Presence Of Stiffness Research Articles

Rigid iatrogenic hallux varus: a decades’ worth experience with arthrodesis of the metatarsophalangeal joint

PurposeArthrodesis of the first ray metatarsophalangeal joint (MPJ) is the gold standard in iatrogenic hallux varus (IHV) in the presence of stiffness and osteoarthritis. The purpose of this study is to collect clinical and radiographic results and complications of MPJ arthrodesis in rigid iatrogenic HV.MethodsA retrospective evaluation of rigid iatrogenic HV undergoing arthrodesis with a minimum follow-up (FU) of two years was performed. The clinical parameters assessed were visual analog scale (VAS), the AOFAS Hallux Metatarsophalangeal-Interphalangeal Scale score and the satisfaction scale. The radiological parameters evaluated the first to second metatarsal angle (IMA) and the angle of hallux valgus (HVA). Complications were also analysed.ResultA total of 18 patients (19 procedures) with a mean FU of 5.5 ± 2.5 years were included. The mean VAS improved from 7.3 ± 1.6 to 1.3 ± 1.2 (p < 0.05) at the last FU. Similarly, the AOFAS Hallux Metatarsophalangeal-Interphalangeal scale score significantly improved to 82 ± 9.2 (p < 0.05). Radiological evaluation demonstrated a 1–2 IMA improvement from 4.4 ± 2.2° preoperatively to 8.9 ± 2.4° at 3 months post-operatively. Similarly, there was a significant (p < 0.05) improvement of the HVA from − 22.7 ± 4.1° to 13.1 ± 4.1° at three months post-operative (p < 0.05). No signification loss of correction was noted at the last follow-up (p > 0.05). In one case, a delayed fusion at the arthrodesis site required surgical revision to promote fusion. No patient experienced pain with stress from the first MTP joint arthrodesis site or identified the arthrodesis site as a source of pain. No patient required implant removal. Re-operation and revision rates were 5.3%. The overall complications rate was 15.8%.ConclusionsMPJ fusion effectively corrects Iatrogenic Hallux Varus in cases of rigid and fixed deformities in the medium- to long-term follow-up, with lasting improvements in AOFAS and VAS scores. The procedure is characterised by a non-negligible risk of complications, reoperations and revisions.Level of evidenceLevel IV, case series.

Prognostic factors and the value of radiographic osteoarthritis for persistent complaints after referral for ankle radiography

BackgroundAnkle symptoms are a common reason to consult the general practitioner and often persist for years. In a population referred for ankle radiography, the prevalence of radiographic osteoarthritis (OA) is substantial, but its additional predictive value for persistent symptoms is unknown. Therefore, we examined the prognosis of symptoms 2–3 years after referral for ankle radiography, assessed clinical prognostic factors, and the additional predictive value of radiographic OA for persistent ankle complaints. MethodsWe included 893 adults referred for ankle radiography and studied the following candidate prognostic factors at baseline: age, sex, body mass index (BMI), referral for chronic complaints (>3 months), pain during activity (NRS-11) and presence of stiffness and functional loss as predominant symptom. X-rays were scored for radiographic OA. After 2–3 years participants were invited for a follow-up questionnaire including persistence of ankle complaints. To assess prognostic factors for persistent complaints, uni- and multivariable logistic regression were used. ResultsOf the 194 responders at follow-up, ankle complaints persisted in 71(36.6 %). BMI (OR 1.08; 95 % CI 1.01–1.15), stiffness as predominant symptom (OR 1.69; 95 % CI 0.89–3.21), and chronic complaints (OR 2.84; 95 % CI 1.45–5.57) were in the initial model for persistent complaints (AUC=0.69). After adding radiographic OA (OR 2.36; 95 % CI 1.01–5.50), the AUC of the final model became 0.70. ConclusionAnkle complaints persist in a considerable proportion of patients 2–3 years after referral for ankle radiography. BMI, chronic complaints and radiographic OA are prognostic factors for persistent complaints, but the additional predictive value of radiographic OA on top of clinical factors is negligible.

