Lagrangian and Hamiltonian two-scale reduction

Studying high-dimensional Hamiltonian systems with microstructure, it is an important and challenging problem to identify reduced macroscopic models that describe some effective dynamics on large spatial and temporal scales. This paper concerns the question how reasonable macroscopic Lagrangian and Hamiltonian structures can by derived from the microscopic system. In the first part we develop a general approach to this problem by considering non-canonical Hamiltonian structures on the tangent bundle. This approach can be applied to all Hamiltonian lattices (or Hamiltonian PDEs) and involves three building blocks: (i) the embedding of the microscopic system, (ii) an invertible two-scale transformation that encodes the underlying scaling of space and time, (iii) an elementary model reduction that is based on a Principle of Consistent Expansions. In the second part we exemplify the reduction approach and derive various reduced PDE models for the atomic chain. The reduced equations are either related to long wave-length motion or describe the macroscopic modulation of an oscillatory microstructure.Comment: 40 page

Unified radio and network control across heterogeneous hardware platforms

Experimentation is an important step in the investigation of techniques for handling spectrum scarcity or the development of new waveforms in future wireless networks. However, it is impractical and not cost effective to construct custom platforms for each future network scenario to be investigated. This problem is addressed by defining Unified Programming Interfaces that allow common access to several platforms for experimentation-based prototyping, research, and development purposes. The design of these interfaces is driven by a diverse set of scenarios that capture the functionality relevant to future network implementations while trying to keep them as generic as possible. Herein, the definition of this set of scenarios is presented as well as the architecture for supporting experimentation-based wireless research over multiple hardware platforms. The proposed architecture for experimentation incorporates both local and global unified interfaces to control any aspect of a wireless system while being completely agnostic to the actual technology incorporated. Control is feasible from the low-level features of individual radios to the entire network stack, including hierarchical control combinations. A testbed to enable the use of the above architecture is utilized that uses a backbone network in order to be able to extract measurements and observe the overall behaviour of the system under test without imposing further communication overhead to the actual experiment. Based on the aforementioned architecture, a system is proposed that is able to support the advancement of intelligent techniques for future networks through experimentation while decoupling promising algorithms and techniques from the capabilities of a specific hardware platform

Boundary effects on the dynamics of chains of coupled oscillators

We study the dynamics of a chain of coupled particles subjected to a restoring force (Klein-Gordon lattice) in the cases of either periodic or Dirichlet boundary conditions. Precisely, we prove that, when the initial data are of small amplitude and have long wavelength, the main part of the solution is interpolated by a solution of the nonlinear Schr\"odinger equation, which in turn has the property that its Fourier coefficients decay exponentially. The first order correction to the solution has Fourier coefficients that decay exponentially in the periodic case, but only as a power in the Dirichlet case. In particular our result allows one to explain the numerical computations of the paper \cite{BMP07}

Bifurcations of discrete breathers in a diatomic Fermi-Pasta-Ulam chain

Discrete breathers are time-periodic, spatially localized solutions of the equations of motion for a system of classical degrees of freedom interacting on a lattice. Such solutions are investigated for a diatomic Fermi-Pasta-Ulam chain, i. e., a chain of alternate heavy and light masses coupled by anharmonic forces. For hard interaction potentials, discrete breathers in this model are known to exist either as ``optic breathers'' with frequencies above the optic band, or as ``acoustic breathers'' with frequencies in the gap between the acoustic and the optic band. In this paper, bifurcations between different types of discrete breathers are found numerically, with the mass ratio m and the breather frequency omega as bifurcation parameters. We identify a period tripling bifurcation around optic breathers, which leads to new breather solutions with frequencies in the gap, and a second local bifurcation around acoustic breathers. These results provide new breather solutions of the FPU system which interpolate between the classical acoustic and optic modes. The two bifurcation lines originate from a particular ``corner'' in parameter space (omega,m). As parameters lie near this corner, we prove by means of a center manifold reduction that small amplitude solutions can be described by a four-dimensional reversible map. This allows us to derive formally a continuum limit differential equation which characterizes at leading order the numerically observed bifurcations.Comment: 30 pages, 10 figure

Subacute dislocation of the elbow following Galeazzi fracture-dislocation of the radius: A case report

