Nambu representation of an extended Lorenz model with viscous heating

We consider the Nambu and Hamiltonian representations of Rayleigh-Benard convection with a nonlinear thermal heating effect proportional to the Eckert number (Ec). The model we use is an extension of the classical Lorenz-63 model with 4 kinematic and 6 thermal degrees of freedom. The conservative parts of the dynamical equations which include all nonlinearities satisfy Liouville's theorem and permit a conserved Hamiltonian H for arbitrary Ec. For Ec=0 two independent conserved Casimir functions exist, one of these is associated with unavailable potential energy and is also present in the Lorenz-63 truncation. This Casimir C is used to construct a Nambu representation of the conserved part of the dynamical system. The thermal heating effect can be represented either by a second canonical Hamiltonian or as a gradient (metric) system using the time derivative of the Casimir. The results demonstrate the impact of viscous heating in the total energy budget and in the Lorenz energy cycle for kinetic and available potential energy.Comment: 15 pages, no figur

Detection and correction of the misplacement error in THz Spectroscopy by application of singly subtractive Kramers-Kronig relations

In THz reflection spectroscopy the complex permittivity of an opaque medium is determined on the basis of the amplitude and of the phase of the reflected wave. There is usually a problem of phase error due to misplacement of the reference sample. Such experimental error brings inconsistency between phase and amplitude invoked by the causality principle. We propose a rigorous method to solve this relevant experimental problem by using an optimization method based upon singly subtractive Kramers-Kronig relations. The applicability of the method is demonstrated for measured data on an n-type undoped (100) InAs wafer in the spectral range from 0.5 up to 2.5 THz.Comment: 16 pages, 5 figure

Return levels of temperature extremes in southern Pakistan

Southern Pakistan (Sindh) is one of the hottest regions in the world and is highly vulnerable to temperature extremes. In order to improve rural and urban planning, it is useful to gather information about the recurrence of temperature extremes. In this work, return levels of the daily maximum temperature Tmax are estimated, as well as the daily maximum wet-bulb temperature TWmax extremes. We adopt the peaks over threshold (POT) method, which has not yet been used for similar studies in this region. Two main datasets are analyzed: temperatures observed at nine meteorological stations in southern Pakistan from 1980 to 2013, and the ERA-Interim (ECMWF reanalysis) data for the nearest corresponding locations. The analysis provides the 2-, 5-, 10-, 25-, 50-, and 100-year return levels (RLs) of temperature extremes. The 90 % quantile is found to be a suitable threshold for all stations. We find that the RLs of the observed Tmax are above 50 °C at northern stations and above 45 °C at the southern stations. The RLs of the observed TWmax exceed 35 °C in the region, which is considered as a limit of survivability. The RLs estimated from the ERA-Interim data are lower by 3 to 5 °C than the RLs assessed for the nine meteorological stations. A simple bias correction applied to ERA-Interim data improves the RLs remarkably, yet discrepancies are still present. The results have potential implications for the risk assessment of extreme temperatures in Sindh

Effects of stochastic parametrization on extreme value statistics

Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations are computational tools used in the Earth system models, which are aimed at reproducing the impact of unresolved scales on resolved scales. The performance of parametrizations has usually been examined on typical events rather than on extreme events. In this paper, we consider a modified version of the two-level Lorenz’96 model and investigate how two parametrizations of the fast degrees of freedom perform in terms of the representation of extreme events. One parametrization is constructed following Wilks [Q. J. R. Meteorol. Soc. 131, 389–407 (2005)] and is constructed through an empirical fitting procedure; the other parametrization is constructed through the statistical mechanical approach proposed by Wouters and Lucarini [J. Stat. Mech. Theory Exp. 2012, P03003 (2012); J. Stat. Phys. 151, 850–860 (2013)]. The two strategies show different advantages and disadvantages. We discover that the agreement between parametrized models and true model is in general worse when looking at extremes rather than at the bulk of the statistics. The results suggest that stochastic parametrizations should be accurately and specifically tested against their performance on extreme events, as usual optimization procedures might neglect them. The provision of accurate parametrizations is a task of paramount importance in many scientific areas and specifically in weather and climate modeling. Parametrizations are needed for representing accurately and efficiently the impact of the scales of motions and of the processes that cannot be explicitly represented by the numerical model. Parametrizations are usually constructed in order to optimize the overall performance of the model, thus aiming at an accurate representation of the bulk of the statistics. Nonetheless, numerical models are key to estimating, anticipating, and predicting extreme events. Here, we analyze critically in a simple yet illustrative example the performance of parametrizations in describing extreme events, and we conclude that good performance on typical conditions cannot be in any way extrapolated for rare conditions, which could, nonetheless, be of great practical relevance