Comparative Efficacy of Oxitard Capsules and Immusante Tablets in Early Stages of Oral Submucous Fibrosis - A Randomized Controlled Trial

Objective: Oral submucous fibrosis (OSMF) is manifested by symptoms such as palpable fibrotic bands, ulceration, presence of stiffness in the mouth and lip, xerostomia, pigmentation in the oral mucosal layer, and burning sensation and drying of the mouth. It poses a challenge for researchers as there is no viable therapy for this gradually debilitating disorder with a high malignancy potential. Ayurveda is a traditional medicinal practice of the past and present times which can be useful in providing a viable cure. Thus, the current study was designed to assess and compare the effect of Oxitard capsule and Immusante tablet on the clinical and subjective symptoms of OSMF. Material and Methods: The study included 36 patients with clinically diagnosed OSMF who were split evenly into two groups: Group A, the Oxitard group, and Group B, the Immusante group. For three months, Group A received two Oxitard capsules twice daily, while Group B received two Immusante tablets twice daily. At regular intervals, the clinical parameters were evaluated, and the data were analysed using repeated measures ANOVA and the Bonferroni post hoc test. P-value≤0.05 was regarded as statistically significant. Results: On assessment of mouth opening, tongue protrusion, cheek flexibility and subjective symptoms there was significant improvement reported in both groups. In group comparison, the Oxitard and Immusante groups showed a significant difference in cheek flexibility at 3 months. There were no significant differences in subjective symptoms in either of the groups pre- and post-treatment. Conclusion: Efficacy of both the drugs were equall was found to be similar when used as an adjunct to tobacco cessation counselling in the management of early stages of oral submucous fibrosis when used as an adjunct to behavioral management.

Observation of avalanche-like transport in Heliotron J and JT-60U plasmas

The avalanche type of transport can induce a long-radial transport and thus can contribute to the global profile formation. In this study, we observed the heat perturbations exhibiting avalanche-like transport in the stellarator/heliotron device, Heliotron J, and the tokamak device, JT-60U. We found that the electron heat propagation in Heliotron J is mainly generated from the heating source region. The relatively high value of the Hurst exponent, which is a signature of avalanches, depends on the total heating power. On the other hand, the electron and ion heat avalanches measured in JT-60U tend to spread from the local peak of the temperature gradient and are not influenced by the heating source profiles. The contrasting features of avalanches in stellarator/heliotrons and tokamaks potentially imply the difference in the temperature profile formation, such as the presence of stiffness.

Incidence and risk factors for shoulder stiffness after open and arthroscopic rotator cuff repair.

The aim of this study was to estimate the incidence of stiffness during the first 6 months after rotator cuff repair and to evaluate postoperative stiffness with respect to its risk factors and its influence on the outcome at 6 months postoperatively. In a prospective cohort of 117 patients (69 women, 48 men; average age 59) from our institutional rotator cuff registry, who underwent either arthroscopic (n = 77) or open (n = 40) rotator cuff repair, we measured shoulder range of motion (ROM) at 3 and 6 months post-surgery. We evaluated the incidence of stiffness and analyzed functional outcomes, comparing various preoperative and intraoperative factors in patients with stiffness to those without at the 6-month mark. Shoulder stiffness was observed in 31% of patients (36/117) at 3 months postoperatively, decreasing to 20% (23/117) at 6 months. No significant link was found between stiffness at 6 months and demographic factors, preoperative stiffness, tear characteristics, or the type of repair. Notably, patients undergoing arthroscopic repair exhibited a 4.3-fold higher risk (OR 4.3; 95% CI 1.2-15.6, p = 0.02) of developing stiffness at 6 months compared to those with mini-open repair. Despite these differences in stiffness rates, no significant variation was seen in the American Shoulder and Elbow Surgeons (ASES) score, Single Assessment Numeric Evaluation (SANE) score, or Visual Analog Scale (VAS) scores at 6 months between the groups. The incidence of postoperative shoulder stiffness following rotator cuff repair was substantial at 31% at 3 months, reducing to 20% by 6 months. Mini-open repair was associated with a lower 6-month stiffness incidence than arthroscopic repair, likely due to variations in rehabilitation protocols. However, the presence of stiffness at 6 months post-surgery did not significantly affect functional outcomes or pain levels.

