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Individuals that possess and utilize their strengths have higher reports of subjective and psychological well-being. However, it remains unclear as to whether certain domains of strengths (e.g., strengths at home, at school, within the community) are more strongly associated with certain indices of well-being (e.g., stress management, social connectedness). This information is important given the complex presentation of strengths and idiosyncratic ways in which individuals place value on different aspects of well-being. High school students (N = 236, 51% female) from a rural northern community completed a set of online questionnaires while in class: The Strength Assessment Inventory-Youth Version (Rawana & Brownlee, 2010 (See CR51)); Perceived Stress Scale (Cohen, Kamarck, & Mermelstein, 1983 (See CR10)); and Multidimensional Scale of Perceived Social Support (Zimet, Dahlem, Zimet, & Farley, 1988 (See CR77)). Together, the measures examined different domains of strengths (character and environmental) and subjective and psychological well-being (i.e., perceived stress and relatedness adequacy, respectively). Bivariate correlations were used to identify strength domains that would be further analyzed through hierarchical regression modeling. Results showed that the strength of self-knowledge was relevant for both subjective and psychological well-being, whereas strengths at home, strengths at school, and strengths from having goals and dreams were relevant for only psychological well-being. Adolescents with a sense of self-knowledge (i.e., positive self-concept, confidence in abilities, sense of right from wrong when making decisions) may be better equipped to manage daily stresses and form connections to others. By examining specific domains and indices, a more refined understanding can be gained of the association between strengths and well-being., Author(s): Tiffany Leung [sup.1] , Edward Rawana [sup.1] , Rupert Klein [sup.1] Author Affiliations: (1) grid.258900.6, 0000 0001 0687 7127, Department of Psychology, Lakehead University, , Thunder Bay, Canada Introduction [...]

In this work we study the global solvability of the primitive equations for the atmosphere coupled to moisture dynamics with phase changes for warm clouds, where water is present in the form of water vapor and in the liquid state as cloud water and rain water. This moisture model contains closures for the phase changes condensation and evaporation, as well as the processes of auto conversion of cloud water into rainwater and the collection of cloud water by the falling rain droplets. It has been used by Klein and Majda in [17] and corresponds to a basic form of the bulk microphysics closure in the spirit of Kessler [16] and Grabowski and Smolarkiewicz [12]. The moisture balances are strongly coupled to the thermodynamic equation via the latent heat associated to the phase changes. In [14] we assumed the velocity field to be given and proved rigorously the global existence and uniqueness of uniformly bounded solutions of the moisture balances coupled to the thermodynamic equation. In this paper we present the solvability of a full moist atmospheric flow model, where the moisture model is coupled to the primitive equations of atmospherical dynamics governing the velocity field. For the derivation of a priori estimates for the velocity field we thereby use the ideas of Cao and Titi [6], who succeeded in proving the global solvability of the primitive equations.

The "Shockless Explosion Combustion" (SEC) concept for gas turbine combustors, introduced in 2014, approximates constant volume combustion (CVC) by harnessing acoustic confinement of auto-igniting gas packets. The resulting pressure waves simultaneously transmit combustion energy to a turbine plenum and facilitate the combustor's recharging against an average pressure gain. Challenges in actualizing an SEC-driven gas turbine include (i) the creation of charge stratifications for nearly homogeneous auto-ignition, (ii) protecting the turbocomponents from combustion-induced pressure fluctuations, (iii) providing evidence that efficiency gains comparable to those of CVC over deflagrative combustion can be realized, and (iv) designing an effective one-way intake valve. This work addresses challenges (i)-(iii) utilizing computational engine models incorporating a quasi-one-dimensional combustor, zero- and two-dimensional (2D) compressor and turbine plena, and quasi-stationary turbocomponents. Two SEC operational modes are identified which fire at roughly one and two times the combustors' acoustic frequencies. Results for SEC-driven gas turbines with compressor pressure ratios of 6:1 and 20:1 reveal 1.5-fold mean pressure gains across the combustors. Assuming ideally efficient compressors and turbines, efficiency gains over engines with deflagration-based combustors of 30% and 18% are realized, respectively. With absolute values of 52% and 66%, the obtained efficiencies are close to the theoretical Humphrey cycle efficiencies of 54% and 65% for the mentioned precompression ratios. Detailed thermodynamic cycle analyses for individual gas parcels suggest that there is room for further efficiency gains through optimized plenum and combustor designs. [ABSTRACT FROM AUTHOR]