Avalanches, breathers, and flow reversal in a continuous Lorenz-96 model

For the discrete model suggested by Lorenz in 1996, a one-dimensional long-wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low-order truncation, weak external forcing of the zonal mean flow induces avalanchelike breather solutions which cause reversal of the mean flow by a wave-mean flow interaction. The mechanism is an outburst-recharge process similar to avalanches in a sandpile model

Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

Stochastic resonance for nonequilibrium systems

Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy systems, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values. We propose here a general mathematical framework based on large deviation theory and, specifically, on the theory of quasipotentials, for describing SR in noisy N -dimensional nonequilibrium systems possessing two metastable states and undergoing a periodically modulated forcing. The drift and the volatility fields of the equations of motion can be fairly general, and the competing attractors of the deterministic dynamics and the edge state living on the basin boundary can, in principle, feature chaotic dynamics. Similarly, the perturbation field of the forcing can be fairly general. Our approach is able to recover as special cases the classical results previously presented in the literature for systems obeying detailed balance and allows for expressing the parameters describing SR and the statistics of residence times in the two-state approximation in terms of the unperturbed drift field, the volatility field, and the perturbation field. We clarify which specific properties of the forcing are relevant for amplifying or suppressing SR in a system and classify forcings according to classes of equivalence. Our results indicate a route for a detailed understanding of SR in rather general systems

News on immune checkpoint inhibitors as immunotherapy strategies in adult and pediatric solid tumors

Immune checkpoint inhibitors (ICIs) have shown unprecedented benefits in various adult cancers, and this success has prompted the exploration of ICI therapy even in childhood malignances. Although the use of ICIs as individual agents has achieved disappointing response rates, combinational therapies are likely to promise better results. However, only a subset of patients experienced prolonged clinical effects, thus suggesting the need to identify robust bio-markers that predict individual clinical response or resistance to ICI therapy as the main challenge. In this review, we focus on how the use of ICIs in adult cancers can be translated into pediatric malignances. We discuss the physiological mechanism of action of each IC, including PD-1, PD-L1 and CTLA-4 and the new emerging ones, LAG-3, TIM-3, TIGIT, B7-H3, BTLA and IDO-1, and evaluate their prognostic value in both adult and childhood tumors. Furthermore, we offer an overview of preclinical models and clinical trials currently under investigation to improve the effectiveness of cancer immunotherapies in these patients. Finally, we outline the main predictive factors that influence the efficacy of ICIs, in order to lay the basis for the development of a pan-cancer immunogenomic model, able to direct young patients towards more specific immunotherapy

Entropy production and coarse graining of the climate fields in a general circulation model

We extend the analysis of the thermodynamics of the climate system by investigating the role played by processes taking place at various spatial and temporal scales through a procedure of coarse graining. We show that the coarser is the graining of the climatic fields, the lower is the resulting estimate of the material entropy production. In other terms, all the spatial and temporal scales of variability of the thermodynamic fields provide a positive contribution to the material entropy production. This may be interpreted also as that, at all scales, the temperature fields and the heating fields resulting from the convergence of turbulent fluxes have a negative correlation, while the opposite holds between the temperature fields and the radiative heating fields. Moreover, we obtain that the latter correlations are stronger, which confirms that radiation acts as primary driver for the climatic processes, while the material fluxes dampen the resulting fluctuations through dissipative processes. We also show, using specific coarse-graining procedures, how one can separate the various contributions to the material entropy production coming from the dissipation of kinetic energy, the vertical sensible and latent heat fluxes, and the large scale horizontal fluxes, without resorting to the full three-dimensional time dependent fields. We find that most of the entropy production is associated to irreversible exchanges occurring along the vertical direction, and that neglecting the horizontal and time variability of the fields has a relatively small impact on the estimate of the material entropy production. The approach presented here seems promising for testing climate models, for assessing the impact of changing their parametrizations and their resolution, as well as for investigating the atmosphere of exoplanets, because it allows for evaluating the error in the estimate of their thermodynamical properties due to the lack of high-resolution data. The findings on the impact of coarse graining on the thermodynamic fields on the estimate of the material entropy production deserve to be explored in a more general context, because they provide a way for understanding the relationship between forced fluctuations and dissipative processes in continuum systems

Universal Properties of Nonlinear Response Functions of Nonequilibrium Steady States

We derive universal properties of nonlinear response functions of nonequilibrium steady states. In particular, sum rules and asymptotic behaviors are derived. Their consequences are illustrated for nonlinear optical materials and nonlinear electrical conductors.Comment: 10 pages, 1 figure; added a few sentences and references to explain detail