Computational Investigation of Vessel Injury Due to Catheter Tracking During Transcatheter Aortic Valve Replacement.

Catheter reaction forces during transcatheter valve replacement (TAVR) may result in injury to the vessel or plaque rupture, triggering distal embolization or thrombosis. In vitro test methods represent the arterial wall using synthetic proxies to determine catheter reaction forces during tracking, but whether they can account for reaction forces within the compliant aortic wall tissue in vivo is unknown. Moreover, the role of plaque inclusions is not well understood. Computational approaches have predicted the impact of TAVR positioning, migration, and leaflet distortion, but have not yet been applied to investigate aortic wall reaction forces and stresses during catheter tracking. In this study, we investigate the role that catheter design and aorta and plaque mechanical properties have on the risk of plaque rupture during TAVR catheter delivery. We report that, for trackability testing, a rigid test model provides a reasonable estimation of the peak reaction forces experienced during catheter tracking within compliant vessels. We investigated the risk of rupture of both the aortic tissue and calcified plaques. We report that there was no risk of diseased aortic tissue rupture based on an accepted aortic tissue stress threshold (4.2MPa). However, we report that both the aortic and plaque tissue exceed a rupture stress threshold (300kPa) with and without the presence of stiff and soft plaque inclusions. We also highlight the potential risks associated with shorter catheter tips during catheter tracking and demonstrate that increasing the contact surface will reduce peak contact pressures experienced in the tissue.

Ultrahigh‐Pressure Acoustic Velocities of Aluminous Silicate Glass up to 155 GPa With Implications for the Structure and Dynamics of the Deep Terrestrial Magma Ocean

AbstractWe have carried out in situ high‐pressure acoustic velocity measurements of (Fe2+, Al)‐bearing MgSiO3 glass up to pressures of 155 GPa, which confirmed a distinct pressure‐induced trend change in the transverse acoustic velocity (VS) profile around 98 GPa, likely caused by the Si‐O coordination number (CN) change from 6 to 6+. Although it has been reported that the substitution of Fe2+ in MgSiO3 glass induces almost linear velocity reduction up to ∼160 GPa, we revealed that the VS profile of (Fe2+, Al)‐bearing MgSiO3 becomes anomalously steeper above ∼100 GPa and eventually came to be equivalent to MgSiO3 glass above ∼125 GPa. This implies the incorporation of Al into Fe‐bearing MgSiO3 glass significantly facilitates making it far elastically stiffer and thus the densification under pressures well within the Earth's lower mantle. Our results indicate the possible presence of stiff and highly dense silicate melts in deep MOs in the rocky terrestrial planets.

Study on the Ramie Fabric Treated with Copper Ammonia to Slenderize Fiber for Eliminating Prickle

ABSTRACT Ramie fabrics are suitable for summer clothing due to their excellent moisture absorption and breathability. Still, their application in the garment industry is limited by the presence of stiff, coarse hairiness that tends to prickle when it comes into contact with the skin. Herein, a low concentration copper ammonia solution was used to slenderize the fiber of the ramie fabric for a short time at room temperature to eliminate prickle and improve the softness of the fabric. Scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), and thermal gravity analysis (TG) were used to investigate the morphology and structure of treated ramie fabric. And its softness, smoothness, fiber diameter, breaking strength, air permeability, and moisture absorption were also studied. The results showed that the fibers were slenderized, the stiff, coarse hairiness was reduced, and the softness of the fabric was improved, while its other properties remained good after the ramie fabric was treated under appropriate conditions. The use of copper ammonia solution at room temperature to eliminate the prickle of ramie fabrics was simple and inexpensive, suitable for use in practical production.

