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Phase transitions to superionic Li₂Te and Li₂Se - A high-temperature neutron powder diffraction study, atom displacements, probability density functions and atom potentials

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SOLID STATE IONICS 2018年 325卷 90-101页

作者： Schneider, Julius Schroeder, Thorsten Hoelzel, Markus Kluge, Oliver Schmahl, Wolfgang W. Oeckler, Oliver Ludwig Maximilian Univ Munich Crystallog Sect Dept Geo & Environm Sci Theresienstr 41 D-80333 Munich Germany Tech Univ Munich Heinz Maier Leibnitz Zentrum MLZ D-85748 Garching Germany Univ Leipzig Inst Inorgan Chem Johannisallee 29 D-04103 Leipzig Germany Univ Leipzig Inst Mineral Crystallog & Mat Sci Scharnhorststr 20 D-04275 Leipzig Germany

Despite much research on Li ion batteries at ambient temperature, Li-ion conductors at high temperature have received less attention. In the series of ionic Li2X compounds (X = O, S, Se, Te), superionic phase transitions have been reported for Li2O and Li2S. The lower transition temperature of Li2S, supposedly caused by the larger anion size of S, inspired the investigation of the superionic behavior of Li2Se and Li2Te. Their thermal expansion and thermally excited spatial distribution of Li cations and Se/Te anions was monitored by neutron diffraction up to 800 degrees C for Li2Te and up to 1000 degrees C for Li2Se. Both compounds exhibit positive thermal expansion with changing coefficient of expansivity at the superionic transition temperatures. No deviation from cubic metrics or abrupt changes of the cell volume were observed. Rietveld refinements of the fluorite-type structures (space group Fm (3) over barm) employing Gaussian spatial distribution functions reveal discontinuities in the slope of the increasing mean square displacement parameters as a function of temperature. At similar to 600 degrees C (Li2Te) and similar to 780 degrees C (Li2Se), the mean square displacements of Li atoms increase abruptly, indicating a superionic transition. For the Te/Se anions, similar discontinuities occur at slightly lower temperatures. Difference Fourier syntheses reveal strongly anisotropic Li spatial distribution density around the 8c (1/4 1/4 1/4) positions of cubic site symmetry m (3) over barm. Moving the maximum of the density distribution to adjacent 32f (xxx) (site symmetry.3 m) positions introduces four virtual split atoms. In addition to the small displacement x along <111>, denoting the mean positions of the split atoms, anisotropic spatial distributions may then be refined. Whereas x deviates from 1/4 as an almost linear function of temperature, the abrupt changes in the increase of mean square amplitudes of thermal displacements with temperature are retained.

关键词： Superionic phase transitions Lithium chalcogenides High-temperature neutron powder diffraction Atom displacement parameters probability density functions

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Low-density parity check coded orthogonal frequency division multiplexing for PLC in non-Gaussian noise using LLRs derived from effective noise probability density functions

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IET COMMUNICATIONS 2017年第16期11卷 2425-2432页

作者： Al-Rubaye, Ghanim A. Tsimenidis, Charalampos C. Johnston, Martin Newcastle Univ Sch Elect & Elect Engn Merz Court Newcastle Upon Tyne NE1 7RU Tyne & Wear England

In this study, the performance of irregular low-density parity check (LDPC) coded orthogonal frequency division multiplexing (COFDM) utilising 4096 quadrature amplitude modulation (4096-QAM) is investigated over multipath power-line communication (PLC) channel. The effective complex-valued ratio distributions of the noise samples at the zero-forcing equaliser output considering both frequency-selective multipath PLCs, background and impulsive noise are derived, in addition to the condition for optimum detection of 4096-QAM and the bit error rate (BER). Moreover, the performance of the LDPC decoder is improved by computing the log-likelihood ratios (LLRs) required for soft decoding based on the derived probability density functions. Numerical results obtained using the newly derived LLRs demonstrate a significant performance improvement compared to the conventional receiver that uses blanking impulsive noise mitigation method and LLR computed based on the Gaussian distribution. Furthermore, EXtrinsic Information Transfer chart analysis demonstrates that the proposed approach requires fewer iterations for convergence compared to the conventional receiver. Finally, utilising channel bandwidth of 22.4MHz, the proposed system offers an improvement of 111Mbps over the conventional system to reach a maximum data throughput of 256Mbps for a signal-to-noise ratio of 39dB and BER of 10(-5).