<p>Abstract</p> <p>Introduction</p> <p>The Galeazzi fracture-dislocation was originally described by Sir Astley Cooper in 1822 but was named after Italian surgeon Ricardo Galeazzi in 1934. It is an injury classified as a radial shaft fracture with associated dislocation of the distal radioulnar joint and disruption of the forearm axis joint. The associated distal radioulnar joint injury may be purely ligamentous in nature, tearing the triangular fibrocartilaginous complex, or involve bony tissue (that is, ulnar styloid avulsions) or both. We report this case because of the rare association of posterior dislocation of the elbow along with Galeazzi fracture-dislocation. To the best of our knowledge, this has not been previously reported in the English literature.</p> <p>Case presentation</p> <p>A 26-year-old Caucasian man presented to our department after a fall from a motorbike. He sustained a closed, isolated Galeazzi fracture-dislocation of the right forearm and no associated elbow injuries, and this necessitated open reduction and internal fixation of the radius. Post-operative radiographs films were satisfactory. However, clinical and radiological evidence of ipsilateral elbow dislocation was noted at a five-week follow-up, subsequently requiring open reduction of the joint and collateral ligament repair. Our patient was noted to have full elbow and forearm function at three months.</p> <p>Conclusions</p> <p>Although the Galeazzi fracture-dislocation has been classically described as involving only the distal radioulnar joint, traumatic forces can be transmitted to the elbow via the interosseous membrane of the forearm. This can lead to instability of the elbow joint. Therefore, we recommend that, in every case of forearm fracture, both elbow and wrist joints be assessed clinically as well as radiologically for subluxation or dislocation.</p

Isochronism and tangent bifurcation of band edge modes in Hamiltonian lattices

In {\em Physica D} {\bf 91}, 223 (1996), results were obtained regarding the tangent bifurcation of the band edge modes ($q=0,\pi$) of nonlinear Hamiltonian lattices made of $N$ coupled oscillators. Introducing the concept of {\em partial isochronism} which characterises the way the frequency of a mode, $\omega$, depends on its energy, $\epsilon$, we generalize these results and show how the bifurcation energies of these modes are intimately connected to their degree of isochronism. In particular we prove that in a lattice of coupled purely isochronous oscillators ($\omega(\epsilon)$ strictly constant), the in-phase mode ($q=0$) never undergoes a tangent bifurcation whereas the out-of-phase mode ($q=\pi$) does, provided the strength of the nonlinearity in the coupling is sufficient. We derive a discrete nonlinear Schr\"odinger equation governing the slow modulations of small-amplitude band edge modes and show that its nonlinear exponent is proportional to the degree of isochronism of the corresponding orbits. This equation may be seen as a link between the tangent bifurcation of band edge modes and the possible emergence of localized modes such as discrete breathers.Comment: 23 pages, 1 figur

Sub-micromolar pulse dipolar EPR spectroscopy reveals increasing CuII-labelling of double-histidine motifs with lower temperature

Electron paramagnetic resonance (EPR) distance measurements are making increasingly important contributions to the studies of biomolecules by providing highly accurate geometric constraints. Combining double-histidine motifs with CuII spin labels can further increase the precision of distance measurements. It is also useful for proteins containing essential cysteines that can interfere with thiol-specific labelling. However, the non-covalent CuII coordination approach is vulnerable to low binding-affinity. Herein, dissociation constants (KD) are investigated directly from the modulation depths of relaxation-induced dipolar modulation enhancement (RIDME) EPR experiments. This reveals low- to sub-μm CuII KDs under EPR distance measurement conditions at cryogenic temperatures. We show the feasibility of exploiting the double-histidine motif for EPR applications even at sub-μm protein concentrations in orthogonally labelled CuII–nitroxide systems using a commercial Q-band EPR instrument.Publisher PDFPeer reviewe

What Ukraine Taught NATO about Hybrid Warfare

Russia’s invasion of Ukraine in 2022 forced the United States and its NATO partners to be confronted with the impact of hybrid warfare far beyond the battlefield. Targeting Europe’s energy security, Russia’s malign influence campaigns and malicious cyber intrusions are affecting global gas prices, driving up food costs, disrupting supply chains and grids, and testing US and Allied military mobility. This study examines how hybrid warfare is being used by NATO’s adversaries, what vulnerabilities in energy security exist across the Alliance, and what mitigation strategies are available to the member states. Cyberattacks targeting the renewable energy landscape during Europe’s green transition are increasing, making it urgent that new tools are developed to protect these emerging technologies. No less significant are the cyber and information operations targeting energy security in Eastern Europe as it seeks to become independent from Russia. Economic coercion is being used against Western and Central Europe to stop gas from flowing. China’s malign investments in Southern and Mediterranean Europe are enabling Beijing to control several NATO member states’ critical energy infrastructure at a critical moment in the global balance of power. What Ukraine Taught NATO about Hybrid Warfare will be an important reference for NATO officials and US installations operating in the European theater.https://press.armywarcollege.edu/monographs/1952/thumbnail.jp