Stiffness of probability distributions of work and Jarzynski relation for initial microcanonical and energy eigenstates

We consider closed quantum systems which are driven such that only negligible heating occurs. If driving only affects small parts of the system, it may nonetheless be strong. Our analysis aims at clarifying under which conditions the Jarzynski relation (JR) holds in such setups, if the initial states are microcanonical or even energy eigenstates. We find that the validity of the JR for the microcanonical initial state hinges on an exponential density of states and on stiffness. The latter indicates an independence of the probability density functions (PDFs) of work of the energy of the respective microcanonical initial state. The validity of the JR for initial energy eigenstates is found to additionally require smoothness. The latter indicates an independence of the work PDFs of the specific energy eigenstates within a microcanonical energy shell. As the validity of the JR for pure initial energy eigenstates has no analog in classical systems, we consider it a genuine quantum phenomenon.

Centre of Rotation of the Human Subtalar Joint Using Weight-Bearing Clinical Computed Tomography

Accurate in vivo quantification of subtalar joint kinematics can provide important information for the clinical evaluation of subtalar joint function; the analysis of outcome of surgical procedures of the hindfoot; and the design of a replacement subtalar joint prosthesis. The objective of the current study was to explore the potential of full weight-bearing clinical computed tomography (CT) to evaluate the helical axis and centre of rotation of the subtalar joint during inversion and eversion motion. A subject specific methodology was proposed for the definition of the subtalar joint motion combining three-dimensional (3D) weight-bearing imaging at different joint positions with digital volume correlation (DVC). The computed subtalar joint helical axis parameters showed consistency across all healthy subjects and in line with previous data under simulated loads. A sphere fitting approach was introduced for the computation of subtalar joint centre of rotation, which allows to demonstrate that this centre of rotation is located in the middle facet of the subtalar joint. Some translation along the helical axis was also observed, reflecting the elasticity of the soft-tissue restraints. This study showed a novel technique for non-invasive quantitative analysis of bone-to-bone motion under full weight-bearing of the hindfoot. Identifying different joint kinematics in patients with ligamentous laxity and instability, or in the presence of stiffness and arthritis, could help clinicians to define optimal patient-specific treatments.

Shape oscillations of single blood drops: applications to human blood and sickle cell disease

Sickle cell disease (SCD) is an inherited blood disorder associated with severe anemia, vessel occlusion, poor oxygen transport and organ failure. The presence of stiff and often sickle-shaped red blood cells is the hallmark of SCD and is believed to contribute to impaired blood rheology and organ damage. Most existing measurement techniques of blood and red blood cell physical properties require sample contact and/or large sample volume, which is problematic for pediatric patients. Acoustic levitation allows rheological measurements in a single drop of blood, simultaneously eliminating the need for both contact containment and manipulation of samples. The technique shows that the shape oscillation of blood drops is able to assess blood viscosity in normal and SCD blood and demonstrates an abnormally increased viscosity in SCD when compared with normal controls. Furthermore, the technique is sensitive enough to detect viscosity changes induced by hydroxyurea treatment, and their dependence on the total fetal hemoglobin content of the sample. Thus this technique may hold promise as a monitoring tool for assessing changes in blood rheology in sickle cell and other hematological diseases.

Factors affecting the results of analgesic therapy. Results of the Russian multicentre study of NOTE (NSAID: Open-label Trial of Efficacy).