We study a moisture model for warm clouds that has been used by Klein and Majda (2006 Theor. Comput. Fluid Dyn. 20 525-551) as a basis for multiscale asymptotic expansions for deep convective phenomena. These moisture balance equations correspond to a bulk microphysics closure in the spirit of Kessler (1969 Meteorol. Monogr. 10 1-84) and Grabowski and Smolarkiewicz (1996 Mon. Weather Rev. 124 487-97), in which water is present in the gaseous state as water vapor and in the liquid phase as cloud water and rain water. It thereby contains closures for the phase changes condensation and evaporation, as well as the processes of autoconversion of cloud water into rainwater and the collection of cloud water by the falling rain droplets. Phase changes are associated with enormous amounts of latent heat and therefore provide a strong coupling to the thermodynamic equation. In this work we assume the velocity field to be given and prove rigorously the global existence and uniqueness of uniformly bounded solutions of the moisture model with viscosity, diffusion and heat conduction. To guarantee local well-posedness we first need to establish local existence results for linear parabolic equations, subject to the Robin boundary conditions on the cylindric type of domains under consideration. We then derive a priori estimates, for proving the maximum principle, using the Stampacchia method, as well as the iterative method by Alikakos (1979 J. Differ. Equ. 33 201-25) to obtain uniform boundedness. The evaporation term is of power law type, with an exponent in general less or equal to one and therefore making the proof of uniqueness more challenging. However, these difficulties can be circumvented by introducing new unknowns, which satisfy the required cancellation and monotonicity properties in the source terms.

WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schrödinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum–classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics "on the fly," with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available. [ABSTRACT FROM AUTHOR]

A model for the motion of slender vortex filaments is extended to include the effect of gravity. The model, initially introduced by Callegari and Ting ["Motion of a curved vortex filament with decaying vortical core and axial velocity," SIAM J. Appl. Math. 35, 148–175 (1978)], is based on a matched asymptotic expansion in which the outer solution, given by the Biot–Savart law, is matched with the inner solution derived from the Navier–Stokes equations. Building on recent work by Harikrishnan et al. ["On the motion of hairpin filaments in the atmospheric boundary layer," Phys. Fluids 35, 076603 (2023)], the Boussinesq approximation is applied such that the density variations only enter in the gravity term. However, unlike Harikrishnan et al. ["On the motion of hairpin filaments in the atmospheric boundary layer," Phys. Fluids 35, 076603 (2023)], the density variation enters at a lower order in the asymptotic expansion and, thus, has a more significant impact on the self-induced velocity of the vortex filament. In this regime, which corresponds to the regime studied by Chang and Smith ["The motion of a buoyant vortex filament," J. Fluid Mech. 857, R1 (2018)], the effect of gravity is given by an alteration of the core constant, which couples the motion of the filament to the motion within the vortical core, in addition to a change in the compatibility conditions (evolution equations), which determine the leading order azimuthal and tangential velocity fields in the vortex core. The results are used to explain certain properties of buoyant vortex rings, as well as qualitatively explore the impact of gravity on tornado-type atmospheric vortices. [ABSTRACT FROM AUTHOR]

We demonstrate how to apply the tensor-train format to solve the time-independent Schrödinger equation for quasi-one-dimensional excitonic chain systems with and without periodic boundary conditions. The coupled excitons and phonons are modeled by Fröhlich–Holstein type Hamiltonians with on-site and nearest-neighbor interactions only. We reduce the memory consumption as well as the computational costs significantly by employing efficient decompositions to construct low-rank tensor-train representations, thus mitigating the curse of dimensionality. In order to compute also higher quantum states, we introduce an approach that directly incorporates the Wielandt deflation technique into the alternating linear scheme for the solution of eigenproblems. Besides systems with coupled excitons and phonons, we also investigate uncoupled problems for which (semi-)analytical results exist. There, we find that in the case of homogeneous systems, the tensor-train ranks of state vectors only marginally depend on the chain length, which results in a linear growth of the storage consumption. However, the central processing unit time increases slightly faster with the chain length than the storage consumption because the alternating linear scheme adopted in our work requires more iterations to achieve convergence for longer chains and a given rank. Finally, we demonstrate that the tensor-train approach to the quantum treatment of coupled excitons and phonons makes it possible to directly tackle the phenomenon of mutual self-trapping. We are able to confirm the main results of the Davydov theory, i.e., the dependence of the wave packet width and the corresponding stabilization energy on the exciton–phonon coupling strength, although only for a certain range of that parameter. In future work, our approach will allow calculations also beyond the validity regime of that theory and/or beyond the restrictions of the Fröhlich–Holstein type Hamiltonians. [ABSTRACT FROM AUTHOR]

