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We compute the sphere and disk partition functions in semiclassical Liouville and analogous quantities in double-scaled matrix integrals. The quantity sphere/disk2 is unambiguous and we find a precise numerical match between the Liouville answer and the matrix integral answer. An application is to show that the sphere partition function in JT gravity is infinite.
We investigate the disk partition function for the open string. This is a subtle problem because of the presence of a residual gauge group PSL(2, R) on the worldsheet even after fixing the conformal gauge. It naively has infinite volume and leads to a vanishing answer. We use different methods that all demonstrate that PSL(2, R) effectively behaves like a group with finite negative volume in the path integral, which leads to a simple prescription for the computation of the disk partition function. We apply our findings to give a simple rederivation of the D-brane tensions.
We extend the results of [1], computing one loop partition functions for massive fields with spin half in AdS 2 using the quasinormal mode method proposed by Denef, Hartnoll, and Sachdev [2]. We find the finite representations of SO(2,1) for spin zero and spin half, consisting of a highest weight state |hi and descendants with non-unitary values of h. These finite representations capture the poles and zeroes of the one loop determinants. Together with the asymptotic behavior of the partition functions (which can be easily computed using a large mass heat kernel expansion), these are sufficient to determine the full answer for the one loop determinants. We also discuss extensions to higher dimensional AdS 2n and higher spins.
We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.
We review some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G. We focus on the case G = SL(N, C) and with M a knot complement. The main result presented in this note is the cluster partition function, a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral. We also review various applications and open questions regarding the cluster partition function and some of its relation with string theory.
A method is established and validated using molecular dynamics (MD) to determine the displacement threshold energies as Ed in nanolayered, multilayered systems of dissimilar metals. The method is applied to specifically oriented nanolayered films of Al-Ti where the crystal structure and interface orientations are varied in atomic models and Ed is calculated. Methods for defect detection are developed and discussed based on prior research in the literature and based on specific crystallographic directions available in the nanolayered systems. These are compared and contrasted to similar calculations in corresponding bulk materials, including fcc Al, fcc Ti, hcp Al, and hcp Ti. In all cases, the calculated Ed in the multilayers are intermediate to the corresponding bulk values but exhibit some important directionality. In the nanolayer, defect detection demonstrated systematic differences in the behavior of Ed in each layer. Importantly, collision cascade damage exhibits significant defect partitioning within the Al and Ti layers that is hypothesized to be an intrinsic property of dissimilar nanolayered systems. This type of partitioning could be partly responsible for observed asymmetric radiation damage responses in many multilayered systems. In addition, a pseudo-random direction was introduced to approximate the average Ed without performing numerous simulations with random directions.
Partition functions of a canonical ensemble of non-interacting bound electrons are a key ingredient of the super-transition-array approach to the computation of radiative opacity. A few years ago, we published a robust and stable recursion relation for the calculation of such partition functions. In this work, we propose an optimization of the latter method and explain how to implement it in practice. The formalism relies on the evaluation of elementary symmetric polynomials, which opens the way to further improvements.
We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in a implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems together with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode the- ory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized- Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and dif- fusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. Lastly, the CHAMP scheme is also developed for general curvilinear grids and CHT ex- amples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.
There is a critical need for the development and verification of practically useful multiscale modeling strategies for simulating the mechanical response of multiphase metallic materials with heterogeneous microstructures. In this contribution, we present data-driven reduced order models for effective yield strength and strain partitioning in such microstructures. These models are built employing the recently developed framework of Materials Knowledge Systems that employ 2-point spatial correlations (or 2-point statistics) for the quantification of the heterostructures and principal component analyses for their low-dimensional representation. The models are calibrated to a large collection of finite element (FE) results obtained for a diverse range of microstructures with various sizes, shapes, and volume fractions of the phases. The performance of the models is evaluated by comparing the predictions of yield strength and strain partitioning in two-phase materials with the corresponding predictions from a classical self-consistent model as well as results of full-field FE simulations. The reduced-order models developed in this work show an excellent combination of accuracy and computational efficiency, and therefore present an important advance towards computationally efficient microstructure-sensitive multiscale modeling frameworks. - Graphical abstract:.
