Stability of the Iteration Method for non Expansive Mappings

The general iteration method for nonexpansive mappings on a Banach space is considered. Under some assumption of fast enough convergence on the sequence of (“almost” nonexpansive) perturbed iteration mappings, if the basic method is τ−convergent for a suitable topology τ weaker than the norm topology, then the perturbed method is also τ−convergent. Application is presented to the gradient-prox method for monotone inclusions in Hilbert spaces

Well-Posedness, Conditioning and Regularization of Minimization, Inclusion and Fixed-Point Problems

AMS subject classification: 65K10, 49M07, 90C25, 90C48.Well-posedness, conditioning and regularization of fixed-point problems are studied in connexion with well-posedness, conditioning and Tikhonov regularization of minimization and inclusion problems. Equivalence theorems are proved. Coupling iteration and well-posedness as well as iteration and regularization are also considered

Tunable Passive Shock and Vibration Isolators for Rotational Isolation

Shock and vibration isolation are a critical need in helmets, which are widely used to protect athletes, workers, soldiers, and astronauts. Passive vibration isolation systems are a good option when mass and volume should be minimized and when the experienced loadings can be predicted. However, it is frequently challenging to find materials and structures which exhibit the optimal vibration and impact isolation properties for an application. As a case study illustrating a novel design paradigm for rotational shock absorption, a family of optimal solutions for the physical properties of American football helmets is presented. Lumped parameter Simulink models simulate a variety of impacts to a helmeted head. These models were optimized to minimize the Head Injury Criterion (HIC) and Helmet Performance Score (HPS) metrics and determine the optimal values of rotational and translational stiffness and damping between the head and helmet. The optimization of the 1-dimensional simulations was validated with an analytical solution to the optimization problem. The 3-dimensional simulation suggested that a helmet optimized considering both rotational and translational accelerations could improve the Helmet Performance Score by 48% or more as compared to translational accelerations only. The optimal stiffness and damping computed from the models was used to drive the design of multi-material shock absorbing elements. A custom impact testing machine was used to test the mechanical properties of prototype isolators. A 3D printed TPU shock absorber was designed within 2.2% of the target optimal stiffness; however, no materials were found that could provide enough damping. This research illustrates a new design paradigm for independent tuning of rotational energy storage and dissipation that can be translated to a variety of applications

Effect of Hydrodynamic Force on Microcantilever Vibrations: Applications to Liquid-Phase Chemical Sensing

At the microscale, cantilever vibrations depend not only on the microstructure’s properties and geometry but also on the properties of the surrounding medium. In fact, when a microcantilever vibrates in a fluid, the fluid offers resistance to the motion of the beam. The study of the influence of the hydrodynamic force on the microcantilever’s vibrational spectrum can be used to either (1) optimize the use of microcantilevers for chemical detection in liquid media or (2) extract the mechanical properties of the fluid. The classical method for application (1) in gas is to operate the microcantilever in the dynamic transverse bending mode for chemical detection. However, the performance of microcantilevers excited in this standard out-of-plane dynamic mode drastically decreases in viscous liquid media. When immersed in liquids, in order to limit the decrease of both the resonant frequency and the quality factor, and improve sensitivity in sensing applications, alternative vibration modes that primarily shear the fluid (rather than involving motion normal to the fluid/beam interface) have been studied and tested: these include in-plane vibration modes (lateral bending mode and elongation mode). For application (2), the classical method to measure the rheological properties of fluids is to use a rheometer. However, such systems require sampling (no in-situ measurements) and a relatively large sample volume (a few milliliters). Moreover, the frequency range is limited to low frequencies (less than 200Hz). To overcome the limitations of this classical method, an alternative method based on the use of silicon microcantilevers is presented. The method, which is based on the use of analytical equations for the hydrodynamic force, permits the measurement of the complex shear modulus of viscoelastic fluids over a wide frequency range

Influence of Fluid-Structure Interaction on Microcantilever Vibrations: Applications to Rheological Fluid Measurement and Chemical Detection

At the microscale, cantilever vibrations depend not only on the microstructure’s properties and geometry but also on the properties of the surrounding medium. In fact, when a microcantilever vibrates in a fluid, the fluid offers resistance to the motion of the beam. The study of the influence of the hydrodynamic force on the microcantilever’s vibrational spectrum can be used to either (1) optimize the use of microcantilevers for chemical detection in liquid media or (2) extract the mechanical properties of the fluid. The classical method for application (1) in gas is to operate the microcantilever in the dynamic transverse bending mode for chemical detection. However, the performance of microcantilevers excited in this standard out-of-plane dynamic mode drastically decreases in viscous liquid media. When immersed in liquids, in order to limit the decrease of both the resonant frequency and the quality factor, alternative vibration modes that primarily shear the fluid (rather than involving motion normal to the fluid/beam interface) have been studied and tested: these include inplane vibration modes (lateral bending mode and elongation mode). For application (2), the classical method to measure the rheological properties of fluids is to use a rheometer. To overcome the limitations of this classical method, an alternative method based on the use of silicon microcantilevers is presented. The method, which is based on the use of analytical equations for the hydrodynamic force, permits the measurement of the complex shear modulus of viscoelastic fluids over a wide frequency range

When virulence originates from non-agricultural hosts: New insights into plant breeding

Monogenic plant resistance breakdown is a model for testing evolution in action in pathogens. As a rule, plant pathologists argue that virulence – the allele that allows pathogens to overcome resistance – is due to a new mutation at the avirulence locus within the native/endemic population that infects susceptible crops. In this article, we develop an alternative and neglected scenario where a given virulence pre-exists in a non-agricultural host and might be accidentally released or introduced on the matching resistant cultivar in the field. The main difference between the two scenarios is the divergence time expected between the avirulent and the virulent populations. As a consequence, population genetic approaches such as genome scans and Approximate Bayesian Computation methods allow explicit testing of the two scenarios by timing the divergence. This review then explores the fundamental implications of this alternative scenario for plant breeding, including the invasion of virulence or the evolution of more aggressive hybrids, and proposes concrete solutions to achieve a sustainable resistance

Search for Randall-Sundrum excitations of gravitons decaying into two photons for CMS at LHC

The CMS detector discovery potential to the resonant production of massive Kaluza - Klein excitations expected in Randall-Sundrum model is studied. Full simulation and reconstruction are used to study diphoton decay of Randall-Sundrum gravitons. For an integrated luminosity of 30 fb^-1 diphoton decay of Randall-Sundrum graviton can be discovered at 5 sigma level for masses up to 1.61~tevsucqua in case of weak coupling between graviton excitations and Standard model particles (c=0.01). Heavier resonances can be detected for larger coupling constant (c=0.1), with mass reach of 3.95~tevsucqua