The traditional approximation neglects the cosine components of the Coriolis acceleration, and this approximation has been widely used in the study of geophysical phenomena. However, the justification of the traditional approximation is questionable under a few circumstances. In particular, dynamics with substantial vertical velocities or geophysical phenomena in the tropics have non-negligible cosine Coriolis terms. Such cases warrant investigations with the non-traditional setting, i.e. the full Coriolis acceleration. In this manuscript, we study the effect of the non-traditional setting on an isothermal, hydrostatic and compressible atmosphere assuming a meridionally homogeneous flow. Employing linear stability analysis, we show that, given appropriate boundary conditions, i.e. a bottom boundary condition that allows for a vertical energy flux and non-reflecting boundary at the top, the atmosphere at rest becomes prone to a novel unstable mode. The validity of assuming a meridionally homogeneous flow is investigated via scale analysis. Numerical experiments were conducted, and Rayleigh damping was used as a numerical approximation for the non-reflecting top boundary. Our three main results are as follows: (i) experiments involving the full Coriolis terms exhibit an exponentially growing instability, yet experiments subjected to the traditional approximation remain stable; (ii) the experimental instability growth rate is close to the theoretical value; (iii) a perturbed version of the unstable mode arises even under sub-optimal bottom boundary conditions. Finally, we conclude our study by discussing the limitations, implications and remaining open questions. Specifically, the influence on numerical deep-atmosphere models and possible physical interpretations of the unstable mode are discussed. [ABSTRACT FROM AUTHOR]

A recent work of Harikrishnan et al. ["Geometry and organization of coherent structures in stably stratified atmospheric boundary layers," arXiv:2110.02253 (2021)] has revealed an abundance of hairpin-like vortex structures, oriented in a similar direction, in the turbulent patches of a stably stratified Ekman flow. In this study, hairpin-like structures are investigated by treating them as slender vortex filaments, i.e., a vortex filament whose diameter d is small when compared to its radius of curvature R. The corrected thin-tube model of Klein and Knio ["Asymptotic vorticity structure and numerical simulation of slender vortex filaments," J. Fluid Mech. 284, 275 (1995)] is used to compute the motion of these filaments with the atmospheric boundary layer as a background flow. Our results suggest that the orientation of the hairpin filament in the spanwise direction is linked to its initial starting height under stable stratification, whereas no such dependency can be observed with the neutrally stratified background flow. An improved feature tracking scheme based on spatial overlap for tracking Q-criterion vortex structures on the direct numerical simulation data is also developed. It overcomes the limitation of using a constant threshold in time by dynamically adjusting the thresholds to accommodate the growth or deterioration of a feature. A comparison between the feature tracking and the filament simulation reveals qualitatively similar temporal developments. Finally, an extension of the asymptotic analysis of Callegari and Ting ["Motion of a curved vortex filament with decaying vortical core and axial velocity," J. Appl. Math. 35, 148–175 (1978)] is carried out to include the effect of gravity. The results show that, in the regime considered here, a contribution from the gravity term occurs only when the tail of an infinitely long filament is tilted at an angle relative to the wall. [ABSTRACT FROM AUTHOR]

For both the meso‐ and synoptic scales, reduced mathematical models give insight into their dynamical behaviour. For the mesoscale, the weak temperature gradient approximation is one of several approaches, while for the synoptic scale the quasigeostrophic theory is well established. However, the way these two scales interact with each other is usually not included in such reduced models, thereby limiting our current perception of flow‐dependent predictability and upscale error growth. Here, we address the scale interactions explicitly by developing a two‐scale asymptotic model for the meso‐ and synoptic scales with two coupled sets of equations for the meso‐ and synoptic scales respectively. The mesoscale equations follow a weak temperature gradient balance and the synoptic‐scale equations align with quasigeostrophic theory. Importantly, the equation sets are coupled via scale‐interaction terms: eddy correlations of mesoscale variables impact the synoptic potential vorticity tendency and synoptic variables force the mesoscale vorticity (for instance due to tilting of synoptic‐scale wind shear). Furthermore, different diabatic heating rates—representing the effect of precipitation—define different flow characteristics. With weak mesoscale heating relatable to precipitation rates of 풪(6mm·h−1), the mesoscale dynamics resembles two‐dimensional incompressible vorticity dynamics and the upscale impact of the mesoscale on the synoptic scale is only of a dynamical nature. With a strong mesosocale heating relatable to precipitation rates of 풪(60mm·h−1), divergent motions and three‐dimensional effects become relevant for the mesoscale dynamics and the upscale impact also includes thermodynamical effects. [ABSTRACT FROM AUTHOR]