关键词： parity check codes OFDM modulation carrier transmission on power lines probability Gaussian distribution quadrature amplitude modulation error statistics low-density parity check coded orthogonal frequency division multiplexing LPDC OFDM quadrature amplitude modulation multipath power-line communication channel complex-valued ratio distributions zero-forcing equaliser frequency-selective multipath PLC bit error rate BER log-likelihood ratios LLR probability density functions Gaussian distribution blanking impulsive noise mitigation method extrinsic information transfer chart analysis bandwidth 22 4 MHz

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NASA Technical Reports Server (Ntrs) 19930003211: probability density functions in Turbulent Channel Flow

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2017年

NASA Technical Reports Server (Ntrs) 19930003211: probability density functions in Turbulent Channel Flow by NASA Technical Reports Server (Ntrs); published by

关键词： (ntrs) 19930003211: channel channel flow density derivation dinavahi, surya p. g. dissipation functions kinetic energy nasa technical reports server (ntrs) probability density functions turbulent flow walls

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An approximation of small-time probability density functions in a general jump diffusion model

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APPLIED MATHEMATICS AND COMPUTATION 2016年 273卷 741-758页

作者： Zhang, Le Schmidt, Wolfgang M. Frankfurt Sch Finance & Management D-06031 Frankfurt Germany

We propose a method for approximating probability density functions related to multidimensional jump diffusion processes. For small-time horizons, a closed-form approximation of the characteristic function is derived based on the Ito-Taylor expansion. The probability density function is then approximated numerically by inverting the characteristic function using fast Fourier transform. As application we consider a general stochastic volatility model, which involves time-/state-dependent drift and diffusion functions as well as jump components. We test our approach under the Heston model and the Bates model and show that our method provides accurate approximations. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Jump diffusion process Ito-Taylor expansions Stochastic volatility models Characteristic functions probability density functions

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Lie symmetry analysis of the Lundgren-Monin-Novikov equations for multi-point probability density functions of turbulent flow

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2017年第17期50卷 175501-175501页

作者： Waclawczyk, M. Grebenev, V. N. Oberlack, M. Univ Warsaw Fac Phys Inst Geophys Pasteura 7 PL-02093 Warsaw Poland Russian Acad Sci Inst Computat Technol Lavrentjev Ave 6 Novosibirsk 630090 Russia Univ Fed Amazonas BR-69067005 Manaus Amazonas Brazil Tech Univ Darmstadt Chair Fluid Dynam Dept Mech Engn Otto Berndt Str 2 D-64287 Darmstadt Germany Tech Univ Darmstadt Grad Sch Computat Engn Dolivostr 15 D-64293 Darmstadt Germany

The problem of turbulence statistics described by the Lundgren-Monin-Novikov (LMN) hierarchy of integro-differential equations is studied in terms of its group properties. For this we perform a Lie group analysis of a truncated LMN chain which presents the first two equations in an infinite set of integro-differential equations for the multi-point probability density functions (pdf's) of velocity. A complete set of point transformations is derived for the one-point pdf's and the independent variables: sample space of velocity, space and time. For this purpose we use a direct method based on the canonical Lie-Backlund operator. Due to the one-way coupling of correlation equations, the present results are complete in the sense that no additional symmetries exist for the first leading equation, even if the full infinite hierarchy is considered.

关键词： turbulence Lundgren-Monin-Novikov hierarchy probability density functions Lie group analysis integro-differential equations

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NASA Technical Reports Server (Ntrs) 20120017458: Representation of probability density functions from Orbit Determination Using the Particle Filter

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2016年

NASA Technical Reports Server (Ntrs) 20120017458: Representation of probability density functions from Orbit Determination Using the Particle Filter by NASA Technical Reports Server (Ntrs); NASA Technical Reports Serv... 详细信息

关键词： (ntrs) 20120017458: carpenter, j. russell covariance density determination estimates filter garrison, james mashiku, alinda k. nasa technical reports server (ntrs) nonlinearity orbit determination principal components analysis probability density functions probability theory statistical analysis

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Reconstruction of one-dimensional chaotic maps from sequences of probability density functions

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NONLINEAR DYNAMICS 2015年第3期80卷 1373-1390页

作者： Nie, Xiaokai Coca, Daniel Univ Sheffield Dept Automat Control & Syst Engn Sheffield S1 3JD S Yorkshire England

In many practical situations, it is impossible to measure the individual trajectories generated by an unknown chaotic system, but we can observe the evolution of probability density functions generated by such a system. The paper proposes for the first time a matrix-based approach to solve the generalized inverse Frobenius-Perron problem, that is, to reconstruct an unknown one-dimensional chaotic transformation, based on a temporal sequence of probability density functions generated by the transformation. Numerical examples are used to demonstrate the applicability of the proposed approach and evaluate its robustness with respect to constantly applied stochastic perturbations.

