggregates such as dimers and trimers of either cyclic or linear geometry, which somehow seems to control molecular mobility of that drug [Brás et al. J. Phys. Chem. B2008, 112 (35), 11 087-11 099]. For such hydrogen-bonded liquids, superpositioning of dynamics under various temperature T, pressure P, and volume V conditions, when plotted versus the scaling function of T(-1)V(-γ) (where γ is a material constant), may not always be satisfying. In the present work, we have tested the validity of this scaling for supercooled ibuprofen. In order to do that, pressure-volume-temperature (PVT) measurements combined with isobaric and isothermal dielectric relaxation studies (pressure up to 310 MPa) were carried out. The scaling properties of the examined drug were derived from the fitting of the τ(α)(T,V) dependences to the modified Avramov equation and by analyzing in double logarithmic scale the T(g)(V(g)) dependences, where the glass transition temperature T(g) and volume V(g) were defined for various relaxation times. In view of the obtained results, we conjecture that for ibuprofen the thermodynamic scaling idea works but not perfectly. The slight departure from the scaling behavior is discussed in the context of the hydrogen bonding abilities of the examined system and compared with the results reported for other strongly associated liquids.
Directory of Open Access Journals (Sweden)
D. G. Partridge
2012-03-01
Full Text Available This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov chain Monte Carlo (MCMC algorithm to an adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools to investigate the global sensitivity of a cloud model to input aerosol physiochemical parameters. Using numerically generated cloud droplet number concentration (CDNC distributions (i.e. synthetic data as cloud observations, this inverse modelling framework is shown to successfully estimate the correct calibration parameters, and their underlying posterior probability distribution.
The employed analysis method provides a new, integrative framework to evaluate the global sensitivity of the derived CDNC distribution to the input parameters describing the lognormal properties of the accumulation mode aerosol and the particle chemistry. To a large extent, results from prior studies are confirmed, but the present study also provides some additional insights. There is a transition in relative sensitivity from very clean marine Arctic conditions where the lognormal aerosol parameters representing the accumulation mode aerosol number concentration and mean radius and are found to be most important for determining the CDNC distribution to very polluted continental environments (aerosol concentration in the accumulation mode >1000 cm^{−3} where particle chemistry is more important than both number concentration and size of the accumulation mode.
The competition and compensation between the cloud model input parameters illustrates that if the soluble mass fraction is reduced, the aerosol number concentration, geometric standard deviation and mean radius of the accumulation mode must increase in order to achieve the same CDNC distribution.
This study demonstrates that inverse modelling provides a flexible, transparent and
On Markov Chains and Filtrations
1997-01-01
In this paper we rederive some well known results for continuous time Markov processes that live on a finite state space.Martingale techniques are used throughout the paper. Special attention is paid to the construction of a continuous timeMarkov process, when we start from a discrete time Markov chain. The Markov property here holds with respect tofiltrations that need not be minimal.
A new Markov Binomial distribution
Leda D. Minkova; Omey, Edward
2011-01-01
In this paper, we introduce a two state homogeneous Markov chain and define a geometric distribution related to this Markov chain. We define also the negative binomial distribution similar to the classical case and call it NB related to interrupted Markov chain. The new binomial distribution is related to the interrupted Markov chain. Some characterization properties of the Geometric distributions are given. Recursion formulas and probability mass functions for the NB distribution and the new...
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
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 wher...
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...
Smith, R. M.
1991-01-01
Numerous applications in the area of computer system analysis can be effectively studied with Markov reward models. These models describe the behavior of the system with a continuous-time Markov chain, where a reward rate is associated with each state. In a reliability/availability model, upstates may have reward rate 1 and down states may have reward rate zero associated with them. In a queueing model, the number of jobs of certain type in a given state may be the reward rate attached to that state. In a combined model of performance and reliability, the reward rate of a state may be the computational capacity, or a related performance measure. Expected steady-state reward rate and expected instantaneous reward rate are clearly useful measures of the Markov reward model. More generally, the distribution of accumulated reward or time-averaged reward over a finite time interval may be determined from the solution of the Markov reward model. This information is of great practical significance in situations where the workload can be well characterized (deterministically, or by continuous functions e.g., distributions). The design process in the development of a computer system is an expensive and long term endeavor. For aerospace applications the reliability of the computer system is essential, as is the ability to complete critical workloads in a well defined real time interval. Consequently, effective modeling of such systems must take into account both performance and reliability. This fact motivates our use of Markov reward models to aid in the development and evaluation of fault tolerant computer systems.
Directory of Open Access Journals (Sweden)
D. G. Partridge
2011-07-01
Full Text Available This paper presents a novel approach to investigate cloud-aerosol interactions by coupling a Markov Chain Monte Carlo (MCMC algorithm to a pseudo-adiabatic cloud parcel model. Despite the number of numerical cloud-aerosol sensitivity studies previously conducted few have used statistical analysis tools to investigate the sensitivity of a cloud model to input aerosol physiochemical parameters. Using synthetic data as observed values of cloud droplet number concentration (CDNC distribution, this inverse modelling framework is shown to successfully converge to the correct calibration parameters.
The employed analysis method provides a new, integrative framework to evaluate the sensitivity of the derived CDNC distribution to the input parameters describing the lognormal properties of the accumulation mode and the particle chemistry. To a large extent, results from prior studies are confirmed, but the present study also provides some additional insightful findings. There is a clear transition from very clean marine Arctic conditions where the aerosol parameters representing the mean radius and geometric standard deviation of the accumulation mode are found to be most important for determining the CDNC distribution to very polluted continental environments (aerosol concentration in the accumulation mode >1000 cm^{−3} where particle chemistry is more important than both number concentration and size of the accumulation mode.
The competition and compensation between the cloud model input parameters illustrate that if the soluble mass fraction is reduced, both the number of particles and geometric standard deviation must increase and the mean radius of the accumulation mode must increase in order to achieve the same CDNC distribution.
For more polluted aerosol conditions, with a reduction in soluble mass fraction the parameter correlation becomes weaker and more non-linear over the range of possible solutions
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...
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. We then moved on to investigate the basic proper...
Simulation study of water and sugar dynamics in supercooled mixtures
Molinero, Valeria; Cagin, Tahir; Goddard, William A.
2003-03-01
Water dynamics in concentrated carbohydrate solutions is of utmost importance in food and pharmaceutical technology, where low water mobility is desirable to slow down chemical degradation and preserve biomolecules. We have studied the microscopic mechanism of water diffusion in binary and polydisperse malto-oligosaccharides and water mixtures by means of molecular dynamics simulations. The computations were performed with a coarse grain model (M3B), derived from atomistic simulations of water and malto-oligosaccharides. The use of the M3B model permits simulations of the order of 0.1 microsecond, thus allowing us to explore water dynamics from the liquid to the deep supercooled regime. The dynamics of water confined in the sugar matrix is slowed down with respect to bulk water. We found that at low moisture content and low temperature, ranslational diffusion of water and glucose rotation proceed through a hopping-diffusion mechanism. Moreover, we found water mobility to be heterogeneous: there is a broad distribution of time scales for different water molecules in the mixtures. We discuss whether there is a relationship between the heterogeneous structure of these mixtures in the sub-nanometer scale and the heterogeneous dynamics of water molecules.
Krnc, Katja
2014-01-01
The diploma thesis presents two interesting thermodynamic experiments which were executed and described by Joseph Black in 18th Century. These are: depression of the freezing point of water with salt and supercooled water. We meet water in three states of matter in nature: in the state of ice, liquid water, and water steam. Phase crossing from water to ice (and vice versa from ice to water) is done with normal air pressure with the state temperature of 0°C. If we add certain matters to wat...
Energy Technology Data Exchange (ETDEWEB)
Ueno, K; Farzaneh, M [NSERC/Hydro-Quebec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) and Canada Research Chair on Engineering of Power Network Atmospheric Icing (INGIVRE), Universite du Quebec a Chicoutimi, 555 Boulevard de l' Universite, Chicoutimi, Quebec, G7H 2B1 (Canada); Yamaguchi, S [Snow and Ice Research Center, National Research Institute for Earth Science and Disaster Prevention, Nagaoka, 940-0821 (Japan); Tsuji, H [Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, 816-8580 (Japan)], E-mail: kazuto.ueno@uqac.ca
2010-04-15
Little is known about morphological instability of a solidification front during the crystal growth of a thin film of flowing supercooled liquid with a free surface: for example, the ring-like ripples on the surface of icicles. The length scale of the ripples is nearly 1 cm. Two theoretical models for the ripple formation mechanism have been proposed. However, these models lead to quite different results because of differences in the boundary conditions at the solid-liquid interface and liquid-air surface. The validity of the assumption used in the two models is numerically investigated and some of the theoretical predictions are compared with experiments.
Adrjanowicz, K; Kaminski, K; Wlodarczyk, P; Grzybowska, K; Tarnacka, M; Zakowiecki, D; Garbacz, G; Paluch, M; Jurga, S
2013-10-07
This paper presents comprehensive studies on the molecular dynamics of a pharmaceutically important substance, posaconazole. In order to characterize relaxation dynamics in the supercooled liquid and glassy states, dielectric and mechanical spectroscopies were applied. Dielectric data have indicated multiple relaxation processes that appear above and below the glass transition temperature Tg (τα=100 s) of posaconazole. From the curvature of the dielectric log10(τα) versus inverse of temperature dependence, we determine so-called "fragility", being a very popular parameter for classifying the structural dynamics of supercooled liquids and polymers. From the calculations, we get m=150, which means that is one of the most fragile glass-forming liquids. In this paper, the relaxation dynamics of supercooled posaconazole extracted from the dielectric response function was also confronted with shear-mechanical relaxation. Finally, we have also presented a direct comparison of the fragility and the number of dynamically correlated molecules Nc determined from dynamic calorimetry curves and dielectric and mechanical spectroscopies, showing a clear deviation in the picture of glass-transition dynamics generated by calorimetric and spectroscopic techniques.
Institute of Scientific and Technical Information of China (English)
Xiaoyun MO; Jieming ZHOU; Hui OU; Xiangqun YANG
2013-01-01
Given a new Double-Markov risk model DM =(μ,Q,v,H; Y,Z) and Double-Markov risk process U ={U(t),t ≥ 0}.The ruin or survival problem is addressed.Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained.Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained.The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.
Enhanced small-angle scattering connected to the Widom line in simulations of supercooled water.
Wikfeldt, K T; Huang, C; Nilsson, A; Pettersson, L G M
2011-06-07
We present extensive simulations on the TIP4P∕2005 water model showing significantly enhanced small-angle scattering (SAS) in the supercooled regime. The SAS is related to the presence of a Widom line (T(W)) characterized by maxima in thermodynamic response functions and Ornstein-Zernike correlation length. Recent experimental small-angle x-ray scattering data [Huang et al., J. Chem. Phys. 133, 134504 (2010)] are excellently reproduced, albeit with an increasing temperature offset at lower temperatures. Assuming the same origin of the SAS in experiment and model this suggests the existence of a Widom line also in real supercooled water. Simulations performed at 1000 bar show an increased abruptness of a crossover from dominating high-density (HDL) to dominating low-density (LDL) liquid and strongly enhanced SAS associated with crossing T(W), consistent with a recent determination of the critical pressure of TIP4P∕2005 at 1350 bar. Furthermore, good agreement with experimental isothermal compressibilities at 1000, 1500, and 2000 bar shows that the high pressure supercooled thermodynamic behavior of water is well described by TIP4P∕2005. Analysis of the tetrahedrality parameter Q reveals that the HDL-LDL structural transition is very sharp at 1000 bar, and that structural fluctuations become strongly coupled to density fluctuations upon approaching T(W). Furthermore, the tetrahedrality distribution becomes bimodal at ambient temperatures, an observation that possibly provides a link between HDL-LDL fluctuations and the structural bimodality in liquid water indicated by x-ray spectroscopic techniques. Computed x-ray absorption spectra are indeed found to show sensitivity to the tetrahedrality parameter.
Spectral Analysis of Markov Chains
2007-01-01
The paper deals with the problem of a statistical analysis of Markov chains connected with the spectral density. We present the expressions for the function of spectral density. These expressions may be used to estimate the parameter of the Markov chain.
Model Checking Interactive Markov Chains
Neuhausser, M.; Zhang, Lijun; Esparza, J.; Majumdar, R.
2010-01-01
Hermanns has introduced interactive Markov chains (IMCs) which arise as an orthogonal extension of labelled transition systems and continuous-time Markov chains (CTMCs). IMCs enjoy nice compositional aggregation properties which help to minimize the state space incrementally. However, the model chec
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.
Growth rate of crystalline ice and the diffusivity of supercooled water from 126 to 262 K
Energy Technology Data Exchange (ETDEWEB)
Xu, Yuntao; Petrik, Nikolay G.; Smith, R. Scott; Kay, Bruce D.; Kimmel, Greg A.
2016-12-12
Understanding deeply supercooled water is key to unraveling many of water’s anomalous properties. However, this has proven difficult due to rapid and uncontrolled crystallization. Using a pulsed laser heating technique, we measure the growth rate of crystalline ice, G(T), for 180 K < T < 262 K, i.e. deep within water’s “no man’s land.” The self-diffusion of supercooled liquid water, D(T), is obtained from G(T) using the Wilson-Frenkel model of crystal growth. For T > 237 K, G(T) and D(T) have super-Arrhenius (“fragile”) temperature dependences, but both crossover to Arrhenius (“strong”) behavior with a large activation energy in “no man’s land.” The fact that G(T) and D(T) are smoothly varying rules out the hypothesis that liquid water’s properties have a singularity at or near 228 K. However the results are consistent with a previous prediction for D(T) that assumed no thermodynamic transitions occur in “no man’s land.
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.
Supercooled water in austral summer in Prydz Bay,Antarctica
Institute of Scientific and Technical Information of China (English)
SHI Jiuxin; CHENG Yaoyao; JIAO Yutian; HOU Jiaqiang
2011-01-01
Supercooled water with temperatures below freezing point, was identified from hydrographic data obtained by Chinese and Australian expeditions to Prydz Bay, Antarctica, during the austral summer. The study shows that most supercooled waters occurred at depths of 63-271 m in the region north of the Amery Ice Shelf (AIS) front. The maximum supercooling was 0.16℃ below the in-situ freezing point. In temperature and salinity ranges of-2.14 - -1.96℃ and 34.39--34.46, respectively,the water was colder and fresher than peripheral shelf water. The supercooled water had less variability in the vertical profiles compared to shelf water. Based on analysis of their thermohaline features and spatial distribution, as well as the circulation pattern in Prydz Bay, we conclude that these supercooled waters originated from a cavity beneath the AIS and resulted from upwelling just outside of the AIS front. Water emerging from the ice shelf cools to an extremely low temperature (about -2.0℃) by additional cooling from the ice shelf, and becomes buoyant with the addition of melt water from the ice shelf base. When this water flows out of the ice shelf front, its upper boundary is removed, and thus it rises abruptly. Once the temperature of this water reaches below the freezing point, supercooling takes place. In summer, the seasonal pycnocline at ～100 m water depth acts as a barrier to upwelling and supercooling. The upwelling of ice shelf outflow water illuminates a unique mid-depth convection of the polar ocean.
The transient behavior of Peltier junctions pulsed with supercooling
Mao, J. N.; Chen, H. X.; Jia, H.; Qian, X. L.
2012-07-01
There exists the transient thermoelectric supercooling effect that can be enhanced by keeping on increasing the Peltier cooling effect to compensate for the Joule heating effect and Fourier heat conduction effect arriving at the cold junction, in which a transient cold spike can be produced by superimposing an additional shaped current pulse of a large magnitude on the original steady-state optimum value. Most previous work on the transient supercooling mainly focused on the minimum supercooling temperature achievable and separately analyzed the beneficial or detrimental effects on the transient supercooling performance, which was not clarified quantitatively to what extent the interactional effects were on the enhancement of the transient supercooling performance. In this work, we systematically investigate a numerical solution involving time-dependent imposed voltage pulse and time-dependent thermal boundary conditions on the transient supercooling behavior as well as the response of characteristic time and cold-junction temperature distribution to the pulse operation parameters during the periods of pulse start-up, pulse-on time, and pulse-off time, which is served as a theoretical basis for exploiting the coupling interaction of the thermoelectric effects on the heat diffusion from or to the cold junction interrelated with the amount of the availably electrical conversion in the short time scale. Additionally, the advantage of certain pulse forms over others is described. The results indicate that Peltier supercooling capacity shows a decreasing monotonic trend in proportion to the total amount of electrical conversion, and the maximum coefficient of performance for cooling state is about 0.5 to be achieved at steady state. Taking advantage of the temporary Peltier effect focused electrical conversion as the additional cooling for a period long enough against the earlier arrival of the excessively Joule heating dominated heat accumulation is the key parameter
Wetting hysteresis induced by temperature changes: Supercooled water on hydrophobic surfaces.
Heydari, Golrokh; Sedighi Moghaddam, Maziar; Tuominen, Mikko; Fielden, Matthew; Haapanen, Janne; Mäkelä, Jyrki M; Claesson, Per M
2016-04-15
The state and stability of supercooled water on (super)hydrophobic surfaces is crucial for low temperature applications and it will affect anti-icing and de-icing properties. Surface characteristics such as topography and chemistry are expected to affect wetting hysteresis during temperature cycling experiments, and also the freezing delay of supercooled water. We utilized stochastically rough wood surfaces that were further modified to render them hydrophobic or superhydrophobic. Liquid flame spraying (LFS) was utilized to create a multi-scale roughness by depositing titanium dioxide nanoparticles. The coating was subsequently made non-polar by applying a thin plasma polymer layer. As flat reference samples modified silica surfaces with similar chemistries were utilized. With these substrates we test the hypothesis that superhydrophobic surfaces also should retard ice formation. Wetting hysteresis was evaluated using contact angle measurements during a freeze-thaw cycle from room temperature to freezing occurrence at -7°C, and then back to room temperature. Further, the delay in freezing of supercooled water droplets was studied at temperatures of -4°C and -7°C. The hysteresis in contact angle observed during a cooling-heating cycle is found to be small on flat hydrophobic surfaces. However, significant changes in contact angles during a cooling-heating cycle are observed on the rough surfaces, with a higher contact angle observed on cooling compared to during the subsequent heating. Condensation and subsequent frost formation at sub-zero temperatures induce the hysteresis. The freezing delay data show that the flat surface is more efficient in enhancing the freezing delay than the rougher surfaces, which can be rationalized considering heterogeneous nucleation theory. Thus, our data suggests that molecular flat surfaces, rather than rough superhydrophobic surfaces, are beneficial for retarding ice formation under conditions that allow condensation and frost
Water and its relatives: the stable, supercooled and particularly the stretched, regimes
Meadley, Stacey L
2014-01-01
While the water molecule is simple, its condensed phase liquid behavior is so complex that no consensus description has emerged despite three centuries of effort. Here we identify features of its behavior that are the most peculiar, hence suggest ways forward. We examine the properties of water at the boundaries of common experience, including stable states at high pressure, the supercooled state at normal and elevated pressure, and the stretched ("negative pressure") state, out to the limits of mechanical stability. The familiar anomalies at moderate pressures (viscosity and density (TMD) behavior, etc.), are not explained by H-bond breaking, according to common bond-breaking criteria. A comparison of data on the TMD, at both positive and negative pressures, with the predictions of popular pair potential models, shows dramatic discrepancies appearing in the stretched liquid domain. This prompts questions on the second critical point (TC2) hypothesis that has been guiding much current thinking. We turn to rel...
Liquid-liquid phase transition in Stillinger-Weber silicon
Energy Technology Data Exchange (ETDEWEB)
Beaucage, Philippe; Mousseau, Normand [Departement de Physique and Regroupement Quebecois sur les Materiaux de Pointe, Universite de Montreal, CP 6128, Succursale Centre-ville, Montreal, QC, H3C 3J7 (Canada)
2005-04-20
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.
Droplet-Sizing Liquid Water Content Sensor Project
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...
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.
Liquid dynamics in partially crystalline glycerol
DEFF Research Database (Denmark)
Sanz, Alejandro; Niss, Kristine
2017-01-01
We present a dielectric study on the dynamics of supercooled glycerol during crystallization. We explore the transformation into a solid phase in real time by monitoring the temporal evolution of the amplitude of the dielectric signal. Neither the initial nucleation nor the crystal growth......, we have found no evidence that supercooled glycerol transforms into a peculiar phase in which either a new solid amorphous state or nano-crystals dispersed in a liquid matrix are formed....
Markov chain Monte Carlo simulation for Bayesian Hidden Markov Models
Chan, Lay Guat; Ibrahim, Adriana Irawati Nur Binti
2016-10-01
A hidden Markov model (HMM) is a mixture model which has a Markov chain with finite states as its mixing distribution. HMMs have been applied to a variety of fields, such as speech and face recognitions. The main purpose of this study is to investigate the Bayesian approach to HMMs. Using this approach, we can simulate from the parameters' posterior distribution using some Markov chain Monte Carlo (MCMC) sampling methods. HMMs seem to be useful, but there are some limitations. Therefore, by using the Mixture of Dirichlet processes Hidden Markov Model (MDPHMM) based on Yau et. al (2011), we hope to overcome these limitations. We shall conduct a simulation study using MCMC methods to investigate the performance of this model.
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
Ivkovic, Stefan
2015-01-01
In this thesis we will consider Markov operators on cones . More precisely, we let X equipped with certain norm be a real Banach space, K in X be a closed, normal cone with nonempty interior, e in Int (K) be an order unit. A bounded, linear operator T from X into X is a Markov operator w.r.t. K and e if K is invariant under T and e is fixed by T. We consider then the adjoint of T, T* and homogeneous, discrete time Markov system given by u_k+1 = T*(u_k), k = 0,1,2 where u_0(x) is nonnegative f...
Supercooling across first-order phase transitions in vortex matter
Indian Academy of Sciences (India)
P Chaddah; S B Roy
2000-06-01
Hysteresis in cycling through ﬁrst-order phase transitions in vortex matter, akin to the well-studied phenomenon of supercooling of water, has been discussed in literature. Hysteresis can be seen while varying either temperature or magnetic ﬁeld (and thus the density of vortices). Our recent work on phase transitions with two control variables shows that the observable region of metastability of the supercooled phase would depend on the path followed in - space, and will be larger when is lowered at constant compared to the case when is lowered at constant . We discuss the effect of isothermal ﬁeld variations on metastable supercooled states produced by ﬁeld-cooling. This path dependence is not a priori applicable to metastability caused by reduced diffusivity or hindered kinetics.
Compressing redundant information in Markov chains
2006-01-01
Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is hence defined and tested on some classical problems.
Markov Chains and Chemical Processes
Miller, P. J.
1972-01-01
Views as important the relating of abstract ideas of modern mathematics now being taught in the schools to situations encountered in the sciences. Describes use of matrices and Markov chains to study first-order processes. (Author/DF)
Bibliometric Application of Markov Chains.
Pao, Miranda Lee; McCreery, Laurie
1986-01-01
A rudimentary description of Markov Chains is presented in order to introduce its use to describe and to predict authors' movements among subareas of the discipline of ethnomusicology. Other possible applications are suggested. (Author)
Entropy: The Markov Ordering Approach
Directory of Open Access Journals (Sweden)
Alexander N. Gorban
2010-05-01
Full Text Available The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant “additivity” properties: (i existence of a monotonic transformation which makes the functional additive with respect to the joining of independent systems and (ii existence of a monotonic transformation which makes the functional additive with respect to the partitioning of the space of states. All Lyapunov functionals for Markov chains which have properties (i and (ii are derived. We describe the most general ordering of the distribution space, with respect to which all continuous-time Markov processes are monotonic (the Markov order. The solution differs significantly from the ordering given by the inequality of entropy growth. For inference, this approach results in a convex compact set of conditionally “most random” distributions.