The chemical diffusion master equation (CDME) describes the probabilistic dynamics of reaction–diffusion systems at the molecular level [del Razo et al., Lett. Math. Phys. 112, 49 (2022)]; it can be considered as the master equation for reaction–diffusion processes. The CDME consists of an infinite ordered family of Fokker–Planck equations, where each level of the ordered family corresponds to a certain number of particles and each particle represents a molecule. The equations at each level describe the spatial diffusion of the corresponding set of particles, and they are coupled to each other via reaction operators—linear operators representing chemical reactions. These operators change the number of particles in the system and, thus, transport probability between different levels in the family. In this work, we present three approaches to formulate the CDME and show the relations between them. We further deduce the non-trivial combinatorial factors contained in the reaction operators, and we elucidate the relation to the original formulation of the CDME, which is based on creation and annihilation operators acting on many-particle probability density functions. Finally, we discuss applications to multiscale simulations of biochemical systems among other future prospects. [ABSTRACT FROM AUTHOR]

Ogura and Phillips derived the original anelastic model through systematic formal asymptotics using the flow Mach number as the expansion parameter. To arrive at a reduced model that would simultaneously represent internal gravity waves and the effects of advection on the same time scale, they had to adopt a distinguished limit requiring that the dimensionless stability of the background state be on the order of the Mach number squared. For typical flow Mach numbers of M ~ 1/30, this amounts to total variations of potential temperature across the troposphere of less than one Kelvin (i.e., to unrealistically weak stratification). Various generalizations of the original anelastic model have been proposed to remedy this issue. Later, Durran proposed the pseudoincompressible model following the same goals, but via a somewhat different route of argumentation. The present paper provides a scale analysis showing that the regime of validity of two of these extended models covers stratification strengths on the order of ([h.sub.sc]/[theta])d[theta]/dz < [M.sup.2/3], which corresponds to realistic variations of potential temperature [theta] across the pressure scale height [h.sub.sc] of [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Specifically, it is shown that (i) for ([h.sub.sc]/[theta])d[theta]/dz < [M.sup.[mu]] with 0 < [mu] < 2, the atmosphere features three asymptotically distinct time scales, namely, those of advection, internal gravity waves, and sound waves; (ii) within this range of stratifications, the structures and frequencies of the linearized internal wave modes of the compressible, anelastic, and pseudoincompressible models agree up to the order of [M.sup.[mu]]: and (iii) if [mu] < 2/3, the accumulated phase differences of internal waves remain asymptotically small even over the long advective time scale. The argument is completed by observing that the three models agree with respect to the advective nonlinearities and that all other nonlinear terms are of higher order in M. DOI: 10.1175/2010JAS3490.1

Starting from the conservation laws for mass, momentum, and energy together with a three-species bulk microphysics model, a model for the interaction of internal gravity waves and deep convective hot towers is derived using multiscale asymptotic techniques. From the leading-order equations, a closed model for the large-scale flow is obtained analytically by applying horizontal averages conditioned on the small-scale hot towers. No closure approximations are required besides adopting the asymptotic limit regime on which the analysis is based. The resulting model is an extension of the anelastic equations linearized about a constant background flow. Moist processes enter through the area fraction of saturated regions and through two additional dynamic equations describing the coupled evolution of the conditionally averaged small-scale vertical velocity and buoyancy. A two-way coupling between the large-scale dynamics and these small-scale quantities is obtained: moisture reduces the effective stability for the large-scale flow, and microscale up- and downdrafts define a large-scale averaged potential temperature source term. In turn, large-scale vertical velocities induce small-scale potential temperature fluctuations due to the discrepancy in effective stability between saturated and nonsaturated regions. The dispersion relation and group velocity of the system are analyzed and moisture is found to have several effects: (i) it reduces vertical energy transport by waves, (ii) it increases vertical wavenumbers but decreases the slope at which wave packets travel, (iii) it introduces a new lower horizontal cutoff wavenumber in addition to the well-known high wavenumber cutoff, and (iv) moisture can cause critical layers. Numerical examples reveal the effects of moisture on steady-state and time-dependent mountain waves in the present hot-tower regime. DOI: 10.1175/2010JAS3269.1