Simulating the implantation and thermal desorption evolution in a reaction-diffusion model requires solving a set of coupled differential equations that describe the trapping and release of atomic species in Plasma Facing Materials (PFMs). These fundamental equations are well outlined by the Tritium Migration Analysis Program (TMAP) which can model systems with no more than three active traps per atomic species. To overcome this limitation, we have developed a Pseudo Trap and Temperature Partition (PTTP) scheme allowing us to lump multiple inactive traps into one pseudo trap, simplifying the system of equations to be solved. For all temperatures, we show the trapping of atoms from solute is exactly accounted for when using a pseudo trap. However, a single effective pseudo trap energy can not well replicate the release from multiple traps, each with its own detrapping energy. However, atoms held in a high energy trap will remain trapped at relatively low temperatures, and thus there is a temperature range in which release from high energy traps is effectively inactive. By partitioning the temperature range into segments, a pseudo trap can be defined for each segment to account for multiple high energy traps that are actively trapping but are effectively not releasing atoms. With increasing temperature, as in controlled thermal desorption, the lowest energy trap is nearly emptied and can be removed from the set of coupled equations, while the next higher energy trap becomes an actively releasing trap. Each segment is thus calculated sequentially, with the last time step of a given segment solution being used as an initial input for the next segment as only the pseudo and actively releasing traps are modeled. This PTTP scheme is then applied to experimental thermal desorption data for tungsten (W) samples damaged with heavy ions, which display six distinct release peaks during thermal desorption. Without modifying the TMAP7 source code the PTTP scheme is shown to successfully model the D retention in all six traps. In conclusion, we demonstrate the full reconstruction from the plasma implantation phase through the controlled thermal desorption phase with detrapping energies near 0.9, 1.1, 1.4, 1.7, 1.9 and 2.1 eV for a W sample damaged at room temperature.
Quenching-partitioning-tempering (Q-P-T) process was used to treat a Ti-microalloyed low-carbon stainless steel after cold rolling. In addition to martensite, ferrite and retained austenite, TiN, coarse TiC, fine TiC, (Fe,Cr){sub 3}C and ultra-fine TiC precipitates were formed after the Q-P-T treatment. Based on field emission-scanning electron microscope (FESEM) and transmission electron microscope (TEM) observations, thermodynamic, crystallographic and statistical analyses were used to reveal the precipitation behaviors of these particles. The effects of partitioning-tempering (P-T) temperature and time on the microstructure and mechanical properties of Q-P-T treated specimens were specially studied. The coarsening and spheroidization of (Fe,Cr){sub 3}C particles during P-T stage were obviously retarded by large Cr addition. The retained austenite was obtained significantly with appropriate P-T parameters. The precipitation of ultra-fine TiC particles in the martensite during the P-T stage at 500 °C induced a secondary hardening. - Highlights: • Some fine TiC with 30–70 nm precipitated in austenite during partial austenization. • A part of fine TiC had K-S OR with martensite after Q-P-T treatment. • A part of fine TiC had a OR specially deviating from K-S OR with martensite. • Coarsening and spheroidization of (Fe,Cr){sub 3}C were retarded during P-T stage. • Ultra-fine TiC with < 10 nm precipitated in martensite during P-T stage at 500 °C.
Highlights: • The impact energy of M50 steels treated by QPT process increases by 35–93% than QT. • Cracks distribution inside impact fracture specimens is studied by 3D X-ray tomography. • The work indicates that QPT process can be applied to high-C steel with little Si. Novel quenching-partitioning-tempering (Q-P-T) and traditional quenching-tempering (Q-T) processes are conducted for M50 ultra-high strength steel. An excellent combination of strength and toughness is obtained via the Q-P-T process. The highest impact absorption energy of the Q-P-T specimen increases by 93% compared to the Q-T specimen. However, the yield and ultimate tensile strength of Q-P-T specimens are almost the same as those of Q-T specimens. Microstructure analysis indicates that the maximum fraction of retained austenite in the Q-P-T specimen is 7.5%, which is much higher than that in the Q-T (2.0%) specimen. Meanwhile, more fine cracks appear in the fracture Q-P-T specimen. The precipitation of fine and diffuse ω phase, Fe{sub 3}C and Cr{sub 23}C{sub 6} is observed during the partitioning process. The present work also reveals that the Q-P-T/Q-P process can be applied to high‑carbon steel with little Si or Al.
Here, this paper presents the phase stability and elemental partitioning in a Co-40Ni-10Al-7.5W-10Cr-3Nb-0.06B-0.6C (at.%) superalloy (referred to as 3Nb) after a two-step heat treatment. The resulting microstructure consisted of γ, γ', MC carbides and µ-Co 7 W 6 phase decorating the regions near and at the grain boundaries. Nb preferentially partitioned to the γ'-phase and other elements such as Ni, Cr and W were responsible for the μ-phase formation.
The use of ion exchange membranes (IEMs) for electrochemical ion-ion separation leverages the selectivity of the IEMs toward like-charged species via valence difference and/or other ion membrane interactions. A mechanistic model that relates selectivity with membrane structural and chemical properties is lacking in the literature. Here, in this study, we extend the Manning’s counter-ion condensation model for describing ion partition and ion mobility inside IEMs to mixed salts scenarios. We evaluate the extended Donnan-Manning model against experimental data from literature and compare the performance the Donnan-Manning model to that of the ideal Donnan model and the Donnan-Affinity model. Our analysis shows that, despite its structural complexity, the Donnan-Manning model has less fitting parameters than the Donnan-Affinity model and generally outperforms the two other models in predicting counter-ion and co-ion partition. With the assumption of a higher mobility of condensed ions than that of uncondensed ions, the generalized Manning’s model can also predict counter-ion mobility selectivity for cation exchange membranes, but its performance for predicting mobility selectivity for anion exchange membranes is still unsatisfactory.