Markov processes, semigroups and generators
Kolokoltsov, Vassili N
2011-01-01
This work offers a highly useful, well developed reference on Markov processes, the universal model for random processes and evolutions. The wide range of applications, in exact sciences as well as in other areas like social studies, require a volume that offers a refresher on fundamentals before conveying the Markov processes and examples for applications. This work does just that, and with the necessary mathematical rigor.
Nature of large aggregates in supercooled aqueous solutions of sodium dodecyl sulfate
Energy Technology Data Exchange (ETDEWEB)
Franses, E.I. (Purdue Univ., West Lafayette, IN); Davis, H.T.; Miller, W.G.; Scriven, L.E.
1980-09-18
Preparations of 2.0 and 5.5 wt % sodium dodecyl sulfate (SDS) in 3.5 wt % (0.6 M) aqueous NaCl are equilibrium micellar solutions above 28/sup 0/C, the Krafft point of the surfactant at this salinity. These systems can be supercooled and remain transparent for hours and days. At 25/sup 0/C at equilibrium they are biphasic, a hydrated crystal phase and an aqueous salt solution phase containing only 0.01/sub 2/ wt % SDS. Conductimetry and /sup 13/C NMR show that these transparent supercooled systems are indeed supersaturated solutions and not microdispersions of the hydrated crystal. The time lag for the onset of nucleation of the crystals depends strongly on stirring details and probably on presence of gas-liquid interface. The big nonequilibrium aggregates present in the supersaturated systems resemble micelles in conductivity and molecular motion, and are likely to be metastable micelles as is presumed by Mazer, Benedek, and Carey. 21 references, 6 figures, 1 table.
An airborne microwave radiometer and measurements of cloud liquid water
Institute of Scientific and Technical Information of China (English)
LEI Hengchi; JIN Dezhen; WEI Chong; SHEN Zhilai
2003-01-01
A single-channel (9.5 mm) airborne microwave radiometer with one antenna is developed. The retrieval methods and primary observation results of cloud liquid water and super-cooled cloud liquid water are discussed. The aircraft experiments show that the cloud liquid water and super-cooled liquid water can be sensitively monitored at some level of accuracy by the radiometer. The results of cloud liquid water content are reasonable and correspond well with the surface radar echo intensity. The design of the airborne radiometer and its retrieval methods are feasible, giving it application value.
On Markov parameters in system identification
Phan, Minh; Juang, Jer-Nan; Longman, Richard W.
1991-01-01
A detailed discussion of Markov parameters in system identification is given. Different forms of input-output representation of linear discrete-time systems are reviewed and discussed. Interpretation of sampled response data as Markov parameters is presented. Relations between the state-space model and particular linear difference models via the Markov parameters are formulated. A generalization of Markov parameters to observer and Kalman filter Markov parameters for system identification is explained. These extended Markov parameters play an important role in providing not only a state-space realization, but also an observer/Kalman filter for the system of interest.
Discrimination of micrometre-sized ice and super-cooled droplets in mixed-phase cloud
Hirst, E.; Kaye, P. H.; Greenaway, R. S.; Field, P.; Johnson, D. W.
Preliminary experimental results are presented from an aircraft-mounted probe designed to provide in situ data on cloud particle shape, size, and number concentration. In particular, the probe has been designed to facilitate discrimination between super-cooled water droplets and ice crystals of 1-25 μm size within mixed-phase clouds and to provide information on cloud interstitial aerosols. The probe acquires spatial light scattering data from individual particles at throughput rates of several thousand particles per second. These data are logged at 100 ms intervals to allow the distribution and number concentration of each particle type to be determined with 10 m spatial resolution at a typical airspeed of 100 m s -1. Preliminary results from flight data recorded in altocumulus castellanus, showing liquid water phase, mixed phase, and ice phase are presented to illustrate the probe's particle discrimination capabilities.
Directory of Open Access Journals (Sweden)
T. Kuhn
2009-10-01
Full Text Available We investigated the relative roles of volume and surface nucleation in the freezing of water droplets. Nucleation experiments were carried out in a cryogenic laminar aerosol flow tube using supercooled liquid water aerosols with radii between about 1 and 3 μ m. Temperature- and size-dependent values of volume- and surface-based homogeneous nucleation rate between 234.8 and 236.2 K are derived with help of a microphysical model from aerosol compositions and size distributions based on infrared extinction measurements in the aerosol flow tube. The results show that the contribution from nucleation at the droplet surface increases with decreasing droplet radius and dominates over nucleation in the bulk droplet volume for droplets with radii smaller than approximately 5 μm. This is interpreted in terms of a lowered free energy of ice germ formation in the surface-based process and has implications for the parameterization of homogeneous ice nucleation in numerical models.
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...
Effects of atmospheric dynamics and aerosols on the fraction of supercooled water clouds
Li, Jiming; Lv, Qiaoyi; Zhang, Min; Wang, Tianhe; Kawamoto, Kazuaki; Chen, Siyu; Zhang, Beidou
2017-02-01
Based on 8 years of (January 2008-December 2015) cloud phase information from the GCM-Oriented Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) Cloud Product (GOCCP), aerosol products from CALIPSO and meteorological parameters from the ERA-Interim products, the present study investigates the effects of atmospheric dynamics on the supercooled liquid cloud fraction (SCF) during nighttime under different aerosol loadings at global scale to better understand the conditions of supercooled liquid water gradually transforming to ice phase. Statistical results indicate that aerosols' effect on nucleation cannot fully explain all SCF changes, especially in those regions where aerosols' effect on nucleation is not a first-order influence (e.g., due to low ice nuclei aerosol frequency). By performing the temporal and spatial correlations between SCFs and different meteorological factors, this study presents specifically the relationship between SCF and different meteorological parameters under different aerosol loadings on a global scale. We find that the SCFs almost decrease with increasing of aerosol loading, and the SCF variation is closely related to the meteorological parameters but their temporal relationship is not stable and varies with the different regions, seasons and isotherm levels. Obviously negative temporal correlations between SCFs versus vertical velocity and relative humidity indicate that the higher vertical velocity and relative humidity the smaller SCFs. However, the patterns of temporal correlation for lower-tropospheric static stability, skin temperature and horizontal wind are relatively more complex than those of vertical velocity and humidity. For example, their close correlations are predominantly located in middle and high latitudes and vary with latitude or surface type. Although these statistical correlations have not been used to establish a certain causal relationship, our results may provide a unique point of view
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
Markov Random Field Surface Reconstruction
DEFF Research Database (Denmark)
Paulsen, Rasmus Reinhold; Bærentzen, Jakob Andreas; Larsen, Rasmus
2010-01-01
) and knowledge about data (the observation model) in an orthogonal fashion. Local models that account for both scene-specific knowledge and physical properties of the scanning device are described. Furthermore, how the optimal distance field can be computed is demonstrated using conjugate gradients, sparse......A method for implicit surface reconstruction is proposed. The novelty in this paper is the adaption of Markov Random Field regularization of a distance field. The Markov Random Field formulation allows us to integrate both knowledge about the type of surface we wish to reconstruct (the prior...
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
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.
On a Result for Finite Markov Chains
Kulathinal, Sangita; Ghosh, Lagnojita
2006-01-01
In an undergraduate course on stochastic processes, Markov chains are discussed in great detail. Textbooks on stochastic processes provide interesting properties of finite Markov chains. This note discusses one such property regarding the number of steps in which a state is reachable or accessible from another state in a finite Markov chain with M…
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...
Confluence reduction for Markov automata
Timmer, Mark; Pol, van de Jaco; Stoelinga, Mariëlle
2013-01-01
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 gener
Relative survival multistate Markov model.
Huszti, Ella; Abrahamowicz, Michal; Alioum, Ahmadou; Binquet, Christine; Quantin, Catherine
2012-02-10
Prognostic studies often have to deal with two important challenges: (i) separating effects of predictions on different 'competing' events and (ii) uncertainty about cause of death. Multistate Markov models permit multivariable analyses of competing risks of, for example, mortality versus disease recurrence. On the other hand, relative survival methods help estimate disease-specific mortality risks even in the absence of data on causes of death. In this paper, we propose a new Markov relative survival (MRS) model that attempts to combine these two methodologies. Our MRS model extends the existing multistate Markov piecewise constant intensities model to relative survival modeling. The intensity of transitions leading to death in the MRS model is modeled as the sum of an estimable excess hazard of mortality from the disease of interest and an 'offset' defined as the expected hazard of all-cause 'natural' mortality obtained from relevant life-tables. We evaluate the new MRS model through simulations, with a design based on registry-based prognostic studies of colon cancer. Simulation results show almost unbiased estimates of prognostic factor effects for the MRS model. We also applied the new MRS model to reassess the role of prognostic factors for mortality in a study of colorectal cancer. The MRS model considerably reduces the bias observed with the conventional Markov model that does not permit accounting for unknown causes of death, especially if the 'true' effects of a prognostic factor on the two types of mortality differ substantially.
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...
Volume analysis of supercooled water under high pressure
Duki, Solomon F.; Tsige, Mesfin
2016-01-01
Motivated by recent experimental findings on the volume of supercooled water at high pressure [O. Mishima, J. Chem. Phys. 133, 144503 (2010)] we performed atomistic molecular dynamics simulations study of bulk water in the isothermal-isobaric ensemble. Cooling and heating cycles at different isobars and isothermal compression at different temperatures are performed on the water sample with pressures that range from 0 to 1.0 GPa. The cooling simulations are done at temperatures that range from...
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)
Directory of Open Access Journals (Sweden)
J. Crosier
2010-08-01
°C level together with liquid water droplets and a few rimed ice particles, (3 Columns were larger and increasingly rimed at colder temperatures. Calculated ice splinter production rates are consistent with observed concentrations if the condition that only droplets greater than 24 μm are capable of generating secondary ice splinters is relaxed.
This case demonstrates the importance of understanding the formation of ice at slightly supercooled temperatures, as it can lead to secondary ice production and the formation of precipitation in clouds which may not otherwise be considered as significant precipitation sources.
Hierarchical Non-Emitting Markov Models
Ristad, E S; Ristad, Eric Sven; Thomas, Robert G.
1998-01-01
We describe a simple variant of the interpolated Markov model with non-emitting state transitions and prove that it is strictly more powerful than any Markov model. More importantly, the non-emitting model outperforms the classic interpolated model on the natural language texts under a wide range of experimental conditions, with only a modest increase in computational requirements. The non-emitting model is also much less prone to overfitting. Keywords: Markov model, interpolated Markov model, hidden Markov model, mixture modeling, non-emitting state transitions, state-conditional interpolation, statistical language model, discrete time series, Brown corpus, Wall Street Journal.
Directory of Open Access Journals (Sweden)
Renato Cesar Sato
2010-09-01
Full Text Available Markov Chains provide support for problems involving decision on uncertainties through a continuous period of time. The greater availability and access to processing power through computers allow that these models can be used more often to represent clinical structures. Markov models consider the patients in a discrete state of health, and the events represent the transition from one state to another. The possibility of modeling repetitive events and time dependence of probabilities and utilities associated permits a more accurate representation of the evaluated clinical structure. These templates can be used for economic evaluation in health care taking into account the evaluation of costs and clinical outcomes, especially for evaluation of chronic diseases. This article provides a review of the use of modeling within the clinical context and the advantages of the possibility of including time for this type of study.
Markov Chain Ontology Analysis (MCOA)
2012-01-01
Background 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. Results 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. Conclusion 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
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...
NMR evidence of a sharp change in a measure of local order in deeply supercooled confined water.
Mallamace, F; Corsaro, C; Broccio, M; Branca, C; González-Segredo, N; Spooren, J; Chen, S-H; Stanley, H E
2008-09-02
Using NMR, we measure the proton chemical shift delta, of supercooled nanoconfined water in the temperature range 195 K < T < 350 K. Because delta is directly connected to the magnetic shielding tensor, we discuss the data in terms of the local hydrogen bond geometry and order. We argue that the derivative -( partial differential ln delta/ partial differentialT)(P) should behave roughly as the constant pressure specific heat C(P)(T), and we confirm this argument by detailed comparisons with literature values of C(P)(T) in the range 290-370 K. We find that -( partial differential ln delta/ partial differentialT)(P) displays a pronounced maximum upon crossing the locus of maximum correlation length at approximately 240 K, consistent with the liquid-liquid critical point hypothesis for water, which predicts that C(P)(T) displays a maximum on crossing the Widom line.
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. PMID:28112152
Hydrodynamic states in water below the temperature of the density maximum: the limit to supercooling
van der Elsken, J.; van Boom, L.; Bot, A.
1988-01-01
Spectra of fluctuations in the total intensity of laser light deflected by supercooled water show that even under carefully controlled conditions large samples give convection when cooled below -0%. This is in agreement with the Rayleigh versus Prandtlnumber relation for supercooled water.
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
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...
Supercooling of rapidly expanding quark-gluon plasma
Zabrodin, E E; Csernai, László P; Stöcker, H; Greiner, W
1998-01-01
We reexamine the scenario of homogeneous nucleation of the quark-gluon plasma produced in ultra-relativistic heavy ion collisions. A generalization of the standard nucleation theory to rapidly expanding system is proposed. The nucleation rate is derived via the new scaling parameter $\\lambda_Z$. It is shown that the size distribution of hadronic clusters plays an important role in the dynamics of the phase transition. The longitudinally expanding system is supercooled to about 3-6%, then it is reheated, and the hadronization is completed within 6-10 fm/c, i.e. 5-10 times faster than it was estimated earlier, in a strongly nonequilibrium way.
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)
Markov and semi-Markov processes as a failure rate
Grabski, Franciszek
2016-06-01
In this paper the reliability function is defined by the stochastic failure rate process with a non negative and right continuous trajectories. Equations for the conditional reliability functions of an object, under assumption that the failure rate is a semi-Markov process with an at most countable state space are derived. A proper theorem is presented. The linear systems of equations for the appropriate Laplace transforms allow to find the reliability functions for the alternating, the Poisson and the Furry-Yule failure rate processes.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelly; 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 coo
Gallagher, Martin; Baumgardner, Darrel; Lloyd, Gary; Beswick, Karl; Freer, Matt; Durant, Adam
2016-04-01
Hazardous encounters with high ice concentrations that lead to temperature and airspeed sensor measurement errors, as well as engine rollback and flameout, continue to pose serious problems for flight operations of commercial air carriers. Supercooled liquid droplets (SLD) are an additional hazard, especially for smaller commuter aircraft that do not have sufficient power to fly out of heavy icing conditions or heat to remove the ice. New regulations issued by the United States and European regulatory agencies are being implemented that will require aircraft below a certain weight class to carry sensors that will detect and warn of these types of icing conditions. Commercial aircraft do not currently carry standard sensors to detect the presence of ice crystals in high concentrations because they are typical found in sizes that are below the detection range of aircraft weather radar. Likewise, the sensors that are currently used to detect supercooled water do not respond well to drizzle-sized drops. Hence, there is a need for a sensor that can fill this measurement void. In addition, the forecast models that are used to predict regions of icing rely on pilot observations as the only means to validate the model products and currently there are no forecasts for the prevalence of high altitude ice crystals. Backscatter Cloud Probes (BCP) have been flying since 2011 under the IAGOS project on six Airbus commercial airliners operated by Lufthansa, Air France, China Air, Iberia and Cathay Pacific, and measure cloud droplets, ice crystals and aerosol particles larger than 5 μm. The BCP can detect these particles and measures an optical equivalent diameter (OED) but is not able to distinguish the type of particle, i.e. whether they are droplets, ice crystals, dust or ash. However, some qualification can be done based on measured temperature to discriminate between liquid water and ice. The next generation BCP (BCPD, Backscatter Cloud Probe with polarization detection) is
Tan, Xiuwen; Song, Enliang; Liu, Xiaomu; Liu, Guifen; Cheng, Haijian; Wan, Fachun
2012-02-01
The purpose of our study was to investigate the feasibility of using less-concentrated cryoprotectants supplemented with ice blocker Supercool X-1000 to vitrify ovarian tissues. Mouse ovaries were cryopreserved in different concentrations of vitrification solution alone or with Supercool X-1000, and fresh non-frozen ovaries were used as control. The proportions of morphological normality of follicles, normal GCs in follicular fluids and developing to blastocysts were higher in 12.5% ethylene glycol (EG) + 12.5% dimethylsulfoxide (DMSO) with Supercool X-1000 than those of treated in 10% EG + 10% DMSO or 15% EG + 15% DMSO alone or with Supercool X-1000. In conclusion, the inclusion of Supercool X-1000 in less-concentrated vitrification solution was effective to improve the efficiency and efficacy of cryopreservation of ovarian tissues.
Markov process functionals in finance and insurance
Institute of Scientific and Technical Information of China (English)
GENG Xian-min; LI Liang
2009-01-01
The Maxkov property of Maxkov process functionals which axe frequently used in economy, finance, engineering and statistic analysis is studied. The conditions to judge Maxkov property of some important Markov process functionals axe presented, the following conclusions are obtained: the multidimensional process with independent increments is a multidimensional Markov process; the functional in the form of path integral of process with independent incre-ments is a Markov process; the surplus process with the doubly stochastic Poisson process is a vector Markov process. The conditions for linear transformation of vector Maxkov process being still a Maxkov process are given.
Metastability of exponentially perturbed Markov chains
Institute of Scientific and Technical Information of China (English)
陈大岳; 冯建峰; 钱敏平
1996-01-01
A family of irreducible Markov chains on a finite state space is considered as an exponential perturbation of a reducible Markov chain. This is a generalization of the Freidlin-Wentzell theory, motivated by studies of stochastic Ising models, neural network and simulated annealing. It is shown that the metastability is a universal feature for this wide class of Markov chains. The metastable states are simply those recurrent states of the reducible Markov chain. Higher level attractors, related attractive basins and their pyramidal structure are analysed. The logarithmic asymptotics of the hitting time of various sets are estimated. The hitting time over its mean converges in law to the unit exponential distribution.
A compositional framework for Markov processes
Baez, John C.; Fong, Brendan; Pollard, Blake S.
2016-03-01
We define the concept of an "open" Markov process, or more precisely, continuous-time Markov chain, which is one where probability can flow in or out of certain states called "inputs" and "outputs." One can build up a Markov process from smaller open pieces. This process is formalized by making open Markov processes into the morphisms of a dagger compact category. We show that the behavior of a detailed balanced open Markov process is determined by a principle of minimum dissipation, closely related to Prigogine's principle of minimum entropy production. Using this fact, we set up a functor mapping open detailed balanced Markov processes to open circuits made of linear resistors. We also describe how to "black box" an open Markov process, obtaining the linear relation between input and output data that holds in any steady state, including nonequilibrium steady states with a nonzero flow of probability through the system. We prove that black boxing gives a symmetric monoidal dagger functor sending open detailed balanced Markov processes to Lagrangian relations between symplectic vector spaces. This allows us to compute the steady state behavior of an open detailed balanced Markov process from the behaviors of smaller pieces from which it is built. We relate this black box functor to a previously constructed black box functor for circuits.
Maximizing Entropy over Markov Processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2013-01-01
computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... 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...
Maximizing entropy over Markov processes
DEFF Research Database (Denmark)
Biondi, Fabrizio; Legay, Axel; Nielsen, Bo Friis
2014-01-01
computation reduces to finding a model of a specification with highest entropy. Entropy maximization for probabilistic process specifications has not been studied before, even though it is well known in Bayesian inference for discrete distributions. We give a characterization of global entropy of a process...... 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...
Dynamical properties of confined supercooled water: an NMR study
Mallamace, Francesco; Broccio, Matteo; Corsaro, Carmelo; Faraone, Antonio; Liu, Li; Mou, Chung-Yuan; Chen, Sow-Hsin
2006-09-01
We report a set of dynamical data of confined water measured in a very deeply supercooled regime (290-190 K). Water is contained in silica matrices (MCM-41-S) which consist of 1D cylindrical pores with diameters d = 14,18 and 24 Å. When confined in these tubular pores, water does not crystallize, and can be supercooled well below 200 K. We use the NMR technique to obtain the characteristic proton relaxation time-constants (the spin-lattice relaxation time-constant T1 and the spin-spin relaxation time-constant T2) and a direct measurement of the self-diffusion coefficient in the whole temperature range. We give evidence of the existence of a fragile-to-strong dynamic crossover (FSC) at TL = 225 K from the temperature dependence of the self-diffusion coefficient. A combination of the NMR self-diffusion coefficient with the average translational relaxation time, as measured by quasi-elastic neutron scattering, shows a well defined decoupling of transport coefficients, i.e. the breakdown of the Stokes-Einstein relation, on approaching the crossover temperature TL.
Dynamical properties of confined supercooled water: an NMR study
Energy Technology Data Exchange (ETDEWEB)
Mallamace, Francesco [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Broccio, Matteo [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Corsaro, Carmelo [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Faraone, Antonio [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Liu Li [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States); Mou, C-Y [Department of Chemistry, National Taiwan University, Taipei, Taiwan (China); Chen, S-H [Department of Nuclear Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139 (United States)
2006-09-13
We report a set of dynamical data of confined water measured in a very deeply supercooled regime (290-190 K). Water is contained in silica matrices (MCM-41-S) which consist of 1D cylindrical pores with diameters d = 14,18 and 24 A. When confined in these tubular pores, water does not crystallize, and can be supercooled well below 200 K. We use the NMR technique to obtain the characteristic proton relaxation time-constants (the spin-lattice relaxation time-constant T1 and the spin-spin relaxation time-constant T2) and a direct measurement of the self-diffusion coefficient in the whole temperature range. We give evidence of the existence of a fragile-to-strong dynamic crossover (FSC) at T{sub L} = 225 K from the temperature dependence of the self-diffusion coefficient. A combination of the NMR self-diffusion coefficient with the average translational relaxation time, as measured by quasi-elastic neutron scattering, shows a well defined decoupling of transport coefficients, i.e. the breakdown of the Stokes-Einstein relation, on approaching the crossover temperature T{sub L}.
Theoretical approaches to the glass transition in simple liquids
Indian Academy of Sciences (India)
Chandan Dasgupta
2005-05-01
Theoretical approaches to the development of an understanding of the behaviour of simple supercooled liquids near the structural glass transition are reviewed and our work on this problem, based on the density functional theory of freezing and replicated liquid state theory, are summarized in this context. A few directions for further work on this problem are suggested.
Entropy Rate for Hidden Markov Chains with rare transitions
2010-01-01
We consider Hidden Markov Chains obtained by passing a Markov Chain with rare transitions through a noisy memoryless channel. We obtain asymptotic estimates for the entropy of the resulting Hidden Markov Chain as the transition rate is reduced to zero.
Kanno, H; Kajiwara, K; Miyata, K
2010-05-21
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 T(H) (homogeneous ice nucleation temperature) and T(m) (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 T(H) 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 P(c2)= approximately 200 MPa and at T(c2)temperature of SCP). The presence of two T(H) peaks for DMSO solutions (R=15, 12, and 10) suggests that phase separation occurs in aqueous DMSO solution (Rtemperatures (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.
Modelling and analysis of Markov reward automata
Guck, Dennis; Timmer, Mark; Hatefi, Hassan; Ruijters, Enno; Stoelinga, Mariëlle
2014-01-01
Costs and rewards are important ingredients for many types of systems, modelling critical aspects like energy consumption, task completion, repair costs, and memory usage. This paper introduces Markov reward automata, an extension of Markov automata that allows the modelling of systems incorporating
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....
Using Games to Teach Markov Chains
Johnson, Roger W.
2003-01-01
Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…
STATISTICS OF A CLASS OF MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
DENG Yingchun; CAO Xianbing
2004-01-01
In this paper we prove that the distributions of their sojourn time and hitting time at one special state for random walks which are allowed to be finite or infinite and Markov chains on star-graphs with discrete time can uniquely determine the probability distribution of the whole chains. This result also suggests a new statistical method for Markov chains.
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...... 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....... 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...
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...