In this study the authors apply a recently developed clustering method for the systematic identification of metastable atmospheric regimes in high-dimensional datasets generated by atmospheric models. The novelty of this approach is that it decomposes the phase space in, possibly, overlapping clusters and simultaneously estimates the most likely switching sequence among the clusters. The parameters of the clustering and switching are estimated by a finite element approach. The switching among the clusters can be described by a Markov transition matrix. Possible metastable regime behavior is assessed by inspecting the eigenspectrum of the associated transition probability matrix. The recently introduced metastable data-analysis method is applied to high-dimensional datasets produced by a barotropic model and a comprehensive atmospheric general circulation model (GCM). Significant and dynamically relevant metastable regimes are successfully identified in both models. The metastable regimes in the barotropic model correspond to blocked and zonal states. Similar regime states were already previously identified in highly reduced phase spaces of just one and two dimensions in the same model. Next, the clustering method is applied to a comprehensive atmospheric GCM in which seven significant flow regimes are identified. The spatial structures of the regimes correspond to, among others, both phases of the Northern Annular Mode and Pacific blocking. The regimes are maintained predominantly by transient eddy fluxes of low-pass-filtered anomalies. It is demonstrated how the dynamical description of the slow process switching between the regimes can be acquired from the analysis results, and an investigation of the resulting simplified dynamical model with respect to predictability is performed. A predictability study shows that a simple Markov model is able to predict the regimes up to six days ahead, comparable to the ability of high-resolution state-of-the-art numerical weather prediction models to accurately predict the onset and decay of blockings. The implications of the results for derivation of reduced models for extended-range predictability are discussed.

A challenge arising from the local Bayesian assimilation of data in an atmospheric flow simulation is the imbalances it may introduce. Acoustic fast-mode imbalances of the order of the slower dynamics can be negated by employing a blended numerical model with seamless access to the compressible and the soundproof pseudo-incompressible dynamics. Here, the blended modeling strategy by Benacchio et al. is upgraded in an advanced numerical framework and extended with a Bayesian local ensemble data assimilation method. Upon assimilation of data, the model configuration is switched to the pseudo-incompressible regime for one time step. After that, the model configuration is switched back to the compressible model for the duration of the assimilation window. The switching between model regimes is repeated for each subsequent assimilation window. An improved blending strategy for the numerical model ensures that a single time step in the pseudo-incompressible regime is sufficient to suppress imbalances coming from the initialization and data assimilation. This improvement is based on three innovations: (i) the association of pressure fields computed at different stages of the numerical integration with actual time levels, (ii) a conversion of pressure-related variables between the model regimes derived from low Mach number asymptotics, and (iii) a judicious selection of the pressure variables used in converting numerical model states when a switch of models occurs. Idealized two-dimensional traveling vortex and buoyancy-driven bubble convection experiments show that acoustic imbalances arising from data assimilation can be eliminated by using this blended model, thereby achieving balanced analysis fields. Significance Statement: Weather forecasting models use a combination of physics-based algorithms and meteorological measurements. A problem with combining outputs from the model with measurements of the atmosphere is that insignificant signals may generate noise and compromise the physical soundness of weather-relevant processes. By selecting atmospheric processes through the toggling of parameters in a mixed model, we propose to suppress the undesirable signals in an efficient way and retain the physical features of solutions produced by the model. The approach is validated here for acoustic imbalances using a compressible/pseudo-incompressible model pair. This development has the potential to improve the techniques used to bring observations into models and with them the quality of atmospheric model output. [ABSTRACT FROM AUTHOR]

