Singular limits of Voigt models in fluid dynamics

We investigate the long-term behavior, as a certain regularization parametervanishes, of the three-dimensional Navier-Stokes-Voigt model of a viscoelasticincompressible fluid. We prove the existence of global and exponentialattractors of optimal regularity. We then derive explicit upper bounds for thedimension of these attractors in terms of the three-dimensional Grashof numberand the regularization parameter. Finally, we also prove convergence of the(strong) global attractor of the 3D Navier-Stokes-Voigt model to the (weak)global attractor of the 3D Navier-Stokes equation. Our analysis improves andextends recent results obtained by Kalantarov and Titi in [31].

The Real Spectrum of the Imaginary Cubic Oscillator: An Expository Proof

We give a partially alternate proof of reality of the spectrum of the imaginary cubic oscillator in quantum mechanics.

Effective thermal conductivity of helium II: from Landau to Gorter–Mellink regimes

The size-dependent and flux-dependent effective thermal conductivity of narrow channels filled with He II is analyzed. The classical Landau evaluation of the effective thermal conductivity of quiescent He II is extended to describe the transition to fully turbulent regime, where the heat flux is proportional to the cubic root of the temperature gradient (Gorter–Mellink regime). To do so, we use an expression for the quantum vortex line density L in terms of the heat flux considering the influence of the walls. From it, and taking into account the friction force of normal component against the vortices, we compute the effective thermal conductivity as a function of the heat flux, and we discuss in detail the corresponding size dependence

Nitrogen fixation assessment in a legume-dominant alpine community: comparison of different reference species using the 15N isotope dilution technique

Erratum to: Development and implementation of an integrated care pathway at the POLIKUM health centers using the example of anemia

A new and promising tool to evaluate mass and structural changes of skeletal muscle in trauma patients

Effect of suturing the femoral portion of a four‐strand graft during an ACL reconstruction

Purpose A suture passed along the part of the graft that will be inserted into the femoral tunnel is widely used by surgeons, because it could prevent the graft sliding on the femoral fixation device during pulling from the tibial side. The aim of this study was to evaluate the biomechanical effects of suturing the intratunnel femoral part of the graft during an anterior cruciate ligament (ACL) reconstruction. Methods Bovine digital extensor tendons and tibias were harvested from 20 fresh‐frozen mature bovine knees ranging in age from 18 to 24 months. Quadruple‐strand bovine tendons were passed through the tibial tunnel and secured distally with a bioabsorbable interference screw. In one half of all grafts ( N = 10), the looped‐over part of the graft was sutured in a whipstitch technique over a distance of 30 mm (Group 1). In one half of all grafts ( N = 10), the looped‐over part was left free from any suture (Group 2). The grafts were preconditioned at 50 N for 10 min, followed by cyclic loading at 1 Hz between 50 N and 250 N for 1,000 cycles. Load‐to‐failure test was then carried out at a rate of 1 mm/s. Results There was no statistically significant difference between mean stiffness at pullout and yield load between the two groups. In all specimens on Group 1, failure occurred following to partial breaking and then slipping of the tendons between the screw and the tunnel. Concerning Group 2, in six cases failure occurred as described for Group 1 specimens. In the remaining four cases, failure occurred entirely through the ligament mid‐substance. Conclusions Suturing in a whipstitch fashion the femoral portion of the graft doesn't affect the mechanical proprieties of the ACL graft. When suspension fixation device is used, suturing the looped‐over part of the graft could be helpful in order to provide equal tension in all of the strands of the graft at time of tibial fixation.

The analysis of tool life and wear mechanisms in spindle speed variation machining

Regenerative chatter vibrations generally limit the achievable material removal rate in machining. The diffusion of spindle speed variation (SSV) as a chatter suppression strategy is mainly restricted to academy and research centers. A lack of knowledge concerning the effects of non-stationary machining is still limiting its use in real shop floors. This research is focused on the effects of spindle speed variation technique on tool duration and on wear mechanisms. No previous researches have been performed on this specific topic. Tool wear tests in turning were carried out following a factorial design: cutting speed and cutting speed modulation were the investigated factors. The carbide life was the observed process response. A statistical approach was used to analyze the effects of the factors on the tool life. Moreover, the analysis was extended to the wear mechanisms involved during both constant speed machining and SSV. The worn-out carbide surfaces were examined under a scanning electron microscope equipped with an energy dispersive X-ray spectrometer. Significant differences were appreciated. It was observed that SSV tends to detach the coatings of the inserts, entailing a mechanism that is quite unusual in wet steel turning and thus fostering the wear of the tool. The performed analysis allowed to deduce that the intensified tool wear (in SSV cutting) is mainly due to thermo-mechanical fatigue

The Rabin cryptosystem revisited

The Rabin scheme used in public-key cryptosystem is here revisited with a focus limited to a few specific open issues. In particular, message decryption requires one out of four roots of a quadratic equation in a residue ring to be chosen, and a longstanding problem is to identify unambiguously and deterministically the encrypted message at the decryption side by adding the minimum number of extra bits to the cipher-text. While the question has already been solved for pairs of primes of the type 4$\mathit{k}+3, the general problem is here addressed. As one of the major results, an explicit solution with two extra bits is provided for pairs of primes that are congruent 5 modulo 8. The Rabin signature is also reconsidered from a deterministic point of view: a padding mechanism is proposed that avoids relying on a certain number of attempts until a suitable pad is found

A central limit theorem for the effective conductance: Linear boundary data and small ellipticity contrasts

Given a resistor network on $\mathbb Z^d$ with nearest-neighbor conductances,the effective conductance in a finite set with a given boundary condition isthe the minimum of the Dirichlet energy over functions with the prescribedboundary values. For shift-ergodic conductances, linear (Dirichlet) boundaryconditions and square boxes, the effective conductance scaled by the volume ofthe box converges to a deterministic limit as the box-size tends to infinity.Here we prove that, for i.i.d. conductances with a small ellipticity contrast,also a (non-degenerate) central limit theorem holds. The proof is based on thecorrector method and the Martingale Central Limit Theorem; a key integrabilitycondition is furnished by the Meyers estimate. More general domains, boundaryconditions and ellipticity contrasts will be addressed in a subsequent paper.