Directory of Open Access Journals (Sweden)
Masaya eIshikawa
2015-01-01
Full Text Available Wintering Sasa senanensis, dwarf bamboo, has been known to employ deep supercooling as the mechanism of cold hardiness in its most of the tissues from leaves to rhizomes. The unique cold hardiness mechanism of this plant was further characterized using current year leaf blades. Cold hardiness levels increased from August (LT20: –11 °C to December (LT20: –20 °C, which coincided with the initiation temperature of low temperature exotherms (LTE detected in differential thermal analyses. When leaf blades were stored at –5 °C for 1-14 days, there was no nucleation of the supercooled tissue units compartmentalized by the longitudinal and transverse veins either in summer or winter. However, only summer leaves suffered significant injury after prolonged supercooling of the tissue units. This may be a novel type of low temperature-induced injury in supercooled state at subfreezing temperatures. When winter leaf blades were maintained at the threshold temperature (-20 °C, a longer storage period (1-7 days increased lethal freezing of the supercooled tissue units. Within a wintering shoot, the second or third leaf blade from the top was most cold hardy and leaf blades at lower positions tended to suffer more injury due to lethal freezing of the supercooled units, which was not correlated with the leaf water content. LTE were shifted to higher temperatures (2-5 °C after a lethal freeze-thaw cycle. The results demonstrate that the tissue unit compartmentalized with longitudinal and transverse veins serves as the unit of supercooling and temperature- and time-dependent freezing of the units is lethal both in laboratory freeze tests and in the field. To establish such supercooling in the unit, structural ice barriers such as development of sclerenchyma and biochemical mechanisms to increase the stability of supercooling are considered important. We discussed these mechanisms in regard to ecological and physiological significance in winter survival.
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...... the supercooled sodium acetate water mixture was 194 kJ/kg of sodium acetate water mixture in the first test cycles dropping to 179 kJ/kg in the later test cycles. Instability of the supercooling occurred when the charging periods were short and in the last test cycles where the tube connecting the module...
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 ...
Martelli, Fausto; Palmer, Jeremy; Singh, Rakesh; Debenedetti, Pablo; Car, Roberto
By means of unbiased classical molecular dynamics simulations, we identify the microscopic pathways of spontaneous homogeneous crystallization in supercooled ST2 water. By introducing a new order parameter, we are able to monitor formation/disruption of locally ordered regions characterized by small ice clusters with intermediate range order. When two of these regions are close each other, they percolate and form a larger ordered region. The process is slow enough to allow for polymorphic selection in favor of cubic ice (Ic). The formation of an ice nucleus requires percolation of many small clusters so that the transformations at the interface of the nucleus do not involve its core, thus guaranteeing the stability of the nucleus. The growth of the crystalline nucleus is fast and involves direct transformation of interfacial liquid molecules as well as percolation of small Ic/Ih clusters. The growth is too fast to allow conversion of Ih into Ic sites, originating the formation of a stacking fault in the final crystal. We recognize Euclidean structures in the oxygen configuration of the second shell in Ic and Ih clusters. This new point of view allows us to explain the source of the ordered stacking fault geometry.
Structural relaxation mechanisms in liquid Eugenol. A depolarized light scattering study
Bezot, P.; Hesse-Bezot, C.; Roynard, D.; Jeanneaux, F.
1988-07-01
A depolarized light scattering study of liquid Eugenol, over a large temperature range including the supercooled region, is proposed. Comparisons with shear mechanical impedance measurements, obtained at lower frequencies, lead to more precise information on the viscoelastic parameters in the supercooled region. The structural relaxation process measurements by means of the photon correlation technique are compared to the dielectric and mechanical measurements. Molecular mechanisms are proposed.
Revisiting Causality in Markov Chains
Shojaee, Abbas
2016-01-01
Identifying causal relationships is a key premise of scientific research. The growth of observational data in different disciplines along with the availability of machine learning methods offers the possibility of using an empirical approach to identifying potential causal relationships, to deepen our understandings of causal behavior and to build theories accordingly. Conventional methods of causality inference from observational data require a considerable length of time series data to capture cause-effect relationship. We find that potential causal relationships can be inferred from the composition of one step transition rates to and from an event. Also known as Markov chain, one step transition rates are a commonly available resource in different scientific disciplines. Here we introduce a simple, effective and computationally efficient method that we termed 'Causality Inference using Composition of Transitions CICT' to reveal causal structure with high accuracy. We characterize the differences in causes,...
2H NMR studies of supercooled and glassy aspirin
Nath, R.; Nowaczyk, A.; Geil, B.; Bohmer, R.
2007-11-01
Acetyl salicylic acid, deuterated at the methyl group, was investigated using 2H-NMR in its supercooled and glassy states. Just above the glass transition temperature the molecular reorientations were studied using stimulated-echo spectroscopy and demonstrated a large degree of similarity with other glass formers. Deep in the glassy phase the NMR spectra look similar to those reported for the crystal [A. Detken, P. Focke, H. Zimmermann, U. Haeberlen, Z. Olejniczak, Z. T. Lalowicz, Z. Naturforsch. A 50 (1995) 95] and below 20 K they are indicative for rotational tunneling with a relatively large tunneling frequency. Measurements of the spin-lattice relaxation times for temperatures below 150 K reveal a broad distribution of correlation times in the glass. The dominant energy barrier characterizing the slow-down of the methyl group is significantly smaller than the well defined barrier in the crystal.
Mechanism of supercooling in flower bud of Camellia oleifea
Institute of Scientific and Technical Information of China (English)
苏维埃; 潘良文
1995-01-01
It is the first time for MRI to be used in the research of flower buds supercooling. Directobservation on freezing course of living flower buds of Camellia yuhsienensis by MRI and tissue browning test showed that freezing order of the flower organs is bud axis, scale, petal, pistil and stamen. It is coincident with the direction of ice development from bud axes to flower organs upwards. The corresponding results from MRI and freezing-fixation showed that the water translocation from flower organs to axes and scales is carried on in the course of bud freezing. ’H spectral measurement of NMR was used to follow the decrease of unfrozen water in the buds during the cooling.
A molecular dynamics study on surface properties of supercooled water
Institute of Scientific and Technical Information of China (English)
L(U) Yongjun; WEI Bingbo
2006-01-01
Molecular dynamics simulations were performed to study the surface properties of water in a temperature range from 228 to 293 K by using the extended simple point charge (SPC/E) and four-site TIP4P potentials. The calculated surface tension increases with the decrease of temperature, and moreover the slopes of the surface tension-temperature curves show a weak rise below 273 K, whereas no obvious anomalies appear near 228 K, which accords with the previous experiments. Compared with the measured values, the SPC/E potential shows a good agreement, and the TIP4P potential scription of the surface structure of supercooled water for the SPC/E. When simulating the orientational distributions of water molecules near the surface, the SPC/E potential produces higher ordering and larger surface potentials than the TIP4P potential.
Optical and thermodynamic property measurements of liquid metals and alloys
Weber, J. K. Richard; Krishnan, Shankar; Schiffman, Robert A.; Nordine, Paul C.
Optical properties and spectral emissivities of liquid silicon, titanium, niobium, and zirconium were investigated by HeNe laser polarimetry at λ = 632.8 nm. The metals were of a high purity and, except for zirconium, clean. The more demanding environmental requirements for eliminating oxide or nitride phases from zirconium were not met. Containerless conditions were achieved by electromagnetic levitation and heating. CO2 laser beam heating was also used to extend the temperature range for stable levitation and to heat solid silicon to form the metallic liquid phase. Corrections to previously reported calorimetric measurements of the heat capacity of liquid niobium were derived from the measured temperature dependence of its spectral emissivity. Property measurements were obtained for supercooled liquid silicon and supercooling of liquid zirconium was accomplished. The purification of liquid metals and the extension of this work on liquids to the measurement of thermodynamic properties and phase equilibria are discussed.
Directory of Open Access Journals (Sweden)
J. Crosier
2011-01-01
evidence for the Hallett-Mossop (HM process of secondary ice particle production leading to the formation of the precipitation observed. This includes (1 Ice concentrations in the convective feature were more than an order of magnitude greater than the concentration of primary ice in the overlaying stratus, (2 Large concentrations of small pristine columns were observed at the ~−5 °C level together with liquid water droplets and a few rimed ice particles, (3 Columns were larger and increasingly rimed at colder temperatures. Calculated ice splinter production rates are consistent with observed concentrations if the condition that only droplets greater than 24 μm are capable of generating secondary ice splinters is relaxed.
This case demonstrates the importance of understanding the formation of ice at slightly supercooled temperatures, as it can lead to secondary ice production and the formation of precipitation in clouds which may not otherwise be considered as significant precipitation sources.
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
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
State Truncation for Large Markov Chains
Institute of Scientific and Technical Information of China (English)
JIANGLetian; XUGuozhi; ZHANGHao; YINGRendong
2003-01-01
One of the main issues to apply the Markov modeling method to reliability and availability analysis is the challenge called largeness, I.e., the explosive number of states, for a system with a large number of components.One method to quickly calculate the reliability of a sys-tem is to neglect ‘unimportant’ states in the Markov chain model. In this paper, based on a Markov model that is widely used in practical systems, a criterion of state trun-cation is presented.
Hidden Markov models estimation and control
Elliott, Robert J; Moore, John B
1995-01-01
As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filte
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
Uncertainty quantification for Markov chain models.
Meidani, Hadi; Ghanem, Roger
2012-12-01
Transition probabilities serve to parameterize Markov chains and control their evolution and associated decisions and controls. Uncertainties in these parameters can be associated with inherent fluctuations in the medium through which a chain evolves, or with insufficient data such that the inferential value of the chain is jeopardized. The behavior of Markov chains associated with such uncertainties is described using a probabilistic model for the transition matrices. The principle of maximum entropy is used to characterize the probability measure of the transition rates. The formalism is demonstrated on a Markov chain describing the spread of disease, and a number of quantities of interest, pertaining to different aspects of decision-making, are investigated.
Tanaka, M.; Morita, K.; Mamori, H.; Fukushima, N.; Yamamoto, M.
2017-08-01
The collision of a supercooled water droplet with a surface result an object creates ice accretion on the surface. The icing problem in any cold environments leads to severe damages on aircrafts, and a lot of studies on prevention and prediction techniques for icing have been conducted so far. Therefore, it is very important to know the detail of freezing mechanism of supercooled water droplets to improve the anti-and de-icing devices and icing simulation codes. The icing mechanism of a single supercooled water droplet impacting on an object surface would give us great insights for the purpose. In the present study, we develop a dual-luminescent imaging technique to measure the time-resolved temperature of a supercooled water droplet impacting on the surface under different temperature conditions. We apply this technique to measure the exact temperature of a water droplet, and to discuss the detail of the freezing process.
A scaling analysis of a cat and mouse Markov chain
Litvak, Nelly; Robert, Philippe
2009-01-01
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
Generalized crested products of Markov chains
D'Angeli, Daniele
2010-01-01
We define a finite Markov chain, called generalized crested product, which naturally appears as a generalization of the first crested product of Markov chains. A complete spectral analysis is developed and the $k$-step transition probability is given. It is important to remark that this Markov chain describes a more general version of the classical Ehrenfest diffusion model. As a particular case, one gets a generalization of the classical Insect Markov chain defined on the ultrametric space. Finally, an interpretation in terms of representation group theory is given, by showing the correspondence between the spectral decomposition of the generalized crested product and the Gelfand pairs associated with the generalized wreath product of permutation groups.
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...
Stochastic relations foundations for Markov transition systems
Doberkat, Ernst-Erich
2007-01-01
Collecting information previously scattered throughout the vast literature, including the author's own research, Stochastic Relations: Foundations for Markov Transition Systems develops the theory of stochastic relations as a basis for Markov transition systems. After an introduction to the basic mathematical tools from topology, measure theory, and categories, the book examines the central topics of congruences and morphisms, applies these to the monoidal structure, and defines bisimilarity and behavioral equivalence within this framework. The author views developments from the general
Markov chains and decision processes for engineers and managers
Sheskin, Theodore J
2010-01-01
Markov Chain Structure and ModelsHistorical NoteStates and TransitionsModel of the WeatherRandom WalksEstimating Transition ProbabilitiesMultiple-Step Transition ProbabilitiesState Probabilities after Multiple StepsClassification of StatesMarkov Chain StructureMarkov Chain ModelsProblemsReferencesRegular Markov ChainsSteady State ProbabilitiesFirst Passage to a Target StateProblemsReferencesReducible Markov ChainsCanonical Form of the Transition MatrixTh
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.
APLIKASI MARKOV RANDOM FIELD PADA MASALAH INDUSTRI
Directory of Open Access Journals (Sweden)
Siana Halim
2002-01-01
Full Text Available Markov chain in the stochastic process is widely used in the industrial problems particularly in the problem of determining the market share of products. In this paper we are going to extend the one in the random field so called the Markov Random Field and applied also in the market share problem with restriction the market is considered as a discrete lattice and Pott's models are going to be used as the potential function. Metropolis sampler is going to be used to determine the stability condition. Abstract in Bahasa Indonesia : Rantai Markov dalam proses stokastik seringkali digunakan dalam penyelesaian masalah industri khususnya dalam masalah penentuan market share. Dalam artikel ini akan dibahas perluasan Rantai Markov tesebut ke dalam sebuah random field yang disebut sebagai Markov Random Field (MRF yang juga akan diaplikasikan pada masalah market share dengan batasan daerah pemasarannya dianggap sebagai sebuah lattice diskrit dan fungsi potensial yang akan digunakan adalah Potts models. Akan digunakan Metropolis sampler untuk menentukan kondisi stabil. Kata kunci: proses stokastik, Markov Random Field, Gibbs Random Field, Potts model, Metropolis sampling.
The reversibility and first-order nature of liquid-liquid transition in a molecular liquid
Kobayashi, Mika; Tanaka, Hajime
2016-11-01
Liquid-liquid transition is an intriguing phenomenon in which a liquid transforms into another liquid via the first-order transition. For molecular liquids, however, it always takes place in a supercooled liquid state metastable against crystallization, which has led to a number of serious debates concerning its origin: liquid-liquid transition versus unusual nano-crystal formation. Thus, there have so far been no single example free from such debates, to the best of our knowledge. Here we show experimental evidence that the transition is truly liquid-liquid transition and not nano-crystallization for a molecular liquid, triphenyl phosphite. We kinetically isolate the reverse liquid-liquid transition from glass transition and crystallization with a high heating rate of flash differential scanning calorimetry, and prove the reversibility and first-order nature of liquid-liquid transition. Our finding not only deepens our physical understanding of liquid-liquid transition but may also initiate a phase of its research from both fundamental and applications viewpoints.
Fractional Walden rule for electrolytes in supercooled disaccharide aqueous solutions.
Longinotti, M Paula; Corti, Horacio R
2009-04-23
The electrical conductivity of CsCl, KCl, Bu(4)NBr, and Bu(4)NI was studied in stable and supercooled (metastable) sucrose and trehalose aqueous solutions over a wide viscosity range. The results indicate that large positive deviations from the Walden rule occur in these systems due to the higher tendency of the ions to move in water-rich regions, as previously observed for NaCl and MgCl(2). The electrical molar conductivity viscosity dependence can be described with a fractional Walden rule (Lambdaeta(alpha) = constant), where alpha is a decoupling parameter which increases with ionic size and varies between 0.61 and 0.74 for all of the studied electrolytes. Using the electrical molar conductivity dependence of ion-ion interactions, an effective dielectric constant was calculated for a trehalose 39 wt% aqueous solution as a function of temperature. Above 278 K, the effective and the bulk solution dielectric constants are similar, but at lower temperatures, where the carbohydrate becomes less mobile than water, the effective dielectric constant approaches the dielectric constant of water. We also conclude that the solute-solvent dielectric friction contribution can be neglected, reinforcing the idea that the observed breakdown of the Walden rule is due to the existence of local microheterogeneities. The Walden plots for the studied ionic solutes show a decoupling similar to that found for the diffusion of water in the same solutions.
The Transient Supercooling Enhancement For A Pulsed Thermoelectric Cooler (TEC)
Mao, Jia-ni; Du, Jun-yan; Wang, Shi-fei; Zhou, Jing-wei; Wang, Yu-Gang
2016-01-01
OnceÂ TECÂ excitatedÂ byÂ aÂ high-voltageÂ pulse,Â thereÂ existsÂ aÂ transientÂ thermoelectricÂ supercoolingÂ effect,Â whichÂ canÂ beÂ enhancedÂ byÂ keepingÂ onÂ increasingÂ theÂ PeltierÂ coolingÂ effectÂ toÂ compensateÂ forÂ theÂ negativeÂ self-heatingÂ fromÂ theÂ JouleÂ heatingÂ effectÂ andÂ FourierÂ heatÂ conductionÂ effect.Â AfterÂ superimposingÂ anÂ additionalÂ voltageÂ pulseÂ overÂ aÂ steady-stateÂ referenceÂ valueÂ inÂ aÂ shortÂ timeÂ scale,Â abruptÂ temperatureÂ dropÂ willÂ beÂ produc...
The Transient Supercooling Enhancement For A Pulsed Thermoelectric Cooler (TEC)
Mao, Jia-ni; Du, Jun-yan; Wang, Shi-fei; Zhou, Jing-wei; Wang, Yu-Gang
2016-01-01
OnceÂ TECÂ excitatedÂ byÂ aÂ high-voltageÂ pulse,Â thereÂ existsÂ aÂ transientÂ thermoelectricÂ supercoolingÂ effect,Â whichÂ canÂ beÂ enhancedÂ byÂ keepingÂ onÂ increasingÂ theÂ PeltierÂ coolingÂ effectÂ toÂ compensateÂ forÂ theÂ negativeÂ self-heatingÂ fromÂ theÂ JouleÂ heatingÂ effectÂ andÂ FourierÂ heatÂ conductionÂ effect.Â AfterÂ superimposingÂ anÂ additionalÂ voltageÂ pulseÂ overÂ aÂ steady-stateÂ referenceÂ valueÂ inÂ aÂ shortÂ timeÂ scale,Â abruptÂ temperatureÂ dropÂ willÂ beÂ produc...
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.
Observations on the Freezing of Supercooled Pollen Washing Water by a New Electrodynamic Balance
Tong, Haijie; Pope, Francis D.; Kalberer, Markus
2014-05-01
Primary biological particles can act as efficient ice nuclei (IN) by initiating freezing events at temperatures warmer than the homogenous freezing temperature [1, 2]. For example, pollen grain particles can trigger freezing events at temperatures as warm as -5 °C in the contact freezing mode [3]. More recently pollen residues, which are released by washing pollen grains in water, were also observed to act as efficient IN in the immersion mode [4, 5]. In this study we developed a new cold electrodynamic balance (CEDB) system and investigated the freezing properties of single particles of supercooled pollen washing water (SPWW). The EDB technique allows for a contact free measurement of freezing events. The phase of the particle (liquid or frozen solid) can be distinguished via measuring the Mie scattering signal from the particle. Furthermore the size of liquid (spherical) particles can be determined. The freezing events are characterized through the loss of the regular Mie scattering signal from the levitated droplet as it changes state from liquid to a frozen solid. The statistical freezing probabilities of SPWW were obtained in the temperature range: -15 to -40 °C. Each temperature measurement point consists of the analysis of 30-100 droplets. Preliminary conclusions are that SPWW is IN active in the immersion mode. Further discussion will focus on the temperature range of the IN activity, the important variables (other than temperature) for IN activity, other likely modes of IN activity, and the implications of these results in terms of the atmospheric relevance of SPWW. This study was supported by the NERC. We acknowledge Professor Jonathan Reid and James Davis from the University of Bristol for providing information of the design of the warm EDB system. References: [1] Möhler, O., et al. (2007) Biogeosciences, 4, 1059-1071. [2] Prenni, A. J., et al. (2009) Nat. Geosci., 2, 401-404. [3] Diehl, K., et al. (2002) Atmos. Res., 61, 125-133. [4] Pummer, B. G
The spectra of molecular light scattering in high-viscosity glycerol-like liquids
Lishchuk, Sergey; Malomuzh, N. P.
1996-01-01
The mechanisms of formation of fine structures in the spectra of the polarized and depolarized components of molecular light scattering in high-viscosity liquids are studied. The temperature dependences of spectral parameters are examined. The results are treated in terms of the concept of a microheterogeneous structure of supercooled high-viscosity liquids.
[Decision analysis in radiology using Markov models].
Golder, W
2000-01-01
Markov models (Multistate transition models) are mathematical tools to simulate a cohort of individuals followed over time to assess the prognosis resulting from different strategies. They are applied on the assumption that persons are in one of a finite number of states of health (Markov states). Each condition is given a transition probability as well as an incremental value. Probabilities may be chosen constant or varying over time due to predefined rules. Time horizon is divided into equal increments (Markov cycles). The model calculates quality-adjusted life expectancy employing real-life units and values and summing up the length of time spent in each health state adjusted for objective outcomes and subjective appraisal. This sort of modeling prognosis for a given patient is analogous to utility in common decision trees. Markov models can be evaluated by matrix algebra, probabilistic cohort simulation and Monte Carlo simulation. They have been applied to assess the relative benefits and risks of a limited number of diagnostic and therapeutic procedures in radiology. More interventions should be submitted to Markov analyses in order to elucidate their cost-effectiveness.
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 sy......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....... Finally, we consider three independent tasks of dissipative engineering: dissipatively preparing a maximally entangled state of two atoms trapped in an optical cavity, dissipative preparation of graph states, and dissipative quantum computing construction....
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
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
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.
Effect of drop size on the impact thermodynamics for supercooled large droplet in aircraft icing
Zhang, Chen; Liu, Hong
2016-06-01
Supercooled large droplet (SLD), which can cause abnormal icing, is a well-known issue in aerospace engineering. Although efforts have been exerted to understand large droplet impact dynamics and the supercooled feature in the film/substrate interface, respectively, the thermodynamic effect during the SLD impact process has not received sufficient attention. This work conducts experimental studies to determine the effects of drop size on the thermodynamics for supercooled large droplet impingement. Through phenomenological reproduction, the rapid-freezing characteristics are observed in diameters of 400, 800, and 1300 μm. The experimental analysis provides information on the maximum spreading rate and the shrinkage rate of the drop, the supercooled diffusive rate, and the freezing time. A physical explanation of this unsteady heat transfer process is proposed theoretically, which indicates that the drop size is a critical factor influencing the supercooled heat exchange and effective heat transfer duration between the film/substrate interface. On the basis of the present experimental data and theoretical analysis, an impinging heating model is developed and applied to typical SLD cases. The model behaves as anticipated, which underlines the wide applicability to SLD icing problems in related fields.
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 chains for testing redundant software
White, Allan L.; Sjogren, Jon A.
1988-01-01
A preliminary design for a validation experiment has been developed that addresses several problems unique to assuring the extremely high quality of multiple-version programs in process-control software. The procedure uses Markov chains to model the error states of the multiple version programs. The programs are observed during simulated process-control testing, and estimates are obtained for the transition probabilities between the states of the Markov chain. The experimental Markov chain model is then expanded into a reliability model that takes into account the inertia of the system being controlled. The reliability of the multiple version software is computed from this reliability model at a given confidence level using confidence intervals obtained for the transition probabilities during the experiment. An example demonstrating the method is provided.
Effects of hydrogen-bond environment on single particle and pair dynamics in liquid water
Indian Academy of Sciences (India)
Amalendu Chandra; Snehasis Chowdhuri
2001-10-01
We have performed molecular dynamics simulations of liquid water at 298 and 258 K to investigate the effects of hydrogen-bond environment on various single-particle and pair dynamical properties of water molecules at ambient and supercooled conditions. The water molecules are modelled by the extended simple point charge (SPC/E) model. We first calculate the distribution of hydrogen-bond environment in liquid water at both temperatures and then investigate how the selfdiffusion and orientational relaxation of a single water molecule and also the relative diffusion and relaxation of the hydrogen-bond of a water pair depend on the nature of the hydrogen-bond environment of the tagged molecules. We find that the various dynamical quantities depend significantly on the hydrogen-bond environment, especially at the supercooled temperature. The present study provides a molecular-level insight into the dynamics of liquid water under ambient and supercooled conditions.