This paper presents an extension of the recently developed method for simultaneous dimension reduction and metastability analysis of high-dimensional time series. The modified approach is based on a combination of ensembles of hidden Markov models (HMMs) with state-specific principal component analysis (PCA) in extended space (guaranteeing that the overall dynamics will be Markovian). The main advantage of the modified method is its ability to deal with the gaps in the high-dimensional observation data. The proposed method allows for (i) the separation of the data according to the metastable states, (ii) a hierarchical decomposition of these sets into metastable substates, and (iii) calculation of the state-specific extended empirical orthogonal functions simultaneously with identification of the underlying Markovian dynamics switching between those metastable substates. The authors discuss the introduced model assumptions, explain how the quality of the resulting reduced representation can be assessed, and show what kind of additional insight into the underlying dynamics such a reduced Markovian representation can give (e.g., in the form of transition probabilities, statistical weights, mean first exit times, and mean first passage times). The performance of the new method analyzing 500-hPa geopotential height fields [daily mean values from the 40-yr ECMWF Re-Analysis (ERA-40) dataset for a period of 44 winters] is demonstrated and the results are compared with information gained from a numerically expensive but assumption-free method (Wavelets--PCA), and the identified metastable states are interpreted w.r.t, the blocking events in the atmosphere.

ABSTRACT: The present research investigates the determinants of the cognitive tendency to avoid thoughts about sexually transmitted infection (STI) and examines the association of this tendency with willingness to engage [...]

Systematic multiscale perturbation theory is utilized to develop self-consistent simplified model equations for the interaction across multiple spatial and/or temporal scales in the Tropics. One of these models involves simplified equations for intraseasonal planetary equatorial synoptic-scale dynamics (IPESD). This model includes the self-consistent quasi-linear interaction of synoptic-scale generalized steady Matsuno-Webster-Gill models with planetary-scale dynamics of equatorial long waves. These new models have the potential for providing self-consistent prognostic and diagnostic models for the intraseasonal tropical oscillation. Other applications of the systematic approach reveal three different balanced weak temperature gradient (WTG) approximations for the Tropics with different regimes of validity in space and time: a synoptic equatorial-scale WTG (SEWTG); a mesoscale equatorial WTG (MEWTG), which reduces to the classical models treated by others; and a new seasonal planetary equatorial WTG (SPEWTG). Both the SPEWTG and MEWTG model equations have solutions with general vertical structure, yet have the linearized dispersion relation of barotropic Rossby waves; thus, these models can play an important role in theories for midlatitude connections with the Tropics. The models are derived both from the equatorial shallow water equations in a simplified context and also as distinguished limits from the compressible primitive equations in general.

An investigation of shock diffraction through a non-quiescent background medium is presented using both experimental and numerical techniques. Unlike diffracting shocks in quiescent media, a spatial distortion of the shock front occurs, producing a region of constant shock angle. An example of this process arises in the exhaust from a pulse-detonation combustor. As the background velocity is increased, such as through the inclusion of a converging nozzle at the exhaust, the spatial distortion becomes more apparent. Numerical simulations using a compressible Euler solver demonstrate that the distortion is not due to the geometrical influence of the nozzle, but rather is a function of the magnitude of the background flow velocity. The distortion is studied using a modified geometrical shock dynamics formulation which includes the background flow and is validated against experiments. A simple model is presented to predict the shock distortion angle in the weak-shock limit. Finally, the axial decay behaviour of the shock is investigated and it is shown that the advection of the shock by the background flow delays the arrival of the head and tail of the expansion characteristic at the centreline. This leads to an increase in the rate of decay of the shock Mach number as the background flow velocity is increased. [ABSTRACT FROM AUTHOR]

A physico-mathematical model of open systems proposed in a previous paper (Delle Site and Klein 2020 J. Math. Phys. 61 083102) can represent a guiding reference in designing an accurate simulation scheme for an open molecular system embedded in a reservoir of energy and particles. The derived equations and the corresponding boundary conditions are obtained without assuming the action of an external source of heat that assures thermodynamic consistency of the open system with respect to a state of reference. However, in numerical schemes the temperature in the reservoir must be controlled by an external heat bath otherwise thermodynamic consistency cannot be achieved. In this perspective, the question to address is whether the explicit addition of an external heat bath in the theoretical model modifies the equations of the open system and its boundary conditions. In this work we consider this aspect and explicitly describe the evolution of the reservoir employing the Bergmannâ€"Lebowitz statistical model of thermostat. It is shown that the resulting equations for the open system itself are not affected by this change and an example of numerical application is reviewed where the current result shows its conceptual relevance. Finally, a list of pending mathematical and modelling problems is discussed the solution of which would strengthen the mathematical rigour of the model and offer new perspectives for the further development of a new multiscale simulation scheme. [ABSTRACT FROM AUTHOR]