Fast nonlinear Froude–Krylov force calculation for prismatic floating platforms: a wave energy conversion application case

Computationally fast and accurate mathematical models are essential for effective design, optimization, and control of wave energy converters. However, the energy-maximising control strategy, essential for reaching economic viability, inevitably leads to the violation of linearising assumptions, so the common linear models become unreliable and potentially unrealistic. Partially nonlinear models based on the computation of Froude–Krylov forces with respect to the instantaneous wetted surface are promising and popular alternatives, but they are still too slow when floaters of arbitrary complexity are considered; in fact, mesh-based spatial discretisation, required by such geometries, becomes the computational bottle-neck, leading to simulations 2 orders of magnitude slower than real-time, unaffordable for extensive iterative optimizations. This paper proposes an alternative analytical approach for the subset of prismatic floating platforms, common in the wave energy field, ensuring computations 2 orders of magnitude faster than real-time, hence 4 orders of magnitude faster than state-of-the-art mesh-based approaches. The nonlinear Froude–Krylov model is used to investigate the nonlinear hydrodynamics of the floater of a pitching wave energy converter, extracting energy either from pitch or from an inertially coupled internal degree of freedom, especially highlighting the impact of state constraints, controlled/uncontrolled conditions, and impact on control parameters’ optimization, sensitivity and effectiveness.

A straightforward and Lagrangian proof of the Einsteinian equivalence between the mass and the inernal energy (i.e. rest energy)

I propose a Lagrangian proof of Einstein's well-known law that the mass of any system is its internal energy. The interest of this proof is to show how the distinction between internal degrees of freedom and the center of mass appears in the Lagrangian formalism. Considering that the Lagrangian depends on a particular set of variables for the internal degree of freedom, I show in a standard Lagrangian way how one can naturally find the desired law. This proof does not use the tensors of energy-momentum and can be easily used by students familiar with Lagrangian mechanics and the basis of Special Relativity. I apply the method for the particles and for the field, using the scalar field for simplification but it is easy to generalize for other fields (containing only the first derivative in Lagrangian). I give the example for the gravitation field. The method permits us to observe a strong relation between the Einstein’s E=mc² law and his other famous law of the time dilation. I carefully analyze the meaning of the particular choice of the variable and showing a sort of a modified speed addition formula without contradicting, of course, the one of Einstein (& Poincaré). I also try to untangle, with this point of view, the relation between the mass and the origin of the energy scale. Finally I analyze the reason why in Newtonian mechanic we don’t have a such law. In the annex I give some elements of the Hamiltonian analysis checking again the coherence of the particular set of variables and I apply this way of thinking to the old Lorentz-Poincaré model of the electron (useful for an explicit classical renormalization of the mass).

A straightforward and Lagrangian proof of the Einsteinian equivalence between the mass and the inernal energy (i.e. rest energy) V2

I propose a Lagrangian proof of Einstein's well-known law that the mass system is its internal energy. The interest of this proof is to show how the distinction between internal degrees of freedom and the center of mass appears in the Lagrangian formalism. Considering that the Lagrangian depends on a particular set of variables for the internal degree of freedom, I show in a standard Lagrangian way how one can naturally find the desired law. This proof does not use the tensors of energy-momentum and can be easily used by students familiar with Lagrangian mechanics and the basis of special relativity. I apply the method for the particles and for the field, using the scalar field for simplification but it is easy to generalize for other fields (containing only the first derivative in Lagrangian). I give the example for the gravitation field. The method permits us to observe a strong relation between the Einstein’s E=mc² law and his other famous law of the time dilatation. I carefully analyze the meaning of the particular choice of the variable and showing a sort of a modified speed addition formula without contradicting, of course, the one of Einstein (& Poincaré). I also try to untangle (for myself at least) the relation between the mass and the origin of the energy scale. Finally I analyze the reason why in Newtonian mechanic we don’t have a such law. In future complement I will apply this way of thinking in the toy model of the electron (useful for an explicit classical renormalization of the mass) and the effective description of a complex system in term of a particle in order to better understand the passage from this 2 forms of description often used but never really explained.

Homogeneous open quantum walks on the line: criteria for site recurrence and absorption

In this work, we study open quantum random walks, as described by S. Attal et al.. These objects are given in terms of completely positive maps acting on trace-class operators, leading to one of the simplest open quantum versions of the recurrence problem for classical, discrete-time random walks. This work focuses on obtaining criteria for site recurrence of nearest-neighbor, homogeneous walks on the integer line, with the description presented here making use of recent results of the theory of open walks, most particularly regarding reducibility properties of the operators involved. This allows us to obtain a complete criterion for site recurrence in the case for which the internal degree of freedom of each site (coin space) is of dimension 2. We also present the analogous result for irreducible walks with an internal degree of arbitrary finite dimension and the absorption problem for walks on the semi-infinite line.