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
Parallel Markov chain Monte Carlo simulations.
Ren, Ruichao; Orkoulas, G
2007-06-07
With strict detailed balance, parallel Monte Carlo simulation through domain decomposition cannot be validated with conventional Markov chain theory, which describes an intrinsically serial stochastic process. In this work, the parallel version of Markov chain theory and its role in accelerating Monte Carlo simulations via cluster computing is explored. It is shown that sequential updating is the key to improving efficiency in parallel simulations through domain decomposition. A parallel scheme is proposed to reduce interprocessor communication or synchronization, which slows down parallel simulation with increasing number of processors. Parallel simulation results for the two-dimensional lattice gas model show substantial reduction of simulation time for systems of moderate and large size.
Markov bridges, bisection and variance reduction
DEFF Research Database (Denmark)
Asmussen, Søren; Hobolth, Asger
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....... 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...... where the methods of stratification, importance sampling and quasi Monte Carlo are investigated....
A Noether Theorem for Markov Processes
Baez, John C
2012-01-01
Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer holds, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state.
Markov Model Applied to Gene Evolution
Institute of Scientific and Technical Information of China (English)
季星来; 孙之荣
2001-01-01
The study of nucleotide substitution is very important both to our understanding of gene evolution and to reliable estimation of phylogenetic relationships. In this paper nucleotide substitution is assumed to be random and the Markov model is applied to the study of the evolution of genes. Then a non-linear optimization approach is proposed for estimating substitution in real sequences. This substitution is called the "Nucleotide State Transfer Matrix". One of the most important conclusions from this work is that gene sequence evolution conforms to the Markov process. Also, some theoretical evidences for random evolution are given from energy analysis of DNA replication.
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
Entropy production fluctuations of finite Markov chains
Jiang, Da-Quan; Qian, Min; Zhang, Fu-Xi
2003-09-01
For almost every trajectory segment over a finite time span of a finite Markov chain with any given initial distribution, the logarithm of the ratio of its probability to that of its time-reversal converges exponentially to the entropy production rate of the Markov chain. The large deviation rate function has a symmetry of Gallavotti-Cohen type, which is called the fluctuation theorem. Moreover, similar symmetries also hold for the rate functions of the joint distributions of general observables and the logarithmic probability ratio.
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 locations of the breaks are subsequently obtained by assigning states to data points according to the Maximum Posterior Mode (MPM) algorithm. The Integrated Classification Likelihood-Bayesian Information Criterion (ICL-BIC) allows for the determination of the number of regimes by taking into account...... in the monetary policy of United States, the dierent functional form being variants of the Taylor (1993) rule....
DEFF Research Database (Denmark)
Johansen, Jakob Berg; Dannemand, Mark; Kong, Weiqiang
2015-01-01
Sodium acetate trihydrate and graphite powder mixtures have been evaluated to investigate the influence of the graphite powder on the stability of supercooling. A sodium acetate and water mixture mixed with graphite powder was successfully supercooled at ambient indoor temperatures for five month...
An investigation on supercooling directional solidification process of Cu-Ni single phase alloy
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Supercooling directional solidification (SDS) is put forward by combination of melt supercooling and conventional solidification by application of supercooling inheritance. On the self-designed SDS equipment, SDS of Cu-Ni alloy was achieved successfully. The results are as follows: (ⅰ) The primary arm spacing is about 30 m m, the growth of secondary arms are strongly suppressed. The primary arm spacing is nearly the same as LMC method (GL=25 K/mm, V=500 m m/s), the primary stems are straight, fine and completed, with an inclination angle of about 5.8o. (ⅱ) A semi-quantitative T-T model is brought forward to describe the dendrite growth rate V vs. undercooling D T. The prediction of T-T model agrees well with experimental results. The formation of fine equiaxed dendrites, transition region and dendrite region can be explained successfully by D T-V-x relation of T-T model.
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....... • 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...... 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...
DEFF Research Database (Denmark)
Dannemand, Mark; Johansen, Jakob Berg; Kong, Weiqiang;
2016-01-01
unit was tested with 116.3 kg SAT with 0.5% Xanthan rubber as a thickening agent and 4.4% graphite powder. The heat exchange capacity rate during charge was significantly lower for the unit with SAT and Xanthan rubber compared to the unit with SAT and extra water. This was due to less convection......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...
Modelling and analysis of Markov reward automata (extended version)
Guck, Dennis; Timmer, Mark; Hatefi, Hassan; Ruijters, Enno; Stoelinga, Mariëlle
2014-01-01
Costs and rewards are important ingredients for cyberphysical systems, modelling critical aspects like energy consumption, task completion, repair costs, and memory usage. This paper introduces Markov reward automata, an extension of Markov automata that allows the modelling of systems incorporating
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 ... Markov decision processes have been applied in solving a wide range of optimization ...
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...... to 230 kJ/kg. TRNSYS simulations of a solar combi system including a storage with four heat storage modules of each 200 kg of sodium acetate trihydrate utilizing stable supercooling achieved a solar fraction of 80% for a low energy house in Danish climatic conditions....
Markov Chain Approximations to Singular Stable-like Processes
2012-01-01
We consider the Markov chain approximations for singular stable-like processes. First we obtain properties of some Markov chains. Then we construct the approximating Markov chains and give a necessary condition for weak convergence of these chains to singular stable-like processes.
Stan, Claudiu A; Tang, Sindy K Y; Bishop, Kyle J M; Whitesides, George M
2011-02-10
The freezing of water can initiate at electrically conducting electrodes kept at a high electric potential or at charged electrically insulating surfaces. The microscopic mechanisms of these phenomena are unknown, but they must involve interactions between water molecules and electric fields. This paper investigates the effect of uniform electric fields on the homogeneous nucleation of ice in supercooled water. Electric fields were applied across drops of water immersed in a perfluorinated liquid using a parallel-plate capacitor; the drops traveled in a microchannel and were supercooled until they froze due to the homogeneous nucleation of ice. The distribution of freezing temperatures of drops depended on the rate of nucleation of ice, and the sensitivity of measurements allowed detection of changes by a factor of 1.5 in the rate of nucleation. Sinusoidal alternation of the electric field at frequencies from 3 to 100 kHz prevented free ions present in water from screening the electric field in the bulk of drops. Uniform electric fields in water with amplitudes up to (1.6 ± 0.4) × 10(5) V/m neither enhanced nor suppressed the homogeneous nucleation of ice. Estimations based on thermodynamic models suggest that fields in the range of 10(7)-10(8) V/m might cause an observable increase in the rate of nucleation.
Quantitative timed analysis of interactive Markov chains
Guck, Dennis; Han, Tingting; Katoen, Joost-Pieter; Neuhausser, M.
2012-01-01
This paper presents new algorithms and accompanying tool support for analyzing interactive Markov chains (IMCs), a stochastic timed 1 1/2-player game in which delays are exponentially distributed. IMCs are compositional and act as semantic model for engineering formalisms such as AADL and dynamic fa
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…
Confluence reduction for Markov automata (extended version)
Timmer, M.; Pol, van de J.C.; Stoelinga, M.I.A.
2013-01-01
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 gener
Efficient Modelling and Generation of Markov Automata
Timmer, Mark; Katoen, Joost-Pieter; Pol, van de Jaco; Stoelinga, Mariëlle; Koutny, M.; Ulidowski, I.
2012-01-01
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 M
Efficient Modelling and Generation of Markov Automata
Timmer, Mark; Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette
2012-01-01
This presentation introduces a process-algebraic framework with data for modelling and generating Markov automata. We show how an existing linearisation procedure for process-algebraic representations of probabilistic automata can be reused to transform systems in our new framework to a special
Shift ergodicity for stationary Markov processes
Institute of Scientific and Technical Information of China (English)
东金文
2001-01-01
In this paper shift ergodicity and related topics are studied for certain stationary processes. We first present a simple proof of the conclusion that every stationary Markov process is a generalized convex combination of stationary ergodic Markov processes. A direct consequence is that a stationary distribution of a Markov process is extremal if and only if the corresponding stationary Markov process is time ergodic and every stationary distribution is a generalized convex combination of such extremal ones. We then consider space ergodicity for spin flip particle systems. We prove space shift ergodicity and mixing for certain extremal invariant measures for a class of spin systems, in which most of the typical models, such as the Voter Models and the Contact Models, are included. As a consequence of these results we see that for such systems, under each of those extremal invariant measures, the space and time means of an observable coincide, an important phenomenon in statistical physics. Our results provide partial answers to certain interesting problems in spin systems.
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...
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...
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.
Document Ranking Based upon Markov Chains.
Danilowicz, Czeslaw; Balinski, Jaroslaw
2001-01-01
Considers how the order of documents in information retrieval responses are determined and introduces a method that uses a probabilistic model of a document set where documents are regarded as states of a Markov chain and where transition probabilities are directly proportional to similarities between documents. (Author/LRW)
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.
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.
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...
Estimating an Activity Driven Hidden Markov Model
Meyer, David A.; Shakeel, Asif
2015-01-01
We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent $\\textit{activity levels}$ that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of inferring human mobility on sub-daily time scales from, for example, mobile phone records.
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 determini
One-Counter Markov Decision Processes
Brazdil, T.; Brozek, V.; Etessami, K.; Kucera, A.; Wojtczak, D.K.; Charikar, M.
2010-01-01
We study the computational complexity of central analysis problems for One-Counter Markov Decision Processes (OC-MDPs), a class of finitely-presented, countable-state MDPs. OC-MDPs are equivalent to a controlled extension of (discrete-time) Quasi-Birth-Death processes (QBDs), a stochastic model stud
Piecewise deterministic Markov processes : an analytic approach
Alkurdi, Taleb Salameh Odeh
2013-01-01
The subject of this thesis, piecewise deterministic Markov processes, an analytic approach, is on the border between analysis and probability theory. Such processes can either be viewed as random perturbations of deterministic dynamical systems in an impulsive fashion, or as a particular kind of
An Explicit Microreversibility Violating Thermodynamic Markov Process
Lee, Michael J
2008-01-01
We explicitly construct a non-microreversible transition matrix for a Markov process and apply it to the standard three-state Potts model. This provides a clear and simple demonstration that the usual micoreversibility property of thermodynamical Monte Carlo algorithms is not strictly necessary from a mathemetical point of view.
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...
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.
Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes
Gorban, A N
2015-01-01
The nonlinear Markov processes are the measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic equations allow Lyapunov functionals (entropy, free energy, etc.). This may be considered as a sort of inheritance of the Lyapunov functionals from the microscopic master equations. We study nonlinear Markov processes that inherit thermodynamic properties from the microscopic linear Markov processes. We develop the thermodynamics of nonlinear Markov processes and analyze the asymptotic assumption, which are sufficient for this inheritance.
Grey-Markov Model for Road Accidents Forecasting
Institute of Scientific and Technical Information of China (English)
李相勇; 严余松; 蒋葛夫
2003-01-01
In order to improve the forecasting precision of road accidents, by introducing Markov chains forecasting method, a grey-Markov model for forecasting road accidents is established based on grey forecasting method. The model combines the advantages of both grey forecasting method and Markov chains forecasting method, overcomes the influence of random fluctuation data on forecasting precision and widens the application scope of the grey forecasting. An application example is conducted to evaluate the grey-Markov model, which shows that the precision of the grey-Markov model is better than that of grey model in forecasting road accidents.
Study of Simplification of Markov Model for Analyzing System Dependability
Energy Technology Data Exchange (ETDEWEB)
Son, Gwang Seop; Kim, Dong Hoon; Choi, Jong Gyun [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-05-15
In this paper, we introduce the simplification methodology of the Markov model for analyzing system dependability using system failure rate concept. This system failure rate is the probability that the system is failed or unavailable given that the system was as good as at this time. Using this parameter, the Markov model of sub system can be replaced to the system failure rate and then this parameter just is considered in the Markov model of whole system. In this paper, we proposed the method to simplify the Markov model in complex system architecture. We define the system failure rate and using this parameter, the Markov model of system could be simplified.
POISSON LIMIT THEOREM FOR COUNTABLE MARKOV CHAINS IN MARKOVIAN ENVIRONMENTS
Institute of Scientific and Technical Information of China (English)
方大凡; 王汉兴; 唐矛宁
2003-01-01
A countable Markov chain in a Markovian environment is considered. A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved. In order to prove this theorem, the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the Markov chain in a Markovian environment is shown. It' s well-known that a Markov process in a Markovian environment is generally not a standard Markov chain, so an example of Poisson approximation for a process which is not a Markov process is given. On the other hand, when the environmental process degenerates to a constant sequence, a Poisson limit theorem for countable Markov chains, which is the generalization of Pitskel's result for finite Markov chains is obtained.
Radiative consequences of low-temperature infrared refractive indices for supercooled water clouds
Directory of Open Access Journals (Sweden)
P. M. Rowe
2013-07-01
Full Text Available Simulations of cloud radiative properties for climate modeling and remote sensing rely on accurate knowledge of the complex refractive index (CRI of water. Although conventional algorithms employ a temperature independent assumption (TIA, recent infrared measurements of supercooled water have demonstrated that the CRI becomes increasingly ice-like at lower temperatures. Here, we assess biases that result from ignoring this temperature dependence. We show that TIA-based cloud retrievals introduce spurious ice into pure, supercooled clouds, or underestimate cloud thickness and droplet size. TIA-based downwelling radiative fluxes are lower than those for the temperature-dependent CRI by as much as 1.7 W m−2 (in cold regions, while top-of-atmosphere fluxes are higher by as much as 3.4 W m−2 (in warm regions. Proper accounting of the temperature dependence of the CRI, therefore, leads to significantly greater local greenhouse warming due to supercooled clouds than previously predicted. The current experimental uncertainty in the CRI at low temperatures must be reduced to properly account for supercooled clouds in both climate models and cloud property retrievals.
Radiative consequences of low-temperature infrared refractive indices for supercooled water clouds
Directory of Open Access Journals (Sweden)
P. M. Rowe
2013-12-01
Full Text Available Simulations of cloud radiative properties for climate modeling and remote sensing rely on accurate knowledge of the complex refractive index (CRI of water. Although conventional algorithms employ a temperature-independent assumption (TIA, recent infrared measurements of supercooled water have demonstrated that the CRI becomes increasingly ice-like at lower temperatures. Here, we assess biases that result from ignoring this temperature dependence. We show that TIA-based cloud retrievals introduce spurious ice into pure, supercooled clouds, or underestimate cloud optical thickness and droplet size. TIA-based downwelling radiative fluxes are lower than those for the temperature-dependent CRI by as much as 1.7 W m−2 (in cold regions, while top-of-atmosphere fluxes are higher by as much as 3.4 W m−2 (in warm regions. Proper accounting of the temperature dependence of the CRI, therefore, leads to significantly greater local greenhouse warming due to supercooled clouds than previously predicted. The current experimental uncertainty in the CRI at low temperatures must be reduced to account for supercooled clouds properly in both climate models and cloud-property retrievals.
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...
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...
Supercooling Suppression of Microencapsulated n-Alkanes by Introducing an Organic Gelator
Institute of Scientific and Technical Information of China (English)
ZHU Kong-ying; WANG Shuang; QI Heng-zhi; LI Hui; ZHAO Yun-hui; YUAN Xiao-yan
2012-01-01
Supercooling of the microencapsulated phase change materials(PCMs) during cooling usually happens.This phenomenon can interfere with heat transfer and is necessary to further overcome.In this study,melamine-formaldehyde microcapsules containing two n-alkane PCMs,namely,n-dodecane(C12) or n-tetradecane(C14)were prepared by in situ polymerization.A small amount of n-hexatriacontane(C36) was introduced as an organic gelator into the core of microcapsules to cope with the supercooling problem.Analyses demonstrate that supcrcooling of the microencapsulated C12 or C14 was significantly suppressed by adding 3％(mass fraction) C36,without changing the spherical morphology and dispersibility.It could be also found that the enthalpy of microencapsulated C12 or C14 containing C36 was similar to that of microencapsulated n-alkanes without C36,whereas the difference between onsets of crystallization and melting(degree of supercooling) is similar to that of those of pure n-alkanes,suggesting the remarkable suppression ability of the organic gelator on supercooling.
Anomalous dependence of the heat capacity of supercooled water on pressure and temperature
Directory of Open Access Journals (Sweden)
I.A. Stepanov
2014-01-01
Full Text Available In some papers, dependences of the isobaric heat capacity of water versus pressure and temperature were obtained. It is shown that these dependences contradict both the dependence of heat capacity on temperature for supercooled water, and an important thermodynamic equation for the dependence of heat capacity on pressure. A possible explanation for this contradiction is proposed.
Energy Technology Data Exchange (ETDEWEB)
Khedir, Khedir R.; Kannarpady, Ganesh K.; Ishihara, Hidetaka; Woo, Justin; Asar, Madhu P. [Center for Integrative Nanotechnology Sciences, University of Arkansas at Little Rock, 2801 South University Avenue, Little Rock, AR, 72204 (United States); Ryerson, Charles [Terrestrial and Cryospheric Sciences Branch Cold Regions, Research and Engineering Laboratory, U.S. Army Corps of Engineers, Hanover, NH 03755-1290 (United States); Biris, Alexandru S., E-mail: asbiris@ualr.edu [Center for Integrative Nanotechnology Sciences, University of Arkansas at Little Rock, 2801 South University Avenue, Little Rock, AR, 72204 (United States)
2013-08-15
The bouncing mechanism of warm and supercooled water droplets with temperatures ranging from 20 °C to −10 °C on the surface of superhydrophobic (SHP) tungsten nanorods (WNRs), held at a constant temperature of −10 °C, was investigated. The measurements were carried out inside a chamber kept at a low relative humidity of 20%. A considerable energy loss was observed mainly due to the increase in the viscous forces of the supercooled water droplet. The increase in the values of the capillary number, as a result of the variation in both viscosity and surface energy of the supercooled water droplet, has confirmed the significant role of viscous forces in the dissipation of bouncing energy. However, the contact time and contact line evolution of the supercooled water droplet on the surface remained unaffected by the decrease in its temperature at constant humidity. The calculations of the bouncing restitution and dissipated energy at various water droplet temperatures, using classical mechanics, were also carried out.
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.
Sistem Bonus Malus sebagai Model Rantai Markov
Directory of Open Access Journals (Sweden)
- Supandi
2010-06-01
Full Text Available Sistem bonus-malus (BMS yang dibangun mempunyaiÂ tujuan untuk membuat premi yang dibayarkan oleh tertanggung sedekat mungkin dengan harapan terjadinya klaim setiap tahunnya. Bila kita ingin meneliti bagaimana efisiensi suatu BMS, kita harus melihat bagaimana premi itu bergantungÂ pada frekuensi klaim. Efisiensi sistem bonus-malus dicari melalui model Markovnya,Â yaitu dengan mencari distribusi stasioner dari rantai markov BMS-nya. Dalam paper ini BMS yang digunakan adalah BMS Brasil dan modifkasinya pada nilai preminya untuk keadaan bawah. Dari modifikasi ini akan dibahas pengaruh perubahan premi terhadapÂ efisiensi BMS tersebut. Kata kunci : BMS, rantai markov, stationer,Â efisiensi
A critical appraisal of Markov state models
Schütte, Ch.; Sarich, M.
2015-09-01
Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of attention recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecular sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well beyond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome.
Entangled Markov Chains generated by Symmetric Channels
Miyadera, T
2006-01-01
A notion of entangled Markov chain was introduced by Accardi and Fidaleo in the context of quantum random walk. They proved that, in the finite dimensional case, the corresponding states have vanishing entropy density, but they did not prove that they are entangled. In the present note this entropy result is extended to the infinite dimensional case under the assumption of finite speed of hopping. Then the entanglement problem is discussed for spin 1/2, entangled Markov chains generated by a binary symmetric channel with hopping probability $1-q$. The von Neumann entropy of these states, restricted on a sublattice is explicitly calculated and shown to be independent of the size of the sublattice. This is a new, purely quantum, phenomenon. Finally the entanglement property between the sublattices ${\\cal A}(\\{0,1,...,N\\})$ and ${\\cal A}(\\{N+1\\})$ is investigated using the PPT criterium. It turns out that, for $q\
On nonlinear Markov chain Monte Carlo
Andrieu, Christophe; Doucet, Arnaud; Del Moral, Pierre; 10.3150/10-BEJ307
2011-01-01
Let $\\mathscr{P}(E)$ be the space of probability measures on a measurable space $(E,\\mathcal{E})$. In this paper we introduce a class of nonlinear Markov chain Monte Carlo (MCMC) methods for simulating from a probability measure $\\pi\\in\\mathscr{P}(E)$. Nonlinear Markov kernels (see [Feynman--Kac Formulae: Genealogical and Interacting Particle Systems with Applications (2004) Springer]) $K:\\mathscr{P}(E)\\times E\\rightarrow\\mathscr{P}(E)$ can be constructed to, in some sense, improve over MCMC methods. However, such nonlinear kernels cannot be simulated exactly, so approximations of the nonlinear kernels are constructed using auxiliary or potentially self-interacting chains. Several nonlinear kernels are presented and it is demonstrated that, under some conditions, the associated approximations exhibit a strong law of large numbers; our proof technique is via the Poisson equation and Foster--Lyapunov conditions. We investigate the performance of our approximations with some simulations.
Weak Markov Processes as Linear Systems
Gohm, Rolf
2012-01-01
A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter this is worked out systematically as a theory of representations of structure maps of a system by a weak process. We introduce subprocesses and quotient processes which can be described naturally by a suitable category of weak processes. A corresponding notion of cascade for processes induces a represented cascade of systems. We study the control theoretic notion of observability which turns out to be particularly interesting in connection with a cascade structure. As an application we gain new insights into stationary Markov chains where observability for the system is closely related to asymptotic completeness in the scattering theory of the chain. This motivates a general definition of asymptotic completeness in the category of weak processes.
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...... is computed. Afterwards, this expression is evaluated to a closed form function representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in the growth of the regular expression relative to the number...... of states (n(log n)).We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids this blow up in most practical cases. We give a detailed account of the approach, also extending to parametric...
Boundary value problems and Markov processes
Taira, Kazuaki
2009-01-01
This volume is devoted to a thorough and accessible exposition on the functional analytic approach to the problem of construction of Markov processes with Ventcel' boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-differential operator, called a Waldenfels operator, in the interior of the domain, and it obeys a boundary condition, called the Ventcel' boundary condition, on the boundary of the domain. Probabilistically, a Markovian particle moves both by jumps and continuously in the state space and it obeys the Ventcel' boundary condition, which consists of six terms corresponding to the diffusion along the boundary, the absorption phenomenon, the reflection phenomenon, the sticking (or viscosity) phenomenon, the jump phenomenon on the boundary, and the inward jump phenomenon from the boundary. In particular, second-order elliptic differential operators are called diffusion operators and describe analytically strong Markov pr...
Semigroups, boundary value problems and Markov processes
Taira, Kazuaki
2014-01-01
A careful and accessible exposition of functional analytic methods in stochastic analysis is provided in this book. It focuses on the interrelationship between three subjects in analysis: Markov processes, semi groups and elliptic boundary value problems. The author studies a general class of elliptic boundary value problems for second-order, Waldenfels integro-differential operators in partial differential equations and proves that this class of elliptic boundary value problems provides a general class of Feller semigroups in functional analysis. As an application, the author constructs a general class of Markov processes in probability in which a Markovian particle moves both by jumps and continuously in the state space until it 'dies' at the time when it reaches the set where the particle is definitely absorbed. Augmenting the 1st edition published in 2004, this edition includes four new chapters and eight re-worked and expanded chapters. It is amply illustrated and all chapters are rounded off with Notes ...
