Explicit exactly energy-conserving methods for Hamiltonian systems

For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each time step, or are explicit, but where the exact conservation property depends on the exact evaluation of an integral in continuous time. Under further restrictions, namely that the potential energy contribution to the Hamiltonian is non-negative, newer techniques based on invariant energy quadratisation allow for exact numerical energy conservation and yield linearly implicit updates, requiring only the solution of a linear system at each time step. In this article, it is shown that, for a general class of Hamiltonian systems, and under the non-negativity condition on potential energy, it is possible to arrive at a fully explicit method that exactly conserves numerical energy. Furthermore, such methods are unconditionally stable, and are of comparable computational cost to the very simplest integration methods (such as Störmer-Verlet). A variant of this scheme leading to a conditionally-stable method is also presented, and follows from a splitting of the potential energy. Various numerical results are presented, in the case of the classic test problem of Fermi, Pasta and Ulam and for nonlinear systems of partial differential equations, including those describing high amplitude vibration of strings and plates

Real-Time Implementation of Non-Linear Physical Models with Modal Synthesis and Performance Analysis

Modal decomposition is a popular analysis approach involving the description of a target system via a bank of resonant oscillators called modes. Early sound synthesis frameworks successfully exploited this idea for the simulation of vibrating objects such as bars, plates and strings. While popular, modal synthesis is often applied to linear systems, since the modes become densely coupled in systems presenting distributed or multiple nonlinearities. In this work, the modal approach is used for the simulation of nonlinearly connected systems. When the nonlinearity is of cubic type, a suitable energy-stable modal update can be derived requiring the solution of a single linear system at each time step. A working plugin written in the C++ programming language is presented. Moreover, the performance of the plugin is analysed considering systems of different dimensions, defining the current limits for a real-time application of these models. The analysis also revealed a linear correlation between the number of modes which compose the systems and the CPU usage necessary for their real-time computation

The Dynamic Grid: Time-Varying Parameters for Musical Instrument Simulations Based on Finite-Difference Time-Domain Schemes

Several well-established approaches to physical modeling synthesis for musical instruments exist. Finite-difference time-domain methods are known for their generality and flexibility in terms of the systems one can model but are less flexible with regard to smooth parameter variations due to their reliance on a static grid. This paper presents the dynamic grid, a method to smoothly change grid configurations of finite-difference time-domain schemes based on sub-audio–rate time variation of parameters. This allows for extensions of the behavior of physical models beyond the physically possible, broadening the range of expressive possibilities for the musician. The method is applied to the 1D wave equation, the stiff string, and 2D systems, including the 2D wave equation and thin plate. Results show that the method does not introduce noticeable artefacts when changing between grid configurations for systems, including loss.Several well-established approaches to physical modeling synthesis for musical instruments exist. Finite-difference time-domain methods are known for their generality and flexibility in terms of the systems one can model but are less flexible with regard to smooth parameter variations due to their reliance on a static grid. This paper presents the dynamic grid, a method to smoothly change grid configurations of finite-difference time-domain schemes based on sub- audio–rate time variation of parameters. This allows for extensions of the behavior of physical models beyond the physically possible, broadening the range of expressive possibilities for the musician. The method is applied to the 1D wave equation, the stiff string, and 2D systems, including the 2D wave equation and thin plate. Results show that the method does not introduce noticeable artefacts when changing between grid configurations for systems, including loss

Wave turbulence in vibrating plates

International audienceTurbulence is a general term used for describing the erratic motions displayed by nonlinearsystems that are driven far from their equilibrium position and thus display complicatedmotions involving different time and length scales. Wave turbulence (WT) share many common ideas with turbulence, in particular asbeing a statistical theory for out-of-equilibrium systems. A main difference resides in thefact that the persistence of waves is assumed.The application of WT to vibrating plates started with the theoretical derivation ofthe kinetic equation from the dynamical von Karman equations thatdescribe large-amplitude motions of thin plates. Since this date, numerous papershave been published covering experimental, theoretical and numerical materials. In fact,it appears that the vibrating plate is a perfect candidate for a thorough comparison ofexperiments with theoretical predictions. As compared to other physical systems such ascapillary or gravity waves for example, an experimental set-up with a fine control of energyinjection and a confortable range of wavelength is not too difficult to put in place. Secondly,the available measurement techniques allow one to get a complete and precise picture of thedynamics through the scales, both in the space and frequency domains. Finally, numericalcodes with good accuracy have been developed so that all the underlying assumptions ofthe theory as well as its predictions have been tested, both on the experimental and thenumerical levels