Highlights: ► Element partitioning of waste-to-energy units by means of a substance flow analysis. ► A comparison between moving grate combustors and high temperature gasifiers. ► Classification of key elements according to their behavior during WtE processes. ► Slags and metals from waste gasifiers are completely and immediately recyclable. ► Potential reduction of amounts of solid residue to be sent to landfill disposal. - Abstract: A critical comparison between combustion- and gasification-based waste-to-energy systems needs a deep knowledge of the mass flows of materials and elements inside and throughout the units. The study collected and processed data from several moving grate conventional incinerators and high-temperature shaft gasifiers with direct melting, which are in operation worldwide. A material and substance flow analysis was then developed to systematically assess the flows and stocks of materials and elements within each waste-to-energy unit, by connecting the sources, pathways, and intermediate and final sinks of each species. The patterns of key elements, such as carbon, chloride and heavy metals, in the different solid and gaseous output streams of the two compared processes have been then defined. The combination of partitioning coefficients with the mass balances on atomic species and results of mineralogical characterization from recent literatures was used to estimate a composition of bottom ashes and slags from the two types of waste-to-energy technologies. The results also allow to quantify some of the performance parameters of the units and, in particular, the potential reduction of the amount of solid residues to be sent to final disposal.
Control over the selectivity of catalytic materials is a topic of growing interest. Virus-like particle (VLP) based materials such as protein macromolecular frameworks (PMFs) are promising for catalytic applications due to their ease of assembly, modular ability to encapsulate a variety of enzymes, and ease of separation from a reaction mixture. Here we demonstrate the reversal of the initially negative material charge through the titration of a positively charged polymer into the material, causing the reversal of guest molecule uptake and enzymatic activity of PMFs. The charge-inverse material partitions a charged enzyme substrate to concentrate the substrate near an enzyme incorporated within the material, generating up to 5.9-fold increases in enzyme activity toward the partitioned substrate over the excluded substrate. Here we also show that the polymer distributes heterogeneously through the material up to a point of saturation and the effects of guest macromolecules on the lattice parameters of PMFs.
Exchange of atmospheric organic compounds between gas and particle phases is important in the production and chemistry of particle-phase mass but is poorly understood due to a lack of simultaneous measurements in both phases of individual compounds. Measurements of particle- and gas phase organic compounds are reported here for the southeastern United States and central Amazonia. Polyols formed from isoprene oxidation contribute 8% and 15% on average to particle-phase organic mass at these sites but are also observed to have substantial gas-phase concentrations contrary to many models that treat these compounds as nonvolatile. The results of the present study show that the gas-particle partitioning of approximately 100 known and newly observed oxidation products is not well explained by environmental factors (e.g., temperature). Compounds having high vapor pressures have higher particle fractions than expected from absorptive equilibrium partitioning models. These observations support the conclusion that many commonly measured biogenic oxidation products may be bound in low-volatility mass (e.g., accretion products, inorganic organic adducts) that decomposes to individual compounds on analysis. However, the nature and extent of any such bonding remains uncertain. Similar conclusions are reach for both study locations, and average particle fractions for a given compound are consistent within similar to 25% across measurement sites.
The diffusivity of semivolatile organic compounds (SVOCs) in the bulk particle phase of a viscous atmospheric secondary organic aerosol (SOA) can have a profound impact on aerosol growth and size distribution dynamics. Here, we investigate the bulk diffusivity of SVOCs formed from photo-oxidation of isoprene as they partition to a bimodal aerosol consisting of an Aitken (potassium sulfate) and accumulation mode (aged α-pinene SOA) particles as a function of relative humidity (RH). The model analysis of the observed size distribution evolution shows that liquid-like diffusion coefficient values of D b > 10 –10 cm 2 s –1 fail to explain the growth of the Aitken mode. Instead, much lower values of Db between 2.5 × 10 –15 cm 2 s –1 at 32% RH and 8 × 10 –15 cm 2 s –1 at 82% RH were needed to successfully reproduce the growth of both modes. The diffusivity within the aged α-pinene SOA remains appreciably slow even at 80% RH, resulting in hindered partitioning of SVOCs to large viscous particles and allowing smaller and relatively less viscous particles to effectively absorb the available SVOCs and grow much faster than would be possible otherwise. Our results have important implications for modeling SOA formation and growth in the ambient atmosphere.