Stochastic Dynamics through Hierarchically Embedded Markov Chains
Vasconcelos, Vítor V.; Santos, Fernando P.; Santos, Francisco C.; Pacheco, Jorge M.
2017-02-01
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.
On approximation of Markov binomial distributions
Xia, Aihua; 10.3150/09-BEJ194
2010-01-01
For a Markov chain $\\mathbf{X}=\\{X_i,i=1,2,...,n\\}$ with the state space $\\{0,1\\}$, the random variable $S:=\\sum_{i=1}^nX_i$ is said to follow a Markov binomial distribution. The exact distribution of $S$, denoted $\\mathcal{L}S$, is very computationally intensive for large $n$ (see Gabriel [Biometrika 46 (1959) 454--460] and Bhat and Lal [Adv. in Appl. Probab. 20 (1988) 677--680]) and this paper concerns suitable approximate distributions for $\\mathcal{L}S$ when $\\mathbf{X}$ is stationary. We conclude that the negative binomial and binomial distributions are appropriate approximations for $\\mathcal{L}S$ when $\\operatorname {Var}S$ is greater than and less than $\\mathbb{E}S$, respectively. Also, due to the unique structure of the distribution, we are able to derive explicit error estimates for these approximations.
Persistence of Covalent Bonding in Liquid Silicon Probed by Inelastic X-Ray Scattering
Okada, J. T.; Sit, P. H.-L.; Watanabe, Y.; Wang, Y. J.; Barbiellini, B.; Ishikawa, T.; Itou, M.; Sakurai, Y.; Bansil, A.; Ishikawa, R.; Hamaishi, M.; Masaki, T.; Paradis, P.-F.; Kimura, K.; Ishikawa, T.; Nanao, S.
2012-02-01
Metallic liquid silicon at 1787 K is investigated using x-ray Compton scattering. An excellent agreement is found between the measurements and the corresponding Car-Parrinello molecular dynamics simulations. Our results show persistence of covalent bonding in liquid silicon and provide support for the occurrence of theoretically predicted liquid-liquid phase transition in supercooled liquid states. The population of covalent bond pairs in liquid silicon is estimated to be 17% via a maximally localized Wannier function analysis. Compton scattering is shown to be a sensitive probe of bonding effects in the liquid state.
Blazhnov, Ivan V; Malomuzh, Nikolay P; Lishchuk, Sergey V
2004-10-01
The relationship of the microstructure of supercooled, highly viscous glycerol to the temperature dependence of its density, thermal expansion coefficient, and shear viscosity are discussed. The character of this temperature dependence at the transition from low viscosity state to the solid amorphous state (solidified state without nuclei) is described with help of function psi, which can be interpreted as the effective number of degrees of freedom responsible for the change of viscosity of glycerol over a broad range; these degrees of freedom are those related to the alpha-relaxation process. It is shown that the change in effective activation energy of the viscosity is completely determined by the parameter psi. The change in the shear viscosity of glycerol due to the influence of the solid-phase nuclei is considered. It is shown that the introduction of the parameter phi, equal to the specific volume occupied by the nuclei of the solid phase, together with psi provides a natural explanation of the temperature dependence of density and thermal expansion coefficients of glycerol in its liquid, solid amorphous, glassy, and crystal states. The peculiarities of the temperature dependence of phi(T) and psi(T) for glycerol and o-terphenyl are compared.
RANDOM TIMES TRANSFORMATION OF PROCESSES WITH MARKOV SKELETON%Markov 骨架过程的随机时变换
Institute of Scientific and Technical Information of China (English)
刘万荣; 刘再明; 侯振挺
2000-01-01
In this paper, random time transformations of processes with Markov skeleton are discussed. A class of random time transformations that transform a process with Markov skeleton into a process with Markov skeleton is given.%讨论了 Markov 骨架过程的随机时变换,给出了一类变换 Markov 骨架过程为Markov 骨架过程的随机时变换.
Numerical methods in Markov chain modeling
Philippe, Bernard; Saad, Youcef; Stewart, William J.
1989-01-01
Several methods for computing stationary probability distributions of Markov chains are described and compared. The main linear algebra problem consists of computing an eigenvector of a sparse, usually nonsymmetric, matrix associated with a known eigenvalue. It can also be cast as a problem of solving a homogeneous singular linear system. Several methods based on combinations of Krylov subspace techniques are presented. The performance of these methods on some realistic problems are compared.
Finite State Transducers Approximating Hidden Markov Models
Kempe, A
1999-01-01
This paper describes the conversion of a Hidden Markov Model into a sequential transducer that closely approximates the behavior of the stochastic model. This transformation is especially advantageous for part-of-speech tagging because the resulting transducer can be composed with other transducers that encode correction rules for the most frequent tagging errors. The speed of tagging is also improved. The described methods have been implemented and successfully tested on six languages.
Shift ergodicity for stationary Markov processes
Institute of Scientific and Technical Information of China (English)
CHEN; Jinwen(
2001-01-01
［1］Liggett, T. M., Interacting Particle Systems, New York: Springer-Verlag, 1985.［2］Andjel, E. D., Ergodic and mixing properties of equilibrium measures for Markov processes, Trans. of the AMS, 1990, 318:601－614.［3］Franchi, J., Asymptotic windings of ergodic diffusion, Stoch. Processes Appl., 1996, 62: 277－298.［4］Golden, K. , Goldstein, S., Lebowitz, J. L., Nash estimates and the asymptotic behavior of diffusion, Ann. Prob., 1988,16: 1127－1146.［5］Gordin. M. I., Lifsic, B. A. , The central limit theorem for stationary ergodic Markov process, Dokl, Akad. Nauk SSSR,1978, 19: 392－393.［6］Orey, S., Large deviations in ergodic theory, Seminar on Stochastic Processes, 1985, 12: 195－249.［7］Veretenikov, A. Y., On large deviations for ergodic process empirical measures, Adv. Sov. Math., 1992, 12: 125－133.［8］Deuschel, J. D., Stroock, D. W., Large Deviations, San Diego, CA: Academic Press, 1989.［9］Rosenblatt, M., Markov Processes, Structure and Asymptotic Behavior, Berlin: Springer-Verlag, 1971.［10］Liggett, T. M., Stochastic Interacting Systems: Contact, Voter, and Exclusion Processes, Berlin: Springer-Verlag, 1999.［11］Albevrio, S., Kondratiev, Y. G., Rockner, M., Ergodicity of L2-semigroups and extremality of Gibbs states, J. Funct.Anal. , 1997, 144: 293－423.［12］Liverani, C. , Olla, S. , Ergodicity in infinite Hamiltonian systems with conservative noise, Probab. Th. Rel. Fields, 1996,106: 401－445.［13］Varadhan, S. P. S., Large Deviations and Applications, Philadelphia: SIAM, 1984.［14］Chen, J. W. , A variational principle for Markov processes, J. Stat. Phys. , 1999, 96: 1359－1364.
Modelling the Heterogeneous Markov Attrition Process .
Directory of Open Access Journals (Sweden)
Jau Yeu Menq
1993-01-01
Full Text Available A model for heterogeneous dynamics combat as a continuos-time Markov process has been studied, and on account of the special form of its infinitesimal generator, recursive algorithms are derived to compute the important characteristics of the combat, such as the combat time distribution, expected value and variance, and the probability of winning and expected survivors. Numerical results are also presented. This approach can also be used to consider initial contact forces of both sides as random variables.
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.
Nonlinear Markov Control Processes and Games
2012-11-15
further research we indicated possible extensions to state spaces with nontrivial geometry, to the controlled nonlinear quantum dynamic semigroups and...space nonlinear Markov semigroup is a one-parameter semigroup of (possibly nonlinear) transformations of the unit simplex in n-dimensional Euclidean...certain mixing property of nonlinear transition probabilities. In case of the semigroup parametrized by continuous time one defines its generator as the
Metastability for Markov processes with detailed balance.
Larralde, Hernán; Leyvraz, François
2005-04-29
We present a definition for metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance. In particular, we identify a crucial condition that distinguishes metastable states from other slow decaying modes and which allows us to show that our definition has several desirable properties similar to those postulated in the restricted ensemble approach. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible.
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.
Metrics for Finite Markov Decision Processes
Ferns, Norman; Panangaden, Prakash; Precup, Doina
2012-01-01
We present metrics for measuring the similarity of states in a finite Markov decision process (MDP). The formulation of our metrics is based on the notion of bisimulation for MDPs, with an aim towards solving discounted infinite horizon reinforcement learning tasks. Such metrics can be used to aggregate states, as well as to better structure other value function approximators (e.g., memory-based or nearest-neighbor approximators). We provide bounds that relate our metric distances to the opti...
Online Learning in Discrete Hidden Markov Models
Alamino, Roberto C.; Caticha, Nestor
2007-01-01
We present and analyse three online algorithms for learning in discrete Hidden Markov Models (HMMs) and compare them with the Baldi-Chauvin Algorithm. Using the Kullback-Leibler divergence as a measure of generalisation error we draw learning curves in simplified situations. The performance for learning drifting concepts of one of the presented algorithms is analysed and compared with the Baldi-Chauvin algorithm in the same situations. A brief discussion about learning and symmetry breaking b...
Application of Markov Chains to Stock Trends
Directory of Open Access Journals (Sweden)
Kevin J. Doubleday
2011-01-01
Full Text Available Problem statement: Modeling of the Dow Jones Industrial Average is frequently attempted in order to determine trading strategies with maximum payoff. Changes in the DJIA are important since movements may affect both individuals and corporations profoundly. Previous work showed that modeling a market as a random walk was valid and that a market may be viewed as having the Markov property. Approach: The aim of this research was to determine the relationship between a diverse portfolio of stocks and the market as a whole. To that end, the DJIA was analyzed using a discrete time stochastic model, namely a Markov Chain. Two models were highlighted, where the DJIA was considered as being in a state of (1 gain or loss and (2 small, moderate, or large gain or loss. A portfolio of five stocks was then considered and two models of the portfolio much the same as those for the DJIA. These models were used to obtain transitional probabilities and steady state probabilities. Results: Our results indicated that the portfolio behaved similarly to the entire DJIA, both in the simple model and the partitioned model. Conclusion: When treated as a Markov process, the entire market was useful in gauging how a diverse portfolio of stocks might behave. Future work may include different classifications of states to refine the transition matrices.
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.
The Violation of Stokes-Einstein Relation in Supercooled Water
Chen, Sow-Hsin; Mallamace, Francesco; Mou, Chung-Yuan; Broccio, Matteo; Corsaro, Carmelo; Faraone, Antonio; Liu, Li
2006-01-01
By confining water in nanopores, so narrow that the liquid cannot freeze, it is possible to explore its properties well below its homogeneous nucleation temperature TH ~ 235 K. In particular, the dynamical parameters of water can be measured down to 180 K approaching the suggested glass transition temperature Tg ~ 165 K. Here we present experimental evidence, obtained from Nuclear Magnetic Resonance and Quasi-Elastic Neutron Scattering spectroscopies, of a well defined decoupling of transport...
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.
Molecular kinetics of solid and liquid CHCl$_3$
Caballero, Nirvana B; Carignano, Marcelo A; Serra, Pablo
2013-01-01
We present a detailed analysis of the molecular kinetics of CHCl$_3$ in a range of temperatures covering the solid and liquid phases. Using nuclear quadrupolar resonance we determine the relaxation times for the molecular rotations in solid at pre-melting conditions. Molecular dynamics simulations are used to characterize the rotational dynamics in the solid and liquid phases and to study the local structure of the liquid in terms of the molecular relative orientations. We find that in the pre-melting regime the molecules rotate about the C-H bond, but the rotations are isotropic in the liquid, even at supercooled conditions.
Markov invariants, plethysms, and phylogenetics (the long version)
Sumner, J G; Jermiin, L S; Jarvis, P D
2008-01-01
We explore model based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we establish a commonality in some special cases. We show that the simplest Markov invariant forms the foundation of the Log-Det distance measure. We take as our primary tool group representation theory, and show that it provides a general framework for analysing Markov processes on trees. From this algebraic perspective, the inherent symmetries of these processes become apparent, and focusing on plethysms, we are able to define Markov invariants and give existence proofs. We give an explicit technique for constructing the invariants, valid for any number of character states and taxa. For phylogenetic trees with three and four leaves, we demonstrate that the corresponding Markov invariants can be fruitfully exploited in applied phylogenetic studies.
Dynamic Bandwidth Provisioning Using Markov Chain Based on RSVP
2013-09-01
Cambridge University Press,2008. [20] P. Bremaud, Markov Chains : Gibbs Fields, Monte Carlo Simulation and Queues, New York, NY, Springer Science...is successful. Qualnet, a simulation platform for the wireless environment is used to simulate the algorithm (integration of Markov chain ...in Qualnet, the simulation platform used. 16 THIS PAGE INTENTIONALLY LEFT BLANK 17 III. GENERAL DISCUSSION OF MARKOV CHAIN ALGORITHM AND RSVP
ADAPTIVE LEARNING OF HIDDEN MARKOV MODELS FOR EMOTIONAL SPEECH
Directory of Open Access Journals (Sweden)
A. V. Tkachenia
2014-01-01
Full Text Available An on-line unsupervised algorithm for estimating the hidden Markov models (HMM parame-ters is presented. The problem of hidden Markov models adaptation to emotional speech is solved. To increase the reliability of estimated HMM parameters, a mechanism of forgetting and updating is proposed. A functional block diagram of the hidden Markov models adaptation algorithm is also provided with obtained results, which improve the efficiency of emotional speech recognition.
Deteksi Fraud Menggunakan Metode Model Markov Tersembunyi Pada Proses Bisnis
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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%.
A molecular dynamics study on surface properties of supercooled water
Institute of Scientific and Technical Information of China (English)
Lü; Yongjun
2006-01-01
[1]Basu J K,Hazra S,Sanyal M K.Growth mechanism of Langmuir-Blodgett films.Phys Rev Lett,1999,82:4675-4678[2]Taylor R S,Shields R L.Molecular-dynamics simulations of the ethanol liquid-vapor interface.J Chem Phys,2003,119:12569-12576[3]Velev O D,Gurkov T D,Ivanov I B,et al.Abnormal thickness and stability of nonequilibrium liquid films.Phys Rev Lett,1995,75:264-267[4]Weng J G,Park S,Lukes J R,et al.Molecular dynamics investigation of thickness effect on liquid films.J Chem Phys,2000,113:5917-5923[5]Zakharov V V,Brodskaya E N,Laaksonen A.Surface tension of water droplets:A molecular dynamics study of model and size dependencies.J Chem Phys,1997,107:10675-10683[6]Wang J Z,Chen M,Guo Z Y.A two-dimensional molecular dynamics simulation of liquid-vapor nucleation.Chin Sci Bull,2003,48(7):623-626[7]Guissani Y,Guillot B.A computer simulation study of the liquid-vapor coexistence curve of water.J Chem Phys,1993,98:8221-8235[8]Wilson M A,Pohorille A,Pratt L R.Surface potential of the water liquid-vapor interface.J Chem Phys,1988,88:3281-3285[9]Alejandre J,Tildesley D J,Chapela G A.Molecular dynamics simulation of the orthobaric densities and surface tension of water.J Chem Phys,1995,102:4574-4583[10]Matsumoto M,Kataoka Y.Study on liquid-vapor interface of water (Ⅰ):Simulational results of thermodynamic properties and orientational structure.J Chem Phys,1988,88:3233-3245[11]Floriano M A,Angell C A.Surface tension and molar surface free energy and entropy of water to-27.2℃.J Phys Chem,1990,94:4199-4202[12]Jorgensen W L,Chandrasekhar J,Madura J D.Comparison of simple potential functions for simulating liquid water.J Chem Phys,1993,79:926-935[13]Berendsen H J C,Grigera J R,Straatsma T P.The missing term in effective pair potentials.J Phys Chem,1987,91:6269-6271[14]Arbuckle B W,Clancy P.Effects of the Ewald sum on the free energy of the extended simple point charge model for water.J Chem Phys,2002,116:5090-5098[15]Tarazona P,Chacon E,Reinaldo-Falagan M,et al
Structure and thermal expansion of liquid bismuth
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Mudry S.
2015-12-01
Full Text Available Experimental structural data for liquid Bi were used for estimation of the main structure parameters as well as the thermal expansion coefficient both in supercooled and superheated temperature ranges. It was shown that the equilibrium melt had a positive thermal expansion coefficient within a temperature range upon melting and a negative one at higher temperatures. The former was related to structure changes upon melting, whereas the latter with topologic disordering upon further heating. It was found that the superheated melt had a negative thermal expansion coefficient. The results obtained from structural data were compared with the thermal expansion coefficient calculated from the data of density for liquid Bi.
Directory of Open Access Journals (Sweden)
R.J. Boys
2002-01-01
Full Text Available This paper describes a Bayesian approach to determining the order of a finite state Markov chain whose transition probabilities are themselves governed by a homogeneous finite state Markov chain. It extends previous work on homogeneous Markov chains to more general and applicable hidden Markov models. The method we describe uses a Markov chain Monte Carlo algorithm to obtain samples from the (posterior distribution for both the order of Markov dependence in the observed sequence and the other governing model parameters. These samples allow coherent inferences to be made straightforwardly in contrast to those which use information criteria. The methods are illustrated by their application to both simulated and real data sets.
Supercooling transition in phase separated manganite thin films: An electrical transport study
Singh, Sandeep; Kumar, Pawan; Siwach, P. K.; Tyagi, Pawan Kumar; Singh, H. K.
2014-05-01
The impact of variation in the relative fractions of the ferromagnetic metallic and antiferromagnetic/charge ordered insulator phases on the supercooling/superheating transition in strongly phase separated system, La5/8-yPryCa3/8MnO3 (y ≈ 0.4), has been studied employing magnetotransport measurements. Our study clearly shows that the supercooling transition temperature is non-unique and strongly depends on the magneto-thermodynamic path through which the low temperature state is accessed. In contrast, the superheating transition temperature remains constant. The thermo-magnetic hysteresis, the separation of the two transitions and the associated resistivity, all are functions of the relative fraction of the coexisting phases.
Study on Supercooling Point and Freezing Point in Floral Organs of Apricot
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Under the environment of an artificial climate chamber, supercooling point (SCP) and freezing point (FP) in flower and young fruit at different development stages and freezing injuries of floral organs were studied. The apricot cultivars tested were Kety, Golden Sun and Honghebao. With the development of flower buds, SCP and FP increased, which indicated that their cold resistance decreased. SCP and FP varied with different floral organs. For different apricot cultivars, it was found that, the lower SCP or FP in floral organs was, the more resistant capacity the cultivar had, and the larger the temperature interval from SCP to FP was. SCP was not a constant value, but a range. Frequency distribution of SCP in petals was more dispersing than that in stamens and pistils. Floral organs could maintain a supercooling state to avoid ice formation, but they were sensitive to freezing. Once floral organs froze, they turned brown after thawing.
The water supercooled regime as described by four common water models
Malaspina, David C; Pereyra, Rodolfo G; Szleifer, Igal; Carignano, Marcelo A
2013-01-01
The temperature scale of simple water models in general does not coincide with the natural one. Therefore, in order to make a meaningful evaluation of different water models a temperature rescaling is necessary. In this paper we introduce a rescaling using the melting temperature and the temperature corresponding to the maximum of the heat capacity to evaluate four common water models (TIP4P-Ew, TIP4P-2005, TIP5P-Ew and Six-Sites) in the supercooled regime. Although all the models show the same general qualitative behavior, the TIP5P-Ew appears as the best representation of the supercooled regime when the rescaled temperature is used. We also analyze, using thermodynamic arguments, the critical nucleus size for ice growth. Finally, we speculate on the possible reasons why atomistic models do not usually crystalize while the coarse grained mW model do crystallize.
Quark-gluon plasma freeze-out from a supercooled state?
Csörgö, T
1994-01-01
The quark-gluon plasma, formed in the first 3 fm/c of the heavy ion collisions at RHIC and LHC, supercooles due to nucleation and develops soon a negative pressure in the bag model. The negative pressure yields mechanical instability which may lead to a sudden timelike deflagration to a (super)heated hadron gas. The resulting freeze-out times are shorter than those of the standard nucleation scenario.
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....
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......The primary structure of a protein is the sequence of its amino acids. The secondary structure describes structural properties of the molecule such as which parts of it form sheets, helices or coils. Spacial and other properties are described by the higher order structures. The classification task...
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...
Hybrid Discrete-Continuous Markov Decision Processes
Feng, Zhengzhu; Dearden, Richard; Meuleau, Nicholas; Washington, Rich
2003-01-01
This paper proposes a Markov decision process (MDP) model that features both discrete and continuous state variables. We extend previous work by Boyan and Littman on the mono-dimensional time-dependent MDP to multiple dimensions. We present the principle of lazy discretization, and piecewise constant and linear approximations of the model. Having to deal with several continuous dimensions raises several new problems that require new solutions. In the (piecewise) linear case, we use techniques from partially- observable MDPs (POMDPS) to represent value functions as sets of linear functions attached to different partitions of the state space.
Dynamic system evolution and markov chain approximation
Directory of Open Access Journals (Sweden)
Roderick V. Nicholas Melnik
1998-01-01
Full Text Available In this paper computational aspects of the mathematical modelling of dynamic system evolution have been considered as a problem in information theory. The construction of mathematical models is treated as a decision making process with limited available information.The solution of the problem is associated with a computational model based on heuristics of a Markov Chain in a discrete space–time of events. A stable approximation of the chain has been derived and the limiting cases are discussed. An intrinsic interconnection of constructive, sequential, and evolutionary approaches in related optimization problems provides new challenges for future work.
Performance sensitivities for parameterized Markov systems
Institute of Scientific and Technical Information of China (English)
Xiren CAO; Junyu ZHANG
2004-01-01
It is known that the performance potentials (or equivalently, perturbation realization factors) can be used as building blocks for performance sensitivities of Markov systems. In parameterized systems, the changes in parameters may only affect some states, and the explicit transition probability matrix may not be known. In this paper, we use an example to show that we can use potentials to construct performance sensitivities in a more flexible way; only the potentials at the affected states need to be estimated, and the transition probability matrix need not be known. Policy iteration algorithms, which are simpler than the standard one, can be established.
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.
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...... continuity properties for such distances are identified. We then establish a number of results that show that these two properties are in conflict, and not simultaneously fulfilled by any of our candidate natural distance functions. An impossibility result is derived that explains to some extent...
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.
Gaussian Markov random fields theory and applications
Rue, Havard
2005-01-01
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studies and, online, a c-library for fast and exact simulation. With chapters contributed by leading researchers in the field, this volume is essential reading for statisticians working in spatial theory and its applications, as well as quantitative researchers in a wide range of science fields where spatial data analysis is important.
Markov chains with quasitoeplitz transition matrix: applications
1990-01-01
Application problems are investigated for the Markov chains with quasitoeplitz transition matrix. Generating functions of transient and steady state probabilities, first zero hitting probabilities and mean times are found for various particular cases, corresponding to some known patterns of feedback ( warm-up, switch at threshold etc.), Level depending dams and queue-depending queueing systems of both M/G/1 and MI/G/1 types with arbitrary random sizes of arriving and departing groups are ...
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.
Kaminska, E.; Kaminski, K.; Paluch, M.; Ngai, K. L.