Species-Specific Differences in Expression of G-Protein-Coupled Receptor Kinase (GRK) 7 and GRK1 in Mammalian Cone Photoreceptor Cells: Implications for Cone Cell Phototransduction

Desensitization plays an important role in the rapid termination of G-protein signaling pathways. This process, which involves phosphorylation by a G-protein-coupled receptor kinase (GRK) followed by arrestin binding, has been studied extensively in the rod photoreceptor cell of the mammalian retina. In contrast, less is known regarding desensitization in cone photoreceptor cells, which occurs more rapidly than in rod cells. Recently, our laboratory has cloned a novel GRK family member, GRK7, from the retina of a cone-dominant mammal, the 13-lined ground squirrel. Here we report the cloning of GRK7 from rod-dominant pig and human retinas, suggesting that this kinase plays a role in human visual signaling. Because GRK1 (rhodopsin kinase), the GRK that mediates rhodopsin desensitization in the rod cell, is reportedly expressed in both rods and cones, a detailed comparison of the localization of the two kinases is a necessary step toward determining their potential roles in cone visual signaling. Immunocytochemical analysis using antibodies selective for these two GRKs unexpectedly demonstrated species-specific differences in GRK7 and GRK1 expression in cones. In pigs and dogs, cones express only GRK7, whereas in mice and rats, we detected only GRK1 in cones. These results suggest that either GRK7 or GRK1 may participate in cone opsin desensitization, depending on the expression pattern of the kinases in different species. In contrast, GRK7 and GRK1 are coexpressed in monkey and human cones, suggesting that coordinate regulation of desensitization by both kinases may occur in primates

Efficacy of mRNA anti-SARS-CoV-2 vaccination and dynamics of humoral immune response in patients with solid tumors: results from the institutional registry of an italian tertiary cancer center

Background: Systemic immunosuppression characterizing cancer patients represents a concern regarding the efficacy of anti-severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccination, and real-world evidence is needed to define the efficacy and the dynamics of humoral immune response to mRNA-based anti-SARS-CoV-2 vaccines. Methods: We conducted an observational study that included patients with solid tumors who were candidates for mRNA anti-SARS-CoV-2 vaccination at the Fondazione IRCCS Istituto Nazionale dei Tumori, Milan, Italy. The primary objective was to monitor the immunologic response to the mRNA anti-SARS-CoV-2 vaccination in terms of anti-spike antibody levels. All the patients received two doses of the mRNA-1273 vaccine or the BNT162b2 vaccine. Healthcare workers served as a control group of healthy subjects. Results: Among the 243 patients included in the present analysis, 208 (85.60%) and 238 (97.94%) resulted seroconverted after the first and the second dose of vaccine, respectively. Only five patients (2.06%) had a negative titer after the second dose. No significant differences in the rate of seroconversion after two vaccine doses were observed in patients as compared with the control group of healthy subjects. Age and anticancer treatment class had an independent impact on the antibody titer after the second dose of vaccination. In a subgroup of 171 patients with available data about the third timepoint, patients receiving immunotherapy with immune checkpoint inhibitors seem to have a higher peak of antibodies soon after the second dose (3 weeks after), but a more pronounced decrease at a late timepoint (3 months after). Conclusions: The systemic immunosuppression characterizing cancer patients did not seem to dramatically affect the humoral response to anti-SARS-CoV-2 mRNA vaccines in our population of patients with solid tumors. Further investigation is needed to dissect the interplay between immunotherapy and longitudinal dynamics of humoral response to mRNA vaccines, as well as to analyze the cellular response to mRNA vaccines in cancer patients