关键词： Chaotic maps Inverse Frobenius-Perron problem Nonlinear systems probability density functions

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INSTAT: a program for computing non-ideal probability density functions of |E|

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JOURNAL OF APPLIED CRYSTALLOGRAPHY 2013年第5期46卷 1521-1522页

作者： Shmueli, Uri Tel Aviv Univ Sch Chem IL-69978 Tel Aviv Israel

The purpose of this program is to evaluate probability density functions (p.d.f.s) of the magnitude of the normalized structure factor vertical bar E vertical bar for the space groups of the triclinic, monoclinic and orthorhombic systems, and for any chemical composition of the asymmetric unit, assuming that the atoms are located in general positions. The p.d.f.s are computed by the Fourier and Fourier-Bessel methods [see e.g. Shmueli (2012). J. Appl. Cryst. 45, 389-392]. The p.d.f.s evaluated are scaled together with the histogram of observed vertical bar E vertical bar values and discrepancy criteria are computed. In addition to the above non-ideal p.d.f.s, the ideal p.d.f.s [Wilson (1949). J. Appl. Cryst. 2, 318-321] are also computed and prepared for comparison with an experimental histogram. (C) 2013 International Union of Crystallography Printed in Singapore - all rights reserved

关键词： probability density functions INSTAT computer programs

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The probability density Function Related to Shallow Cumulus Entrainment Rate and Its Influencing Factors in a Large-Eddy Simulation

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Advances in Atmospheric Sciences 2024年第1期41卷 173-187页

作者： Lei ZHU Chunsong LU Xiaoqi XU Xin HE Junjun LI Shi LUO Yuan WANG Fan WANG Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters(CIC-FEMD)and Key Laboratory for Aerosol-Cloud-Precipitation of China Meteorological Administration Nanjing University of Information Science and TechnologyNanjing 210044China Nanjing Joint Institute for Atmospheric Sciences Nanjing 210019China College of Aviation Meteorology Civil Aviation Flight University of ChinaGuanghan 618307China Collaborative Innovation Center for Western Ecological Safety Lanzhou UniversityLanzhou 730000China Department of Geography Hong Kong Baptist UniversityHong Kong SAR 999077China

The process of entrainment-mixing between cumulus clouds and the ambient air is important for the development of cumulus *** obtaining the entrainment rate(λ)is particularly important for its parameterization within the overall cumulus parameterization *** this study,an improved bulk-plume method is proposed by solving the equations of two conserved variables simultaneously to calculateλof cumulus clouds in a large-eddy *** results demonstrate that the improved bulk-plume method is more reliable than the traditional bulk-plume method,becauseλ,as calculated from the improved method,falls within the range ofλvalues obtained from the traditional method using different conserved *** probability density functions ofλfor all data,different times,and different heights can be well-fitted by a log-normal distribution,which supports the assumed stochastic entrainment process in previous *** analysis demonstrate that the relationship betweenλand the vertical velocity is better than other thermodynamic/dynamical properties;thus,the vertical velocity is recommended as the primary influencing factor for the parameterization ofλin the *** results of this study enhance the theoretical understanding ofλand its influencing factors and shed new light on the development ofλparameterization.

关键词： large-eddy simulation cumulus clouds entrainment rate probability density functions spatial and temporal distribution

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The effective radius of Lucas-Washburn dynamics in periodically constricted tubes

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MICROFLUIDICS AND NANOFLUIDICS 2025年第5期29卷 1-9页

作者： Urteaga, Raul Berli, Claudio L. A. Univ Nacl Litoral CONICET IFIS Litoral Guemes 3450 RA-3000 Santa Fe Argentina Univ Nacl Litoral INTEC CONICET Gnuemes 3450 RA-3000 Santa Fe Argentina

Capillary imbibition in periodically constricted tubes (PCTs) plays a critical role in multiple natural and technological processes, where the control of autonomous flows is intrinsically linked to the geometric architecture of the imbibition space. Here we present analytical expressions for the effective radius (r(eff)) of PCTs with different wave shapes and analyze how geometric parameters influence the infiltration dynamics. Our analysis reveals that r(eff) is strongly dependent on the ratio of maximum to minimum radii (alpha) and, for stepped geometries, on the relative segment length proportion (gamma). Increasing alpha enhances r(eff) up to a critical value, beyond which a strong reduction is observed: for alpha>> 2, approximately, the infiltration velocity progressively decreases. This counterintuitive behavior arises from the interplay between hydrodynamic resistance and capillary driving forces. We evaluated the effect on different geometries, achieving different r(eff) that can be analytically predicted by closed-form expressions. The model was also validated against previously reported experimental data. These findings underline the potential of geometric design to optimize capillary-driven flows, providing a framework for tailoring PCTs to specific applications in microfluidics, porous media, and related fields.

关键词： Capillary filling Non-uniform tubes Effective radius probability density functions

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