2006-04-01
Dielectric loss spectra of two glass-forming isomers, eugenol and isoeugenol, measured at ambient and elevated pressures in the normal liquid, supercooled, and glassy states are presented. The isomeric chemical compounds studied differ only by the location of the double bond in the alkyl chain. Above the glass transition temperature Tg, the dielectric loss spectra of both isomers exhibit an excess wing on the high frequency flank of the loss peak of the α relaxation and an additional faster γ process at the megahertz frequency range. By decreasing temperature below Tg at ambient pressure or by elevating pressure above Pg, the glass transition pressure, at constant temperature, the excess wing of isoeugenol shifts to lower frequencies and is transformed into a secondary β-loss peak, while in eugenol it becomes a shoulder. These spectral features enable the β-relaxation time τβ to be determined in the glassy state. These changes indicate that the excess wings in isoeugenol and eugenol are similar and both are secondary β relaxations that are not resolved in the liquid state. While in both isoeugenol and eugenol the loss peak of the β relaxation in the glassy state and the corresponding excess wing in the liquid state shifts to lower frequencies on elevating pressure, the locations of their γ relaxation show little change with increasing pressure. The different pressure sensitivities of the excess wing and γ relaxation are further demonstrated by the nearly perfect superposition of the α-loss peak together with excess wing from the data taken at ambient pressure and at elevated pressure (and higher temperature so as to have the same α-peak frequency), but not the γ-loss peak in both isoeugenol and eugenol. On physical aging isoeugenol, the β-loss peak shifts to lower frequencies, but not the γ relaxation. Basing on these experimental facts, the faster γ relaxation is a local intramolecular process involving a side group and the slower β relaxation
Perspective on the structure of liquid water
Energy Technology Data Exchange (ETDEWEB)
Nilsson, A., E-mail: nilsson@slac.stanford.edu [Stanford Synchrotron Radiation Lightsource, P.O. Box 20450, Stanford, CA 94309 (United States); Department of Physics, AlbaNova University Center, Stockholm University, S-106 91 Stockholm (Sweden); Pettersson, L.G.M. [Department of Physics, AlbaNova University Center, Stockholm University, S-106 91 Stockholm (Sweden)
2011-11-07
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: Black-Right-Pointing-Pointer Two components maximizing either enthalpy (tetrahedral, low-density) or entropy (non-specific H-bonding, higher density). Black-Right-Pointing-Pointer Interconvert discontinuously and ratio depends on temperature. Black-Right-Pointing-Pointer Density fluctuations on 1 nm length scale. Black-Right-Pointing-Pointer Increasing size in supercooled region. Black-Right-Pointing-Pointer 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
The Laplace Functional and Moments for Markov Branching Chains in Random Environments
Institute of Scientific and Technical Information of China (English)
HU Di-he; ZHANG Shu-lin
2005-01-01
The concepts of random Markov matrix, Markov branching chain in random environment (MBCRE) and Laplace functional of Markov branching chain in random environment (LFMBCRE) are introduced. The properties of LFMBCRE and the explicit formulas of moments of MBCRE are given.
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.
Stochastic seismic tomography by interacting Markov chains
Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe
2016-10-01
Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches, they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high-dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case, the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on importance resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non-linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper, the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a simulated annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet-based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.
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.
Remarks on a monotone Markov chain
Directory of Open Access Journals (Sweden)
P. Todorovic
1987-01-01
Full Text Available In applications, considerations on stochastic models often involve a Markov chain {ζn}0∞ with state space in R+, and a transition probability Q. For each x R+ the support of Q(x,. is [0,x]. This implies that ζ0≥ζ1≥…. Under certain regularity assumptions on Q we show that Qn(x,Bu→1 as n→∞ for all u>0 and that 1−Qn(x,Bu≤[1−Q(x,Bu]n where Bu=[0,u. Set τ0=max{k;ζk=ζ0}, τn=max{k;ζk=ζτn−1+1} and write Xn=ζτn−1+1, Tn=τn−τn−1. We investigate some properties of the imbedded Markov chain {Xn}0∞ and of {Tn}0∞. We determine all the marginal distributions of {Tn}0∞ and show that it is asymptotically stationary and that it possesses a monotonicity property. We also prove that under some mild regularity assumptions on β(x=1−Q(x,Bx, ∑1n(Ti−a/bn→dZ∼N(0,1.
Markov transitions and the propagation of chaos
Energy Technology Data Exchange (ETDEWEB)
Gottlieb, Alexander David [Univ. of California, Berkeley, CA (United States)
1998-12-01
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 s how 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.
A Markov model of the Indus script.
Rao, Rajesh P N; Yadav, Nisha; Vahia, Mayank N; Joglekar, Hrishikesh; Adhikari, R; Mahadevan, Iravatham
2009-08-18
Although no historical information exists about the Indus civilization (flourished ca. 2600-1900 B.C.), archaeologists have uncovered about 3,800 short samples of a script that was used throughout the civilization. The script remains undeciphered, despite a large number of attempts and claimed decipherments over the past 80 years. Here, we propose the use of probabilistic models to analyze the structure of the Indus script. The goal is to reveal, through probabilistic analysis, syntactic patterns that could point the way to eventual decipherment. We illustrate the approach using a simple Markov chain model to capture sequential dependencies between signs in the Indus script. The trained model allows new sample texts to be generated, revealing recurring patterns of signs that could potentially form functional subunits of a possible underlying language. The model also provides a quantitative way of testing whether a particular string belongs to the putative language as captured by the Markov model. Application of this test to Indus seals found in Mesopotamia and other sites in West Asia reveals that the script may have been used to express different content in these regions. Finally, we show how missing, ambiguous, or unreadable signs on damaged objects can be filled in with most likely predictions from the model. Taken together, our results indicate that the Indus script exhibits rich synactic structure and the ability to represent diverse content. both of which are suggestive of a linguistic writing system rather than a nonlinguistic symbol system.
Stochastic seismic tomography by interacting Markov chains
Bottero, Alexis; Gesret, Alexandrine; Romary, Thomas; Noble, Mark; Maisons, Christophe
2016-07-01
Markov chain Monte Carlo sampling methods are widely used for non-linear Bayesian inversion where no analytical expression for the forward relation between data and model parameters is available. Contrary to the linear(ized) approaches they naturally allow to evaluate the uncertainties on the model found. Nevertheless their use is problematic in high dimensional model spaces especially when the computational cost of the forward problem is significant and/or the a posteriori distribution is multimodal. In this case the chain can stay stuck in one of the modes and hence not provide an exhaustive sampling of the distribution of interest. We present here a still relatively unknown algorithm that allows interaction between several Markov chains at different temperatures. These interactions (based on Importance Resampling) ensure a robust sampling of any posterior distribution and thus provide a way to efficiently tackle complex fully non linear inverse problems. The algorithm is easy to implement and is well adapted to run on parallel supercomputers. In this paper the algorithm is first introduced and applied to a synthetic multimodal distribution in order to demonstrate its robustness and efficiency compared to a Simulated Annealing method. It is then applied in the framework of first arrival traveltime seismic tomography on real data recorded in the context of hydraulic fracturing. To carry out this study a wavelet based adaptive model parametrization has been used. This allows to integrate the a priori information provided by sonic logs and to reduce optimally the dimension of the problem.
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...
On Chebyshev-Markov rational functions over several intervals
Lukashov, AL
1998-01-01
Chebyshev-Markov rational functions are the solutions of the following extremal problem [GRAPHICS] with K being a compact subset of R and omega(n)(x) being a fixed real polynomial of degree less than n, positive on K. A parametric representation of Chebyshev-Markov rational functions is found for K
Extending Markov Automata with State and Action Rewards
Guck, Dennis; Timmer, Mark; Blom, Stefan; Bertrand, N.; Bortolussi, L.
2014-01-01
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 acqu
Compositional Modeling and Minimization of Time-Inhomogeneous Markov Chains
Han, T.; Katoen, J.P.; Mereacre, A.
2008-01-01
This paper presents a compositional framework for the modeling of interactive continuous-time Markov chains with time-dependent rates, a subclass of communicating piecewise deterministic Markov processes. A poly-time algorithm is presented for computing the coarsest quotient under strong bisimulatio
On Equalities for BLUEs under Misspecified Gauss-Markov Models
Institute of Scientific and Technical Information of China (English)
Yong Ge TIAN
2009-01-01
This paper studies relationships between the best linear unbiased estimators (BLUEs) of an estimable parametric functions Kβ under the Gauss-Markov model {y, Xβ, σ~22∑} and its misspecified model {y, X_0β, σ~2∑_0}. In addition, relationships between BLUEs under a restricted Ganss-Markov model and its misspecified model are also investigated.
Performance evaluation:= (process algebra + model checking) x Markov chains
Hermanns, H.; Katoen, J.P.; Larsen, Kim G.; Nielsen, Mogens
2001-01-01
Markov chains are widely used in practice to determine system performance and reliability characteristics. The vast majority of applications considers continuous-time Markov chains (CTMCs). This tutorial paper shows how successful model specification and analysis techniques from concurrency theory c
Series Expansions for Finite-State Markov Chains
Heidergott, Bernd; Hordijk, Arie; Uitert, van Miranda
2005-01-01
This paper provides series expansions of the stationary distribution of a finite Markov chain. This leads to an efficient numerical algorithm for computing the stationary distribution of a finite Markov chain. Numerical examples are given to illustrate the performance of the algorithm.
Lifting—A nonreversible Markov chain Monte Carlo algorithm
Vucelja, Marija
2016-12-01
Markov chain Monte Carlo algorithms are invaluable tools for exploring stationary properties of physical systems, especially in situations where direct sampling is unfeasible. Common implementations of Monte Carlo algorithms employ reversible Markov chains. Reversible chains obey detailed balance and thus ensure that the system will eventually relax to equilibrium, though detailed balance is not necessary for convergence to equilibrium. We review nonreversible Markov chains, which violate detailed balance and yet still relax to a given target stationary distribution. In particular cases, nonreversible Markov chains are substantially better at sampling than the conventional reversible Markov chains with up to a square root improvement in the convergence time to the steady state. One kind of nonreversible Markov chain is constructed from the reversible ones by enlarging the state space and by modifying and adding extra transition rates to create non-reversible moves. Because of the augmentation of the state space, such chains are often referred to as lifted Markov Chains. We illustrate the use of lifted Markov chains for efficient sampling on several examples. The examples include sampling on a ring, sampling on a torus, the Ising model on a complete graph, and the one-dimensional Ising model. We also provide a pseudocode implementation, review related work, and discuss the applicability of such methods.
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...
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....
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...
Energy Technology Data Exchange (ETDEWEB)
Kalampounias, A. G., E-mail: angelos@chemeng.upatras.gr [Department of Chemistry, University of Ioannina, GR-45110 Ioannina (Greece); Institute of Chemical Engineering Sciences (FORTH-ICE/HT), Foundation for Research and Technology Hellas, P.O. Box 1414, GR-26504 Patras (Greece); Tsilomelekis, G.; Boghosian, S. [Department of Chemical Engineering, University of Patras, P.O. Box 1414, GR-26504 Patras (Greece); Institute of Chemical Engineering Sciences (FORTH-ICE/HT), Foundation for Research and Technology Hellas, P.O. Box 1414, GR-26504 Patras (Greece)
2015-04-21
Polarized (VV) and depolarized (VH) Raman spectra are obtained for glassy, supercooled, and molten TeO{sub 2} at temperatures up to 1000 K in order to elucidate the temperature evolution of the pertinent structural and vibrational properties. The intrinsic tendency of the system for crystallization is avoided by means of a newly applied protocol, thereby enabling the recording of Raman spectra of pure TeO{sub 2} on going from the molten to the supercooled liquid and to the room temperature glass states. Following an appropriate fitting procedure, the revealed bands are assigned to specific modes of structural polymorphs. A weak polarised band at ∼880 cm{sup −1} is assigned to Te=O terminal stretching in agreement with the literature ab initio molecular orbital calculations. Subtle changes to the relative band intensities within the 550-900 cm{sup −1} stretching region are caused by temperature increase. The network-like structure of the glass/melt is composed by TeO{sub 4} trigonal bipyramid and TeO{sub 3} trigonal pyramid units. With increasing temperature, TeO{sub 4} units convert to TeO{sub 3} units with a concurrent increase in the number of Te=O sites resulting from cleavages within the network structure. The fraction of such terminal oxygen atoms has been directly estimated from the spectroscopic data. The relative populations of the basic building blocks and the average number of O atoms around Te have been estimated for a wide temperature range directly from the Raman spectra, implying a gradual transformation of TeO{sub 4/2} to TeO{sub 2/2}(= O) trigonal pyramid units. The results are discussed in the context of the current phenomenological and theoretical status of the field.
Optical Kerr effect of liquid water: a new insight into the vibrational and structural dynamics
Taschin, A; Eramo, R; Righini, R; Torre, R
2013-01-01
The liquid and supercooled states of water show a series of anomalies whose nature is lively debated. A key role is attributed to the formation of structural aggregations induced by critical phenomena occurring deep in the supercooled region, not experimentally accessible for bulk water. This explain why, despite the numerous experimental investigations, the nature of water anomalies and the hidden critical processes remain elusive. Here we present a time-resolved optical Kerr effect investigation of the vibrational and relaxation processes in supercooled bulk water. The experiment measures the water intermolecular vibrations and the structural relaxation process in an extended temperature range, and with unpreceded data quality. A mode-coupling analysis of the experimental data allows the characterization of the intermolecular vibrational modes and of their interplay with the structural relaxation process.
Mori-Zwanzig theory for dissipative forces in coarse-grained dynamics in the Markov limit
Izvekov, Sergei
2017-01-01
We derive alternative Markov approximations for the projected (stochastic) force and memory function in the coarse-grained (CG) generalized Langevin equation, which describes the time evolution of the center-of-mass coordinates of clusters of particles in the microscopic ensemble. This is done with the aid of the Mori-Zwanzig projection operator method based on the recently introduced projection operator [S. Izvekov, J. Chem. Phys. 138, 134106 (2013), 10.1063/1.4795091]. The derivation exploits the "generalized additive fluctuating force" representation to which the projected force reduces in the adopted projection operator formalism. For the projected force, we present a first-order time expansion which correctly extends the static fluctuating force ansatz with the terms necessary to maintain the required orthogonality of the projected dynamics in the Markov limit to the space of CG phase variables. The approximant of the memory function correctly accounts for the momentum dependence in the lowest (second) order and indicates that such a dependence may be important in the CG dynamics approaching the Markov limit. In the case of CG dynamics with a weak dependence of the memory effects on the particle momenta, the expression for the memory function presented in this work is applicable to non-Markov systems. The approximations are formulated in a propagator-free form allowing their efficient evaluation from the microscopic data sampled by standard molecular dynamics simulations. A numerical application is presented for a molecular liquid (nitromethane). With our formalism we do not observe the "plateau-value problem" if the friction tensors for dissipative particle dynamics (DPD) are computed using the Green-Kubo relation. Our formalism provides a consistent bottom-up route for hierarchical parametrization of DPD models from atomistic simulations.
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...
An extensive Markov system for ECG exact coding.
Tai, S C
1995-02-01
In this paper, an extensive Markov process, which considers both the coding redundancy and the intersample redundancy, is presented to measure the entropy value of an ECG signal more accurately. It utilizes the intersample correlations by predicting the incoming n samples based on the previous m samples which constitute an extensive Markov process state. Theories of the extensive Markov process and conventional n repeated applications of m-th order Markov process are studied first in this paper. After that, they are realized for ECG exact coding. Results show that a better performance can be achieved by our system. The average code length for the extensive Markov system on the second difference signals was 2.512 b/sample, while the average Huffman code length for the second difference signals was 3.326 b/sample.
Schirò, Giorgio; Fomina, Margarita; Cupane, Antonio
2013-09-01
In this work, we compare experimental data on myoglobin hydrated powders from elastic neutron scattering, broadband dielectric spectroscopy, and differential scanning calorimetry. Our aim is to obtain new insights on the connection between the protein dynamical transition, a fundamental phenomenon observed in proteins whose physical origin is highly debated, and the liquid-liquid phase transition (LLPT) possibly occurring in protein hydration water and related to the existence of a low temperature critical point in supercooled water. Our results provide a consistent thermodynamic/dynamic description which gives experimental support to the LLPT hypothesis and further reveals how fundamental properties of water and proteins are tightly related.
ON SHARP MARKOV PROPERTY OF TWO-PARAMETER MARKOV PROCESSES%两参数Markov过程的Sharp Markov性
Institute of Scientific and Technical Information of China (English)
陈雄
2011-01-01
It is proven that for two-parameter Markov processes, only when they are the finite or countable unions of rectangles, will they show Sharp Markov property.%证明了两参数Markov过程仅在正位矩形的有限并或可列并区域上才具有Sharp Markov性.
Structural evolution in Ni-Nb and Ni-Nb-Ta liquids and glasses - A measure of liquid fragility?
Energy Technology Data Exchange (ETDEWEB)
Mauro, N. A.; Johnson, M. L.; Bendert, J. C.; Kelton, K. F. [WU
2013-01-07
The structures of Ni_{59.5}Nb_{40.5}, Ni_{62}Nb_{38}, and Ni_{60}Nb_{30}Ta_{10} liquids and glasses were studied using synchrotron high-energy X-ray diffraction. To avoid reactions between the liquids and their containers and to deeply supercool them below their equilibrium liquidus temperatures, the liquids were processed without a container using the beamline electrostatic levitation (BESL) technique. The total static structure factor, S(q), and the total pair-correlation function, g(r), were obtained for all liquid compositions over a temperature range of approximately 250 °C; S(q) and g(r) were measured for the corresponding glasses at room temperature. All of the S(q)s have a shoulder on the high-q side of the second peak; this becomes more pronounced as the liquid is supercooled, and is most prominent in the glass. Based on a Honeycutt–Andersen analysis of the atomic configurations obtained from Reverse Monte Carlo fits to the total structure factors obtained from the scattering data, icosahedral short-range order (ISRO) is dominant in all liquids and becomes particularly pronounced in the glasses. No correlation is noted, however, between the amount of ISRO and easy glass formability. Structural features show evidence for an acceleration of ordering in the supercooled liquid above the glass transition temperature, consistent with the behavior expected for fragile liquids. This suggests that scattering data can provide a new method to assess liquid fragility, which is typically obtained from the temperature behavior of the viscosity near the glass transition temperature.
Knopf, D. A.; Koop, T.; Weers, U. G.; Krieger, U. K.; Peter, T.
2001-12-01
Sulfuric acid and ammonium sulfate aerosol particles can serve as ice condensation nuclei for the formation of upper tropospheric cirrus clouds. These clouds influence the global radiation budget by scattering of short wavelength (solar) radiation as well as by absorbing long wavelength (terrestrial) radiation. Knowledge of the thermodynamics and the nucleation rates of aerosols is fundamental for the understanding of formation processes of cirrus clouds. Here, we present a new investigation tool to observe phase transitions of aerosols supercooled with respect to ice. Confocal Raman microscopy is used to determine the phase changes and the morphology of the particles. Raman spectroscopy is employed to distinguish and to characterize the different phases inside the frozen particles. Single droplets with a diameter of typically 20-120 μ m are deposited on a hydrophobically coated Herasil-plate that is covered by a spacer and another plate. Since the gas phase volume of the cell is small compared to the liquid droplet volume the composition of the droplets remains fixed during temperature changes. The temperature of the droplets can be varied between 150-350~K. We present the first Raman spectra of aqueous H2SO4/H2O and (NH4)2SO4/H2O droplets for several concentrations and temperatures to the homogeneous ice nucleation limits. The analysis of the speciation of the components inside the droplets (e.g. sulfate vs. bisulfate ions) is compared to results from thermodynamic models. Evaluation of the freezing data gives upper limits for ice nucleation rates of droplets as a function of sulfuric acid or ammonium sulfate concentration.
Energy Technology Data Exchange (ETDEWEB)
Li, Y.D., E-mail: ydli@ustc.edu [School of Physics and Material Science, Anhui University, Hefei 230039 (China); Lu, Q.L. [School of Physics and Material Science, Anhui University, Hefei 230039 (China); Wang, C.C., E-mail: ccwang@ahu.edu.cn [School of Physics and Material Science, Anhui University, Hefei 230039 (China); Huang, S.G. [School of Physics and Material Science, Anhui University, Hefei 230039 (China); Liu, C.S. [Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of Sciences, P. O. Box 1129, Hefei 230031 (China)
2013-01-01
Based on the second-moment approximation of tight-binding scheme, constant-pressure molecular dynamics simulations are performed for liquid Cu during the glass transition under different pressures. By means of pair analysis technique and bond orientational order analysis we find that the dominant bond pairs are those related to fcc and hcp crystalline order not those representing icosahedral short-range order (ISRO) when the systems enter into glass transition region. Although these two kinds of bond pairs compete with each other, the system tends towards a mixture of crystalline bond pairs during glass formation. The effect on various bond pairs brought about by higher pressure is much less for liquids than for glasses. The experimental observation of a shoulder on the second peak of the structure factor for supercooled liquids might not merely attribute to ISRO, since supercooled liquid Cu exhibits such a shoulder, but does not display an enhanced icosahedral symmetry.
Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation.
Stathopoulos, Vassilios; Girolami, Mark A
2013-02-13
Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.
Construction of Markov process with Markov resolvent on Lp(E,m)
Institute of Scientific and Technical Information of China (English)
董昭
1997-01-01
Lei E be a Hausdorff topological space and let A(E) be its Borel σ-field.Let m be a σ-finitc measure on (E,A(E)).A necessary and sufficient condition for a Markov resolvent on Lp(E,m ) to be associated with an m-tight m-special standard process (with state space E) is given.Furthermore some new examples which do not belong to the framework of Dirichlet space are also given.
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...... as a deterministic mean value using ordinary differential equations to which a random error is added. This thesis explores methods based on stochastic differential equations (SDEs) to extend the models to more adequately describe both true random biological variations and also variations due to unknown...... the individual in almost any thinkable way. This project focuses on measuring the eects on sleep in both humans and animals. The sleep process is usually analyzed by categorizing small time segments into a number of sleep states and this can be modelled using a Markov process. For this purpose new methods...
Synchronizing Objectives for Markov Decision Processes
Doyen, Laurent; Shirmohammadi, Mahsa; 10.4204/EPTCS.50.5
2011-01-01
We introduce synchronizing objectives for Markov decision processes (MDP). Intuitively, a synchronizing objective requires that eventually, at every step there is a state which concentrates almost all the probability mass. In particular, it implies that the probabilistic system behaves in the long run like a deterministic system: eventually, the current state of the MDP can be identified with almost certainty. We study the problem of deciding the existence of a strategy to enforce a synchronizing objective in MDPs. We show that the problem is decidable for general strategies, as well as for blind strategies where the player cannot observe the current state of the MDP. We also show that pure strategies are sufficient, but memory may be necessary.
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.
Transition-Independent Decentralized Markov Decision Processes
Becker, Raphen; Silberstein, Shlomo; Lesser, Victor; Goldman, Claudia V.; Morris, Robert (Technical Monitor)
2003-01-01
There has been substantial progress with formal models for sequential decision making by individual agents using the Markov decision process (MDP). However, similar treatment of multi-agent systems is lacking. A recent complexity result, showing that solving decentralized MDPs is NEXP-hard, provides a partial explanation. To overcome this complexity barrier, we identify a general class of transition-independent decentralized MDPs that is widely applicable. The class consists of independent collaborating agents that are tied up by a global reward function that depends on both of their histories. We present a novel algorithm for solving this class of problems and examine its properties. The result is the first effective technique to solve optimally a class of decentralized MDPs. This lays the foundation for further work in this area on both exact and approximate solutions.
NONLINEAR EXPECTATIONS AND NONLINEAR MARKOV CHAINS
Institute of Scientific and Technical Information of China (English)
PENG SHIGE
2005-01-01
This paper deals with nonlinear expectations. The author obtains a nonlinear generalization of the well-known Kolmogorov's consistent theorem and then use it to construct filtration-consistent nonlinear expectations via nonlinear Markov chains. Compared to the author's previous results, i.e., the theory of g-expectations introduced via BSDE on a probability space, the present framework is not based on a given probability measure. Many fully nonlinear and singular situations are covered. The induced topology is a natural generalization of Lp-norms and L∞-norm in linear situations.The author also obtains the existence and uniqueness result of BSDE under this new framework and develops a nonlinear type of von Neumann-Morgenstern representation theorem to utilities and present dynamic risk measures.