Large flux-mediated coupling in hybrid electromechanical system with a transmon qubit

Control over the quantum states of a massive oscillator is important for several technological applications and to test the fundamental limits of quantum mechanics. Addition of an internal degree of freedom to the oscillator could be a valuable resource for such control. Recently, hybrid electromechanical systems using superconducting qubits, based on electric-charge mediated coupling, have been quite successful. Here, we show a hybrid device, consisting of a superconducting transmon qubit and a mechanical resonator coupled using the magnetic-flux. The coupling stems from the quantum-interference of the superconducting phase across the tunnel junctions. We demonstrate a vacuum electromechanical coupling rate up to 4 kHz by making the transmon qubit resonant with the readout cavity. Consequently, thermal-motion of the mechanical resonator is detected by driving the hybridized-mode with mean-occupancy well below one photon. By tuning qubit away from the cavity, electromechanical coupling can be enhanced to 40 kHz. In this limit, a small coherent drive on the mechanical resonator results in the splitting of qubit spectrum, and we observe interference signature arising from the Landau-Zener-Stückelberg effect. With improvements in qubit coherence, this system offers a platform to realize rich interactions and could potentially provide full control over the quantum motional states.

Faint trace of a particle in a noisy Vaidman three-path interferometer

We study weak traces of particle passing Vaidman’s nested Mach–Zehnder interferometer. We investigate an effect of decoherence caused by an environment coupled to internal degree of freedom (a spin) of a travelling particle. We consider two models: pure decoherence leading to exact results and weak coupling Davies approximation allowing to include dissipative effects. We show that potentially anomalous discontinuity of particle paths survives an effect of decoherence unless it affects internal part of the nested interferometer.

Large Flux-Mediated Coupling in Hybrid Electromechanical System With A Transmon Qubit

Control over the quantum states of a massive oscillator is important for several technological applications and to test the fundamental limits of quantum mechanics. Addition of an internal degree of freedom to the oscillator could be a valuable resource for such control. Recently, hybrid electromechanical systems using superconducting qubits, based on electric-charge mediated coupling, have been quite successful. Here, we realize a hybrid device, consisting of a superconducting transmon qubit and a mechanical resonator coupled using the magnetic-flux. The coupling stems from the quantum-interference of the superconducting phase across the tunnel junctions. We demonstrate a vacuum electromechanical coupling rate up to 4 kHz by making the transmon qubit resonant with the readout cavity. Consequently, thermal-motion of the mechanical resonator is detected by driving the hybridized-mode with mean-occupancy well below one photon. By tuning qubit away from the cavity, electromechanical coupling can be enhanced to 40 kHz. In this limit, a small coherent drive on the mechanical resonator results in the splitting of qubit spectrum, and we observe interference signature arising from the Landau–Zener–Stückelberg effect. With improvements in qubit coherence, this system offers a novel platform to realize rich interactions and could potentially provide full control over the quantum motional states.

A method for estimating coherence of molecular mechanisms in major human disease and traits

Background Phenotypes such as height and intelligence, are thought to be a product of the collective effects of multiple phenotype-associated genes and interactions among their protein products. High/low degree of interactions is suggestive of coherent/random molecular mechanisms, respectively. Comparing the degree of interactions may help to better understand the coherence of phenotype-specific molecular mechanisms and the potential for therapeutic intervention. However, direct comparison of the degree of interactions is difficult due to different sizes and configurations of phenotype-associated gene networks. Methods We introduce a metric for measuring coherence of molecular-interaction networks as a slope of internal versus external distributions of the degree of interactions. The internal degree distribution is defined by interaction counts within a phenotype-specific gene network, while the external degree distribution counts interactions with other genes in the whole protein–protein interaction (PPI) network. We present a novel method for normalizing the coherence estimates, making them directly comparable. Results Using STRING and BioGrid PPI databases, we compared the coherence of 116 phenotype-associated gene sets from GWAScatalog against size-matched KEGG pathways (the reference for high coherence) and random networks (the lower limit of coherence). We observed a range of coherence estimates for each category of phenotypes. Metabolic traits and diseases were the most coherent, while psychiatric disorders and intelligence-related traits were the least coherent. We demonstrate that coherence and modularity measures capture distinct network properties. Conclusions We present a general-purpose method for estimating and comparing the coherence of molecular-interaction gene networks that accounts for the network size and shape differences. Our results highlight gaps in our current knowledge of genetics and molecular mechanisms of complex phenotypes and suggest priorities for future GWASs.