Markov chain approach to identifying Wiener systems
Institute of Scientific and Technical Information of China (English)
ZHAO WenXiao; CHEN HanFu
2012-01-01
Identification of the Wiener system composed of an infinite impulse response (IIR) linear subsystem followed by a static nonlinearity is considered.The recursive estimates for unknown coefficients of the linear subsystem and for the values of the nonlinear function at any fixed points are given by the stochastic approximation algorithms with expanding truncations (SAAWET).With the help of properties of the Markov chain connected with the linear subsystem,all estimates derived in the paper are proved to be strongly consistent.In comparison with the existing results on the topic,the method presented in the paper simplifies the convergence analysis and requires weaker conditions.A numerical example is given,and the simulation results are consistent with the theoretical analysis.
Estimation and uncertainty of reversible Markov models
Trendelkamp-Schroer, Benjamin; Paul, Fabian; Noé, Frank
2015-01-01
Reversibility is a key concept in the theory of Markov models, simplified kinetic models for the conforma- tion dynamics of molecules. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model relies 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.
Asymptotic Markov inequality on Jordan arcs
Totik, V.
2017-03-01
Markov's inequality for the derivative of algebraic polynomials is considered on C^2-smooth Jordan arcs. The asymptotically best estimate is given for the kth derivative for all k=1,2,\\dots . The best constant is related to the behaviour around the endpoints of the arc of the normal derivative of the Green's function of the complementary domain. The result is deduced from the asymptotically sharp Bernstein inequality for the kth derivative at inner points of a Jordan arc, which is derived from a recent result of Kalmykov and Nagy on the Bernstein inequality on analytic arcs. In the course of the proof we shall also need to reduce the analyticity condition in this last result to C^2-smoothness. Bibliography: 21 titles.
Boundary value problems and Markov processes
Taira, Kazuaki
1991-01-01
Focussing on the interrelations of the subjects of Markov processes, analytic semigroups and elliptic boundary value problems, this monograph provides a careful and accessible exposition of functional methods in stochastic analysis. The author studies a class of boundary value problems for second-order elliptic differential operators which includes as particular cases the Dirichlet and Neumann problems, and proves that this class of boundary value problems provides a new example of analytic semigroups both in the Lp topology and in the topology of uniform convergence. As an application, one can construct analytic semigroups corresponding to the diffusion phenomenon of a Markovian particle moving continuously in the state space until it "dies", at which time it reaches the set where the absorption phenomenon occurs. A class of initial-boundary value problems for semilinear parabolic differential equations is also considered. This monograph will appeal to both advanced students and researchers as an introductio...
Variable length Markov chains and dynamical sources
Cénac, Peggy; Paccaut, Frédéric; Pouyanne, Nicolas
2010-01-01
Infinite random sequences of letters can be viewed as stochastic chains or as strings produced by a source, in the sense of information theory. The relationship between Variable Length Markov Chains (VLMC) and probabilistic dynamical sources is studied. We establish a probabilistic frame for context trees and VLMC and we prove that any VLMC is a dynamical source for which we explicitly build the mapping. On two examples, the ``comb'' and the ``bamboo blossom'', we find a necessary and sufficient condition for the existence and the unicity of a stationary probability measure for the VLMC. These two examples are detailed in order to provide the associated Dirichlet series as well as the generating functions of word occurrences.
Compressed classification learning with Markov chain samples.
Cao, Feilong; Dai, Tenghui; Zhang, Yongquan; Tan, Yuanpeng
2014-02-01
In this article, we address the problem of compressed classification learning. A generalization bound of the support vector machines (SVMs) compressed classification algorithm with uniformly ergodic Markov chain samples is established. This bound indicates that the accuracy of the SVM classifier in the compressed domain is close to that of the best classifier in the data domain. In a sense, the fact that the compressed learning can avoid the curse of dimensionality in the learning process is shown. In addition, we show that compressed classification learning reduces the learning time at the price of decreasing the classification accuracy, but the decrement can be controlled. The numerical experiments further verify the results claimed in this article.
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.
Safe Exploration in Markov Decision Processes
Moldovan, Teodor Mihai
2012-01-01
In environments with uncertain dynamics exploration is necessary to learn how to perform well. Existing reinforcement learning algorithms provide strong exploration guarantees, but they tend to rely on an ergodicity assumption. The essence of ergodicity is that any state is eventually reachable from any other state by following a suitable policy. This assumption allows for exploration algorithms that operate by simply favoring states that have rarely been visited before. For most physical systems this assumption is impractical as the systems would break before any reasonable exploration has taken place, i.e., most physical systems don't satisfy the ergodicity assumption. In this paper we address the need for safe exploration methods in Markov decision processes. We first propose a general formulation of safety through ergodicity. We show that imposing safety by restricting attention to the resulting set of guaranteed safe policies is NP-hard. We then present an efficient algorithm for guaranteed safe, but pot...
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.
Probabilistic Resilience in Hidden Markov Models
Panerati, Jacopo; Beltrame, Giovanni; Schwind, Nicolas; Zeltner, Stefan; Inoue, Katsumi
2016-05-01
Originally defined in the context of ecological systems and environmental sciences, resilience has grown to be a property of major interest for the design and analysis of many other complex systems: resilient networks and robotics systems other the desirable capability of absorbing disruption and transforming in response to external shocks, while still providing the services they were designed for. Starting from an existing formalization of resilience for constraint-based systems, we develop a probabilistic framework based on hidden Markov models. In doing so, we introduce two new important features: stochastic evolution and partial observability. Using our framework, we formalize a methodology for the evaluation of probabilities associated with generic properties, we describe an efficient algorithm for the computation of its essential inference step, and show that its complexity is comparable to other state-of-the-art inference algorithms.
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.
Binary hidden Markov models and varieties
Critch, Andrew J
2012-01-01
The technological applications of hidden Markov models have been extremely diverse and successful, including natural language processing, gesture recognition, gene sequencing, and Kalman filtering of physical measurements. HMMs are highly non-linear statistical models, and just as linear models are amenable to linear algebraic techniques, non-linear models are amenable to commutative algebra and algebraic geometry. This paper examines closely those HMMs in which all the random variables, called nodes, are binary. Its main contributions are (1) minimal defining equations for the 4-node model, comprising 21 quadrics and 29 cubics, which were computed using Gr\\"obner bases in the cumulant coordinates of Sturmfels and Zwiernik, and (2) a birational parametrization for every binary HMM, with an explicit inverse for recovering the hidden parameters in terms of observables. The new model parameters in (2) are hence rationally identifiable in the sense of Sullivant, Garcia-Puente, and Spielvogel, and each model's Zar...
Growth and dissolution of macromolecular Markov chains
Gaspard, Pierre
2016-01-01
The kinetics and thermodynamics of free living copolymerization are studied for processes with rates depending on k monomeric units of the macromolecular chain behind the unit that is attached or detached. In this case, the sequence of monomeric units in the growing copolymer is a kth-order Markov chain. In the regime of steady growth, the statistical properties of the sequence are determined analytically in terms of the attachment and detachment rates. In this way, the mean growth velocity as well as the thermodynamic entropy production and the sequence disorder can be calculated systematically. These different properties are also investigated in the regime of depolymerization where the macromolecular chain is dissolved by the surrounding solution. In this regime, the entropy production is shown to satisfy Landauer's principle.
Growth and Dissolution of Macromolecular Markov Chains
Gaspard, Pierre
2016-07-01
The kinetics and thermodynamics of free living copolymerization are studied for processes with rates depending on k monomeric units of the macromolecular chain behind the unit that is attached or detached. In this case, the sequence of monomeric units in the growing copolymer is a kth-order Markov chain. In the regime of steady growth, the statistical properties of the sequence are determined analytically in terms of the attachment and detachment rates. In this way, the mean growth velocity as well as the thermodynamic entropy production and the sequence disorder can be calculated systematically. These different properties are also investigated in the regime of depolymerization where the macromolecular chain is dissolved by the surrounding solution. In this regime, the entropy production is shown to satisfy Landauer's principle.
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
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
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.
Markov state model of the two-state behaviour of water
Hamm, Peter
2016-10-01
With the help of a Markov State Model (MSM), two-state behaviour is resolved for two computer models of water in a temperature range from 255 K to room temperature (295 K). The method is first validated for ST2 water, for which the so far strongest evidence for a liquid-liquid phase transition exists. In that case, the results from the MSM can be cross-checked against the radial distribution function g5(r) of the 5th-closest water molecule around a given reference water molecule. The latter is a commonly used local order parameter, which exhibits a bimodal distribution just above the liquid-liquid critical point that represents the low-density form of the liquid (LDL) and the high density liquid. The correlation times and correlation lengths of the corresponding spatial domains are calculated and it is shown that they are connected via a simple diffusion model. Once the approach is established, TIP4P/2005 will be considered, which is the much more realistic representation of real water. The MSM can resolve two-state behavior also in that case, albeit with significantly smaller correlation times and lengths. The population of LDL-like water increases with decreasing temperature, thereby explaining the density maximum at 4 °C along the lines of the two-state model of water.
Viscosity properties and strong liquid behavior of Pr60Ni25Al15 bulk metallic glass-forming liquids
Institute of Scientific and Technical Information of China (English)
WANG Dan; ZHANG Di; WANG ShuYing; NING QianYan; ZHENG CaiPing; YAN Yuan; LIU Jia; SUN MinHua
2008-01-01
Pr60Ni25Al15 bulk metallic glass in a cuboid form with dimensions of 2 mm×2 mm×55 mm by copper mold casting method was cast.The dynamic viscosity near the glass transition region for Pr60Ni25Al15 was measured by three-point beam bending methods.The fragility parameter m and activation energy for viscous flow of the liquid sample were calculated to be: m = 31.66, E= 10689.17 K, respectively.It was shown that the supercooled liquid of Pr60Ni25Al15 alloy behaved much closer to strong glasses.The variation of active energy with temperature in supercooled liquid was analyzed.It was found that Kivelson's super-Arrhenius equation is not suitable for description of the activation energy in a supercooled region of Bulk metallic glass, and there is a direct proportion between activation energy crystal-lization and activation energy of viscous flow.
Viscosity properties and strong liquid behavior of Pr60Ni25Al15 bulk metallic glass-forming liquids
Institute of Scientific and Technical Information of China (English)
2008-01-01
Pr60Ni25Al15 bulk metallic glass in a cuboid form with dimensions of 2 mm×2 mm×55 mm by copper mold casting method was cast. The dynamic viscosity near the glass transition region for Pr60Ni25Al15 was measured by three-point beam bending methods. The fragility parameter m and activation energy for viscous flow of the liquid sample were calculated to be:m=31.66,E=10689.17 K,respectively. It was shown that the supercooled liquid of Pr60Ni25Al15 alloy behaved much closer to strong glasses. The variation of active energy with temperature in supercooled liquid was analyzed. It was found that Kivelson’s super-Arrhenius equation is not suitable for description of the activation energy in a supercooled region of Bulk metallic glass,and there is a direct proportion between activation energy crystal-lization and activation energy of viscous flow.
Transformation of state space for two-parameter Markov processes
Institute of Scientific and Technical Information of China (English)
周健伟
1996-01-01
Let X=(X) be a two-parameter *-Markov process with a transition function (p1, p2, p), where X, takes values in the state space (Er,), T=[0,)2. For each r T, let f, be a measurable transformation of (E,) into the state space (E’r, ). Set Y,=f,(X,), r T. A sufficient condition is given for the process Y=(Yr) still to be a two-parameter *-Markov process with a transition function in terms of transition function (p1, p2, p) and fr. For *-Markov families of two-parameter processes with a transition function, a similar problem is also discussed.
Markov Graph Model Computation and Its Application to Intrusion Detection
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Markov model is usually selected as the base model of user action in the intrusion detection system (IDS). However, the performance of the IDS depends on the status space of Markov model and it will degrade as the space dimension grows. Here, Markov Graph Model (MGM) is proposed to handle this issue. Specification of the model is described, and several methods for probability computation with MGM are also presented. Based on MGM,algorithms for building user model and predicting user action are presented. And the performance of these algorithms such as computing complexity, prediction accuracy, and storage requirement of MGM are analyzed.
ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS
Institute of Scientific and Technical Information of China (English)
Hu Dihe; Hu Xiaoyu
2009-01-01
In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with Abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Ф and a random Markov kernel (RMK) p(γ). In Section 3, the authors establish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov branching chain in space-time random environment.
On the Markov-dependent risk model with tax
Institute of Scientific and Technical Information of China (English)
PENG Xing-chun; WANG Wen-yuan; HU Yi-jun
2015-01-01
In this paper we consider the Markov-dependent risk model with tax payments in which the claim occurrence, the claim amount as well as the tax rate are controlled by an irreducible discrete-time Markov chain. Systems of integro-diff erential equations satisfied by the expected discounted tax payments and the non-ruin probability in terms of the ruin probabilities under the Markov-dependent risk model without tax are established. The analytical solutions of the systems of integro-diff erential equations are also obtained by the iteration method.
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
Markov Chain-based Degree Distributions of Evolving Networks
Institute of Scientific and Technical Information of China (English)
Xiang Xing KONG; Zhen Ting HOU; Ding Hua SHI; Quan Rong CHEN; Qing Gui ZHAO
2012-01-01
In this paper,we study a class of stochastic processes,called evolving network Markov chains,in evolving networks. Our approach is to transform the degree distribution problem of an evolving network to a corresponding problem of evolving network Markov chains.We investigate the evolving network Markov chains,thereby obtaining some exact formulas as well as a precise criterion for determining whether the steady degree distribution of the evolving network is a power-law or not.With this new method,we finally obtain a rigorous,exact and unified solution of the steady degree distribution of the evolving network.
Information-Geometric Markov Chain Monte Carlo Methods Using Diffusions
Directory of Open Access Journals (Sweden)
Samuel Livingstone
2014-06-01
Full Text Available Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond statistics. A full exposition of Markov chains and their use in Monte Carlo simulation for statistical inference and molecular dynamics is provided, with particular emphasis on methods based on Langevin diffusions. After this, geometric concepts in Markov chain Monte Carlo are introduced. A full derivation of the Langevin diffusion on a Riemannian manifold is given, together with a discussion of the appropriate Riemannian metric choice for different problems. A survey of applications is provided, and some open questions are discussed.
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 liquid in question. This scaling is demonstrated to work well for simulations of the Kob–Andersen binary Lennard-Jones mixture and two molecular models, as well as for the experimental results for two van der Waals liquids, dibutyl phthalate and decahydroisoquinoline. The often used power-law density...... scaling, h(ρ)∝ργ, is an approximation to the more general form of scaling discussed here. A thermodynamic derivation was previously given for an explicit expression for h(ρ) for liquids of particles interacting via the generalized Lennard-Jones potential. Here a statistical mechanics derivation is given...
Energy Technology Data Exchange (ETDEWEB)
Ito, S.; Hashimoto, A.; Miura, N. [Kanagawa Inst. of Tech., Kanagawa (Japan); Ikemoto, Y.
1999-11-25
An ice storage system using supercooled water was constructed and the performance was tested. The system was consisted of a storage tank with the volume of 1.2 m{sup 3} in which slurry-ice was stared, a spiral double-tube heat exchanger 22 m long for making supercooled water by brine, a refrigerating machine of the rated capacity of 2.2 kW, reservoirs for cold and hot brine, heaters, and pumps. The system was able to be operated for more than 5 hours without freezing mostly if the degree of supercooling was less than about 2 degree C. The COPs based on the power of the refrigerating machine and system were about 1.3 and 0.7, respectively. (author)
Slow dynamics and local quasi-equilibrium-relaxation in supercooled colloidal systems
Energy Technology Data Exchange (ETDEWEB)
RubI, J M; SantamarIa-Holek, I; Perez-Madrid, A [Department de Fisica Fonamental, Facultat de Fisica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona (Spain)
2004-06-09
We present a Fokker-Planck description of supercooled colloidal systems exhibiting slow relaxation dynamics. Assuming the existence of a local quasi-equilibrium state during the relaxation of the system, we derive a non-Markovian Fokker-Planck equation for the non-stationary conditional probability. A generalized Stokes-Einstein relation containing the temperature of the system at local quasi-equilibrium instead of the temperature of the bath is obtained. Our results explain experiments showing that the diffusion coefficient is not proportional to the inverse of the effective viscosity at frequencies related to the diffusion timescale.
DEFF Research Database (Denmark)
Dannemand, Mark; Dragsted, Janne; Fan, Jianhua;
2016-01-01
was filled with 220 kg SAT mixture thickened with 1% carboxymethyl cellulose. The heat exchange capacity rate during the charging of the unit with the extra water was significantly higher than for the unit with the thickening agent due to the different levels of convection. The SAT mixtures in the units were......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...
An Overview of Markov Chain Methods for the Study of Stage-Sequential Developmental Processes
Kapland, David
2008-01-01
This article presents an overview of quantitative methodologies for the study of stage-sequential development based on extensions of Markov chain modeling. Four methods are presented that exemplify the flexibility of this approach: the manifest Markov model, the latent Markov model, latent transition analysis, and the mixture latent Markov model.…
Energy Technology Data Exchange (ETDEWEB)
Rosenfeld, Daniel; Chemke, Rei; DeMott, Paul J.; Sullivan, Ryan C.; Rasmussen, R M.; McDonough, Frank; Comstock, Jennifer M.; Schmid, Beat; Tomlinson, Jason M.; Jonsson, Haf; Suski, Kaitlyn; Cazorla, Alberto; Prather, Kimberly
2013-09-05
The formation of highly supercooled rain was documented by aircraft observations in clouds at a wide range of conditions near the coastal region of the western United States. Several case studies are described in detail using combined cloud and aerosol measurements to document both the highly super-cooled condition and the relatively pristine aerosol conditions under which it forms. The case studies include: (1) Marine convective clouds over the coastal waters of northern California, as measured by cloud physics probes flown on a Gulfstream-1 aircraft during the CALWATER campaign in February and early March 2011. The clouds had extensive drizzle in their tops, which extended downward to the 0°C isotherm as supercooled rain. Ice multiplication was observed only in mature parts of the clouds where cloud water was already depleted. (2) Orographically triggered convective clouds in marine air mass over the foothills of the Sierra Nevada to the east of Sacramento, as measured in CALWATER. Supercooled rain was observed down to -21°C. No indications for ice multiplication were evident. (3) Orographic layer clouds over Yosemite National Park, also measured in CALWATER. The clouds had extensive drizzle at -21°C, which intensified with little freezing lower in the cloud, and (4) Supercooled drizzle drops in layer clouds near Juneau, Alaska, as measured by the Wyoming King Air as part of a FAA project to study aircraft icing in this region. Low concentrations of CCN was a common observation in all these clouds, allowing for the formation of clouds with small concentration of large drops that coalesced into supercooled drizzle and raindrops. Another common observation was the absence of ice nuclei and/or ice crystals in measurable concentrations was associated with the persistent supercooled drizzle and rain. Average ice crystal concentrations were 0.007 l-1 at the top of convective clouds at -12°C and 0.03 l-1 in the case of layer clouds at -21°C. In combination these
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, ...
The Limit Behaviour of Imprecise Continuous-Time Markov Chains
De Bock, Jasper
2016-08-01
We study the limit behaviour of a nonlinear differential equation whose solution is a superadditive generalisation of a stochastic matrix, prove convergence, and provide necessary and sufficient conditions for ergodicity. In the linear case, the solution of our differential equation is equal to the matrix exponential of an intensity matrix and can then be interpreted as the transition operator of a homogeneous continuous-time Markov chain. Similarly, in the generalised nonlinear case that we consider, the solution can be interpreted as the lower transition operator of a specific set of non-homogeneous continuous-time Markov chains, called an imprecise continuous-time Markov chain. In this context, our convergence result shows that for a fixed initial state, an imprecise continuous-time Markov chain always converges to a limiting distribution, and our ergodicity result provides a necessary and sufficient condition for this limiting distribution to be independent of the initial state.
On the Markov Chain Monte Carlo (MCMC) method
Indian Academy of Sciences (India)
Rajeeva L Karandikar
2006-04-01
Markov Chain Monte Carlo (MCMC) is a popular method used to generate samples from arbitrary distributions, which may be speciﬁed indirectly. In this article, we give an introduction to this method along with some examples.
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.
Markov Chain: A Predictive Model for Manpower Planning ...
African Journals Online (AJOL)
ADOWIE PERE
numerous previous studies have applied Markov chain models in describing title or level promotions .... is one of the most crucial, complex and continuing ... computational tools that will enable administrators to ... random variables. ,.... ,.
Determining a Class of Markov Chains by Hitting Time
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
@@1 Introduction In many practical problems we often cannot observe the behavior of all states for a Markov chain (see [3-5]). A natural question is that from the observable data of a part of states, can one still obtain all statistical characteristics of the Markov chains. In this paper we give the positive answer for this question and prove the surprising result that the transition rate matrix of the birth-death chains with reflecting barriers and Markov chains on a star graph can be uniquely determined by the probability density functions (pdfs) of the sojourn times and the hitting times at a single special state. This result also suggest a new special type of statistics for Markov chains.
Recent Applications of Hidden Markov Models in Computational Biology
Institute of Scientific and Technical Information of China (English)
Khar Heng Choo; Joo Chuan Tong; Louxin Zhang
2004-01-01
This paper examines recent developments and applications of Hidden Markov Models (HMMs) to various problems in computational biology, including multiple sequence alignment, homology detection, protein sequences classification, and genomic annotation.
Scaling limits of Markov-Branching trees and applications
Haas, Bénédicte
2016-01-01
The goal of these lectures is to survey some of the recent progress on the description of large-scale structure of random trees. We use the framework of Markov-Branching sequences of trees and discuss several applications.
Sampling Strategies for Fast Updating of Gaussian Markov Random Fields
Brown, D. Andrew; McMahan, Christopher S.
2017-01-01
Gaussian Markov random fields (GMRFs) are popular for modeling temporal or spatial dependence in large areal datasets due to their ease of interpretation and computational convenience afforded by conditional independence and their sparse precision matrices needed for random variable generation. Using such models inside a Markov chain Monte Carlo algorithm requires repeatedly simulating random fields. This is a nontrivial issue, especially when the full conditional precision matrix depends on ...
Risk-Averse Control of Undiscounted Transient Markov Models
Cavus, Ozlem
2012-01-01
We use Markov risk measures to formulate a risk-averse version of the undiscounted total cost problem for a transient controlled Markov process. We derive risk-averse dynamic programming equations and we show that a randomized policy may be strictly better than deterministic policies, when risk measures are employed. We illustrate the results on an optimal stopping problem and an organ transplant problem.
On the extendibility of partially and Markov exchangeable binary sequences
Di Cecco, Davide
2009-01-01
In [Fortini et al., Stoch. Proc. Appl. 100 (2002), 147--165] it is demonstrated that a recurrent Markov exchangeable process in the sense of Diaconis and Freedman is essentially a partially exchangeable process in the sense of de Finetti. In case of finite sequences there is not such an equivalence. We analyze both finite partially exchangeable and finite Markov exchangeable binary sequences and formulate necessary and sufficient conditions for extendibility in both cases.
Approximate N-Gram Markov Model for Natural Language Generation
Chen, H H; Chen, Hsin-Hsi; Lee, Yue-Shi
1994-01-01
This paper proposes an Approximate n-gram Markov Model for bag generation. Directed word association pairs with distances are used to approximate (n-1)-gram and n-gram training tables. This model has parameters of word association model, and merits of both word association model and Markov Model. The training knowledge for bag generation can be also applied to lexical selection in machine translation design.
Hidden Markov Models with Factored Gaussian Mixtures Densities
Institute of Scientific and Technical Information of China (English)
LI Hao-zheng; LIU Zhi-qiang; ZHU Xiang-hua
2004-01-01
We present a factorial representation of Gaussian mixture models for observation densities in Hidden Markov Models(HMMs), which uses the factorial learning in the HMM framework. We derive the reestimation formulas for estimating the factorized parameters by the Expectation Maximization (EM) algorithm. We conduct several experiments to compare the performance of this model structure with Factorial Hidden Markov Models(FHMMs) and HMMs, some conclusions and promising empirical results are presented.
Boudala, Faisal; Wu, Di; Gultepe, Ismail; Anderson, Martha; turcotte, marie-france
2017-04-01
In-flight aircraft icing is one of the major weather hazards to aviation . It occurs when an aircraft passes through a cloud layer containing supercooled drops (SD). The SD in contact with the airframe freezes on the surface which degrades the performance of the aircraft.. Prediction of in-flight icing requires accurate prediction of SD sizes, liquid water content (LWC), and temperature. The current numerical weather predicting (NWP) models are not capable of making accurate prediction of SD sizes and associated LWC. Aircraft icing environment is normally studied by flying research aircraft, which is quite expensive. Thus, developing a ground based remote sensing system for detection of supercooled liquid clouds and characterization of their impact on severity of aircraft icing one of the important tasks for improving the NWPs based predictions and validations. In this respect, Environment and Climate Change Canada (ECCC) in cooperation with the Department of National Defense (DND) installed a number of specialized ground based remote sensing platforms and present weather sensors at Cold Lake, Alberta that includes a multi-channel microwave radiometer (MWR), K-band Micro Rain radar (MRR), Ceilometer, Parsivel distrometer and Vaisala PWD22 present weather sensor. In this study, a number of pilot reports confirming icing events and freezing precipitation that occurred at Cold Lake during the 2014-2016 winter periods and associated observation data for the same period are examined. The icing events are also examined using aircraft icing intensity estimated using ice accumulation model which is based on a cylindrical shape approximation of airfoil and the Canadian High Resolution Regional Deterministic Prediction System (HRDPS) model predicted LWC, median volume diameter and temperature. The results related to vertical atmospheric profiling conditions, surface observations, and the Canadian High Resolution Regional Deterministic Prediction System (HRDPS) model
Numerical investigation on super-cooled large droplet icing of fan rotor blade in jet engine
Isobe, Keisuke; Suzuki, Masaya; Yamamoto, Makoto
2014-10-01
Icing (or ice accretion) is a phenomenon in which super-cooled water droplets impinge and accrete on a body. It is well known that ice accretion on blades and vanes leads to performance degradation and has caused severe accidents. Although various anti-icing and deicing systems have been developed, such accidents still occur. Therefore, it is important to clarify the phenomenon of ice accretion on an aircraft and in a jet engine. However, flight tests for ice accretion are very expensive, and in the wind tunnel it is difficult to reproduce all climate conditions where ice accretion can occur. Therefore, it is expected that computational fluid dynamics (CFD), which can estimate ice accretion in various climate conditions, will be a useful way to predict and understand the ice accretion phenomenon. On the other hand, although the icing caused by super-cooled large droplets (SLD) is very dangerous, the numerical method has not been established yet. This is why SLD icing is characterized by splash and bounce phenomena of droplets and they are very complex in nature. In the present study, we develop an ice accretion code considering the splash and bounce phenomena to predict SLD icing, and the code is applied to a fan rotor blade. The numerical results with and without the SLD icing model are compared. Through this study, the influence of the SLD icing model is numerically clarified.
Ice-lens formation and geometrical supercooling in soils and other colloidal materials
Style, Robert W; Cocks, Alan C F; Wettlaufer, John S
2011-01-01
We present a new, 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 ...
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.
Prognostics for Steam Generator Tube Rupture using Markov Chain model
Energy Technology Data Exchange (ETDEWEB)
Kim, Gibeom; Heo, Gyunyoung [Kyung Hee University, Yongin (Korea, Republic of); Kim, Hyeonmin [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2016-10-15
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.
Optimized Markov State Models for Metastable Systems
Guarnera, Enrico
2016-01-01
A method is proposed to identify target states that optimize a metastability index amongst a set of trial states and use these target states as milestones to build Markov State Models. If the optimized metastability index is small, this automatically guarantees the accuracy of the MSM in the sense that the transitions between the target milestones is indeed approximately Markovian. The method is simple to implement and use, it does not require that the dynamics on the trial milestones be Markovian, and it also offers the possibility to partition the system's state-space by assigning every trial milestone to the target milestones it is most likely to visit next and to identify transition state regions. Here the method is tested on the Gly-Ala-Gly peptide, where it shown to correctly identify the known metastable states in the dihedral angle space of the molecule without a priori information about these states. It is also applied to analyze the folding landscape of the Beta3s min-protein, where it is shown to i...
Reduced-Rank Hidden Markov Models
Siddiqi, Sajid M; Gordon, Geoffrey J
2009-01-01
We introduce the Reduced-Rank Hidden Markov Model (RR-HMM), a generalization of HMMs that can model smooth state evolution as in Linear Dynamical Systems (LDSs) as well as non-log-concave predictive distributions as in continuous-observation HMMs. RR-HMMs assume an m-dimensional latent state and n discrete observations, with a transition matrix of rank k <= m. This implies the dynamics evolve in a k-dimensional subspace, while the shape of the set of predictive distributions is determined by m. Latent state belief is represented with a k-dimensional state vector and inference is carried out entirely in R^k, making RR-HMMs as computationally efficient as k-state HMMs yet more expressive. To learn RR-HMMs, we relax the assumptions of a recently proposed spectral learning algorithm for HMMs (Hsu, Kakade and Zhang 2009) and apply it to learn k-dimensional observable representations of rank-k RR-HMMs. The algorithm is consistent and free of local optima, and we extend its performance guarantees to cover the RR-...
A markov classification model for metabolic pathways
Directory of Open Access Journals (Sweden)
Mamitsuka Hiroshi
2010-01-01
Full Text Available Abstract Background This paper considers the problem of identifying pathways through metabolic networks that relate to a specific biological response. Our proposed model, HME3M, first identifies frequently traversed network paths using a Markov mixture model. Then by employing a hierarchical mixture of experts, separate classifiers are built using information specific to each path and combined into an ensemble prediction for the response. Results We compared the performance of HME3M with logistic regression and support vector machines (SVM for both simulated pathways and on two metabolic networks, glycolysis and the pentose phosphate pathway for Arabidopsis thaliana. We use AltGenExpress microarray data and focus on the pathway differences in the developmental stages and stress responses of Arabidopsis. The results clearly show that HME3M outperformed the comparison methods in the presence of increasing network complexity and pathway noise. Furthermore an analysis of the paths identified by HME3M for each metabolic network confirmed known biological responses of Arabidopsis. Conclusions This paper clearly shows HME3M to be an accurate and robust method for classifying metabolic pathways. HME3M is shown to outperform all comparison methods and further is capable of identifying known biologically active pathways within microarray data.
Relativized hierarchical decomposition of Markov decision processes.
Ravindran, B
2013-01-01
Reinforcement Learning (RL) is a popular paradigm for sequential decision making under uncertainty. A typical RL algorithm operates with only limited knowledge of the environment and with limited feedback on the quality of the decisions. To operate effectively in complex environments, learning agents require the ability to form useful abstractions, that is, the ability to selectively ignore irrelevant details. It is difficult to derive a single representation that is useful for a large problem setting. In this chapter, we describe a hierarchical RL framework that incorporates an algebraic framework for modeling task-specific abstraction. The basic notion that we will explore is that of a homomorphism of a Markov Decision Process (MDP). We mention various extensions of the basic MDP homomorphism framework in order to accommodate different commonly understood notions of abstraction, namely, aspects of selective attention. Parts of the work described in this chapter have been reported earlier in several papers (Narayanmurthy and Ravindran, 2007, 2008; Ravindran and Barto, 2002, 2003a,b; Ravindran et al., 2007).
Markov branching in the vertex splitting model
Stefansson, Sigurdur Orn
2011-01-01
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 $\\alpha \\in [0,1]$ which has a so--called Markov branching property. When $D=\\infty$ we find a two parameter model with an additional parameter $\\gamma \\in [0,1]$ which also has this feature. In the case $D = 3$, the model bears resemblance to Ford's $\\alpha$--model of phylogenetic trees and when $D=\\infty$ it is similar to its generalization, the $\\alpha\\gamma$--model. For $\\alpha = 0$, the model reduces to the well known model of preferential attachment. In the case $\\alpha > 0$, 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 $1/\\alpha$. When $\\gamma = 0$ the model reduces to a model of ...
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.
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.
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.
Tight Markov chains and random compositions
Pittel, Boris
2010-01-01
For an ergodic Markov chain $\\{X(t)\\}$ on $\\Bbb N$, with a stationary distribution $\\pi$, let $T_n>0$ denote a hitting time for $[n]^c$, and let $X_n=X(T_n)$. Around 2005 Guy Louchard popularized a conjecture that, for $n\\to \\infty$, $T_n$ is almost Geometric($p$), $p=\\pi([n]^c)$, $X_n$ is almost stationarily distributed on $[n]^c$, and that $X_n$ and $T_n$ are almost independent, if $p(n):=\\sup_ip(i,[n]^c)\\to 0$ exponentially fast. For the chains with $p(n) \\to 0$ however slowly, and with $\\sup_{i,j}\\,\\|p(i,\\cdot)-p(j,\\cdot)\\|_{TV}<1$, we show that Louchard's conjecture is indeed true even for the hits of an arbitrary $S_n\\subset\\Bbb N$ with $\\pi(S_n)\\to 0$. More precisely, a sequence of $k$ consecutive hit locations paired with the time elapsed since a previous hit (for the first hit, since the starting moment) is approximated, within a total variation distance of order $k\\,\\sup_ip(i,S_n)$, by a $k$-long sequence of independent copies of $(\\ell_n,t_n)$, where $\\ell_n= \\text{Geometric}\\,(\\pi(S_n))$, $t_n$...
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.
Markov state modeling of sliding friction
Pellegrini, F.; Landes, François P.; Laio, A.; Prestipino, S.; Tosatti, E.
2016-11-01
Markov state modeling (MSM) has recently emerged as one of the key techniques for the discovery of collective variables and the analysis of rare events in molecular simulations. In particular in biochemistry this approach is successfully exploited to find the metastable states of complex systems and their evolution in thermal equilibrium, including rare events, such as a protein undergoing folding. The physics of sliding friction and its atomistic simulations under external forces constitute a nonequilibrium field where relevant variables are in principle unknown and where a proper theory describing violent and rare events such as stick slip is still lacking. Here we show that MSM can be extended to the study of nonequilibrium phenomena and in particular friction. The approach is benchmarked on the Frenkel-Kontorova model, used here as a test system whose properties are well established. We demonstrate that the method allows the least prejudiced identification of a minimal basis of natural microscopic variables necessary for the description of the forced dynamics of sliding, through their probabilistic evolution. The steps necessary for the application to realistic frictional systems are highlighted.
Directory of Open Access Journals (Sweden)
Sandeep Singh
2015-02-01
Full Text Available Thin films of La5/8−yPryCa3/8MnO3 (y≈0.4 have been grown on single crystal SrTiO3 (001 by RF sputtering. The structural and surface characterizations confirm the epitaxial nature of these film. However, the difference between the ω-scan of the (002 and (110 peaks and the presence of pits/holes in the step-terrace type surface morphology suggests high density of defect in these films. Pronounced hysteresis between the field cooled cooling (FCC and field cooled warming (FCW magnetization measurements suggest towards the non-ergodic magnetic state. The origin of this nonergodicity could be traced to the magnetic liquid like state arising from the delicacy of the coexisting magnetic phases, viz., ferromagnetic and antiferromagnetic-charge ordered (FM/AFM-CO. The large difference between the insulator metal transitions during cooling and warming cycles (TIMC ∼ 64 K and TIMW ∼ 123 K could be regarded as a manifestation of the nonergodicity leading to supercooling of the magnetic liquid while cooling. The nonergodicity and supercooling are weakened by the AFM-FM phase transition induced by an external magnetic field. TIM and small polaron activation energy corresponding the magnetic liquid state (cooling cycle vary nonlinearly with the applied magnetic field but become linear in the crystalline solid state (warming cycle. The analysis of the low temperature resistivity data shows that electron-phonon interaction is drastically reduced by the applied magnetic field. The resistivity minimum in the lower temperature region of the self-field warming curve has been explained in terms of the Kondo like scattering in the magnetically inhomogeneous regime.
Application of Reed-Vibration Mechanical Spectroscopy for Liquids in Studying Liquid Crystallization
Zhou, Heng-Wei; Wang, Li-Na; Zhang, Li-Li; Huang, Yi-Neng
2013-08-01
By using the reed-vibration mechanical spectroscopy for liquids (RMS-L), we measured the complex Young's modulus of dimethyl phthalate (DP) during a cooling and heating circulation starting from room temperature at about 2 KHz. The results show that there is no crystallization in the cooling supercooled liquid (CSL) of DP, but a crystallization process in the heating supercooled liquid (HSL) after the reverse glass transition. Based on the measured modulus, crystal volume fraction (v) during the HSL crystallization was calculated. Moreover, the Avrami exponent (n) was obtained according to the JJMA equation and v data. In view of n versus temperature and v, the nucleation dynamics was analyzed, and especially, there has already existed saturate nuclei in DP HSL before the crystallization. Furthermore, the authors inferred that the nuclei are induced by the random frozen stress in the glass, but there is no nucleus in CSL. The above results indicated that RMS-L might provide a new way to measure and analyze the crystallization of liquids.
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.
Yu, Shu-Hui; Yang, Pu; Sun, Tao; Qi, Qian; Wang, Xue-Qing; Chen, Xiao-Ming; Feng, Ying; Liu, Bo-Wen
2016-06-01
The Chinese white wax scale insect, Ericerus pela, can survive at extremely low temperatures, and some overwintering individuals exhibit supercooling at temperatures below -30°C. To investigate the deep supercooling ability of E. pela, transcriptomic and proteomic analyses were performed to delineate the major gene and protein families responsible for the deep supercooling ability of overwintering females. Gene Ontology (GO) classification and Kyoto Encyclopedia of Genes and Genomes (KEGG) analysis indicated that genes involved in the mitogen-activated protein kinase, calcium, and PI3K-Akt signaling pathways and pathways associated with the biosynthesis of soluble sugars, sugar alcohols and free amino acids were dominant. Proteins responsible for low-temperature stress, such as cold acclimation proteins, glycerol biosynthesis-related enzymes and heat shock proteins (HSPs) were identified. However, no antifreeze proteins (AFPs) were identified through sequence similarity search methods. A random forest approach identified 388 putative AFPs in the proteome. The AFP gene ep-afp was expressed in Escherichia coli, and the expressed protein exhibited a thermal hysteresis activity of 0.97°C, suggesting its potential role in the deep supercooling ability of E. pela.
Realisation of dynamic ice-making by supercooled water%过冷水动态制冰的研究
Institute of Scientific and Technical Information of China (English)
曲凯阳; 江亿
2001-01-01
Further studies based on the authors' earlier researches the conditions under which no fpeezing occur in the supercooler while sufficient supercooling of water is guaranteed.Establishes a stably opepeting experimental assembly. Water temperature at the entrance of the supercooler reaches as low as 0.45 ℃, and the water temperature drop in supercooler isabout 1℃.%在作者前期研究的基础上，进一步研究了保证过冷水动态制冰系统中过冷却器不发生结冰的条件，建立了能够稳定运行的过冷水动态制冰实验装置。水在过冷却器入口的最低温度为0.45℃，在过冷却器中的温降约为1.0℃。
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.
1983-03-01
53) study by Egelstaff et al Emulsion samples have also been briefly studied but background difficulties have made resolution of the results...Angell, L., Angell, C. A. ., Phys. Chem. (to be published) 52. Bosio, L., Chen, S.-H., Teixeira, 3. Phys. Rev. A (in press) 53. Egelstaff , P. A., Polo, 3
Disease surveillance using a hidden Markov model
Directory of Open Access Journals (Sweden)
Wright Graeme
2009-08-01
Full Text Available Abstract Background Routine surveillance of disease notification data can enable the early detection of localised disease outbreaks. Although hidden Markov models (HMMs have been recognised as an appropriate method to model disease surveillance data, they have been rarely applied in public health practice. We aimed to develop and evaluate a simple flexible HMM for disease surveillance which is suitable for use with sparse small area count data and requires little baseline data. Methods A Bayesian HMM was designed to monitor routinely collected notifiable disease data that are aggregated by residential postcode. Semi-synthetic data were used to evaluate the algorithm and compare outbreak detection performance with the established Early Aberration Reporting System (EARS algorithms and a negative binomial cusum. Results Algorithm performance varied according to the desired false alarm rate for surveillance. At false alarm rates around 0.05, the cusum-based algorithms provided the best overall outbreak detection performance, having similar sensitivity to the HMMs and a shorter average time to detection. At false alarm rates around 0.01, the HMM algorithms provided the best overall outbreak detection performance, having higher sensitivity than the cusum-based Methods and a generally shorter time to detection for larger outbreaks. Overall, the 14-day HMM had a significantly greater area under the receiver operator characteristic curve than the EARS C3 and 7-day negative binomial cusum algorithms. Conclusion Our findings suggest that the HMM provides an effective method for the surveillance of sparse small area notifiable disease data at low false alarm rates. Further investigations are required to evaluation algorithm performance across other diseases and surveillance contexts.
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.
Institute of Scientific and Technical Information of China (English)
闫俊海; 张小松
2012-01-01
To analyze the evaporation characteristics of single water droplet in low temperature and low humidity ratio air in ice production system with evaporative supercooled water, a mathematical model of evaporative supercooling process of single water droplet was proposed. The evaporation process of droplet in supercooling stage was simulated with theoretical model and the results are basically consistent with the experiment on suspended single water droplet, so it is feasible to predict the evaporative supercooling characteristics of small water droplet by the mathematical model. The influence of initial diameter and temperature of water droplet, air temperature, humidity ratio of air, and air velocity on the temperature of water droplet during its evaporative supercooling process was analyzed. The numerical results show that smaller diameter and lower temperature of water droplet and larger air velocity can increase the cooling rate of water droplet and shorten the supercooling time reaching steady state evaporation stage. Additionally, lowering the temperature or humidity ratio of air can not only improve the cooling rate of water droplet, but also increase the supercooling degree of water droplet reaching steady state evaporation stage. The investigation of evaporative supercooling process of water droplet can provide a foundation for improving the efficiency of ice production and optimal design for ice-making system with evaporative supercooled water.%为分析蒸发式过冷水制冰中单个水滴在此低温低湿空气环境中的蒸发特性,建立了水滴蒸发过冷过程的数理模型.通过悬挂水滴实验与模拟结果的对比,验证了模型的有效性.因此利用该数学模型预测微小直径水滴的蒸发特性是可行的.通过模拟计算获得了水滴初始直径、初始水温、空气温度、空气含湿量和空气流速对水滴蒸发过冷过程的影响.结果表明,水滴初始直径越小、温度越低或空气流速越大,
The skew product Markov chain%Markov－双链
Institute of Scientific and Technical Information of China (English)
张王月; 张金洪; 邹健
2001-01-01
就随机环境下的 Markov－链，介绍了 Markov－双链的构造，并证明了以已给 P(θ )为转移概率的 Markov－双链的存在性 .当环境空间和状态空间均可数时，希望通过对 Markov－双链的研究，进而实现对随机环境下的 Markov－链的研究 .%The process of the construction of the skew product Markov Chain on the basic of the Markov Chain in random environments is introduced and the existence of the skew product Markov Chain is proven, taking the given P(θ ) as the transition probability. The Markov Chain in random environments by studying the skew product Markov chain , can be studied when the environment space and the state space are countable.
Weighted Markov Chain Based Aggregation of Bio-molecule Orderings.
Sengupta, Debarka; Maulik, Ujjwal; Bandyopadhyay, Sanghamitra
2012-01-31
The scope and effectiveness of rank aggregation have already been established in contemporary bioinformatics research. Rank aggregation helps in meta analysis of putative results collected from different analytic or experimental sources. For example, we often receive considerably differing ranked lists of genes or microRNAs from various target prediction algorithms or microarray studies. Sometimes combining them all, in some sense, yields more effective ordering of the set of objects. Also, assigning a certain level of confidence to each source of ranking is a natural demand of aggregation. Assignment of weights to the sources of orderings can be performed by experts. Several rank aggregation approaches like those based on Markov chains (MC), evolutionary algorithms etc., exist in the literature. Markov chains, in general are faster than the evolutionary approaches. Unlike the evolutionary computing approaches Markov chains have not been used for weighted aggregation scenarios. This is because of the absence of a formal framework of weighted Markov chain. In this article we propose the use of a modified version of MC4 (one of the Markov chains proposed by Dwork et al., 2001), followed by the weighted analog of local Kemenization for performing rank aggregation, where the sources of rankings can be prioritized by an expert.
Markov Model of Wind Power Time Series UsingBayesian Inference of Transition Matrix
DEFF Research Database (Denmark)
Chen, Peiyuan; Berthelsen, Kasper Klitgaard; Bak-Jensen, Birgitte
2009-01-01
This paper proposes to use Bayesian inference of transition matrix when developing a discrete Markov model of a wind speed/power time series and 95% credible interval for the model verification. The Dirichlet distribution is used as a conjugate prior for the transition matrix. Three discrete Markov...... models are compared, i.e. the basic Markov model, the Bayesian Markov model and the birth-and-death Markov model. The proposed Bayesian Markov model shows the best accuracy in modeling the autocorrelation of the wind power time series....
Volume and structural analysis of super-cooled water under high pressure
Duki, Solomon F.; Tsige, Mesfin
2012-02-01
Motivated by recent experimental study of super-cooled water at high pressure [1], we performed atomistic molecular dynamic simulations study on bulk water molecules at isothermal-isobaric ensemble. These simulations are performed at temperatures that range from 40 K to 380 K using two different cooling rates, 10K/ns and 10K/5ns, and pressure that ranges from 1atm to 10000 atm. Our analysis for the variation of the volume of the bulk sample against temperature indicates a downward concave shape for pressures above certain values, as reported in [1]. The same downward concave behavior is observed at high pressure on the mean-squared-displacements (MSD) of the water molecules when the MSD is plotted against time. To get further insight on the effect of the pressure on the sample we have also performed a structural analysis of the sample.[4pt] [1] O. Mishima, J. Chem. Phys. 133, 144503 (2010);
DEFF Research Database (Denmark)
Kuntsche, Judith; Koch, Michel; Drechsler, M;
2005-01-01
Supercooled smectic nanoparticles based on physiological cholesterol esters are under investigation as a potential novel carrier system for lipophilic drugs. The present study investigates the very complex crystallization behavior of such nanoparticles stabilized with the aid of phospholipids....... Phospholipid and phospholipid/bile salt stabilized cholesteryl myristate dispersions were prepared by high-pressure melt homogenization and characterized by particle size measurements, differential scanning calorimetry, X-ray diffraction and electron microscopy. To obtain fractions with very small smectic...... nanoparticles, selected dispersions were ultracentrifuged. A mixture of cholesteryl myristate and the phospholipid used for the stabilization of the dispersions was also investigated by light microscopy. The nanoparticles usually display a bimodal crystallization event which depends on the thermal treatment...
Local order in a supercooled colloidal fluid observed by confocal microscopy
Gasser, U; Weitz, D A
2003-01-01
The local order in a supercooled monodisperse colloidal fluid is studied by direct imaging of the particles with a laser scanning confocal microscope. The local structure is analysed with a bond order parameter method, which allows one to discern simple structures that are relevant in this system. As expected for samples that crystallize eventually, a large fraction of the particles are found to sit in surroundings with dominant face-centred cubic or hexagonally close-packed character. Evidence for local structures that contain fragments of icosahedra is found, and, moreover, the icosahedral character increases with volume fraction phi, which indicates that it might play an important role at volume fractions near the glass transition.