To identify factors affecting the effectiveness of NSAIDs in patients with OA and LBP. An observational study was conducted to evaluate the effectiveness of a 2-week course of NSAIDs in OA and LBP in real clinical practice. The study group consisted of 3604 patients with OA and LBP (60.6% women and 39.4% men, mean age 55.0±13.4 years). According to the study design, aceclofenac (Airtal) and other NSAIDs used in the ratio 1:1. The main criterion of effectiveness was the frequency of complete pain relief after 2 weeks of therapy. In addition, the decrease of pain and general health were determined on a 10-point numerical rating scale (NRS). We compared the frequency of complete pain relief in patients who had and did not have the studied factors. The value of the studied factors was determined using OR (95% CI). Most patients received aceclofenac (54.9%), as well as diclofenac (2.0%), ketoprofen (1.9%), lornoxicam (2.2%), meloxicam (13.7%), naproxen (2.1%), nimesulide (5.8%), celecoxib (5.9%), ethicoxib (7.1%) and other NSAIDs (4.4%); 56.2% of patients received muscle relaxants, mainly tolperisone (74.7%), vitamin B (10.4%), and proton pump inhibitors (42.8%). Complete pain relief was achieved in 54.8% of patients. The pain decrease and general health improvement were (for NRS) 63.9±13.4% and 61.7±14.8%, respectively. The efficacy of aceclofenac was slightly higher than in the whole group: complete pain relief was in 59.9% of patients. Adverse events in aceclofenac use were observed in 2.3% of patients, other NSAIDs-from 2.4 to 14.1%. The frequency of complete pain relief was higher in men: OR 1,239 (95% CI 1.08-1.418; p=0.002), who had the first episode of pain - OR 3.341 (95% CI 2.873-3.875; p=0.000), a good&quot; response &quot; to NSAIDs in history - OR 1.656 (95% CI 1.385-1.980; p=0.000) and received NSAIDs in combination with muscle relaxants - OR 1.218 (95% CI 1.067-1.390; p=0.004). The effect of therapy is lower in patients 65 years and older-OR 0,378 (95% CI 0.324-0.442; p=0,000), with body mass index &gt;30 kg/m² - OR 0.619 (95% CI 0.529-0.723; p=0.000), with severe pain (≥7 points NRS) - OR 0.662 (95% CI 0.580-0.756; p=0.002), with pain at rest, - OR 0.515 (95% CI 0.450-0,589; p=0.000), pain at night - OR 0.581 (95% CI 0.501-0.672; p=0.000) and the presence of stiffness - OR 0.501 (95% CI 0.438-0,573; p=0.000). Treatment results are significantly worse in the cases of combination of LBP and joint pain, as well as pain in the trochanter major and pes anserinus area (p&lt;0.001). NSAIDs are the first-line medications for the pain treatment in LBP and OA. Aceclofenac is effective and safe in this conditions. When carrying out analgesic therapy should take into account factors that affect the effectiveness of treatment: old age, overweight, insufficient effect of NSAIDs in history, severe pain, signs of &quot;inflammatory&quot; pain, multiple sources of pain.

Fast and Precise Emulation of Stochastic Biochemical Reaction Networks With Amplified Thermal Noise in Silicon Chips.

The analysis and simulation of complex interacting biochemical reaction pathways in cells is important in all of systems biology and medicine. Yet, the dynamics of even a modest number of noisy or stochastic coupled biochemical reactions is extremely time consuming to simulate. In large part, this is because of the expensive cost of random number and Poisson process generation and the presence of stiff, coupled, nonlinear differential equations. Here, we demonstrate that we can amplify inherent thermal noise in chips to emulate randomness physically, thus alleviating these costs significantly. Concurrently, molecular flux in thermodynamic biochemical reactions maps to thermodynamic electronic current in a transistor such that stiff nonlinear biochemical differential equations are emulated exactly in compact, digitally programmable, highly parallel analog "cytomorphic" transistor circuits. For even small-scale systems involving just 80 stochastic reactions, our 0.35-μm BiCMOS chips yield a 311× speedup in the simulation time of Gillespie's stochastic algorithm over COPASI, a fast biochemical-reaction software simulator that is widely used in computational biology; they yield a 15500× speedup over equivalent MATLAB stochastic simulations. The chip emulation results are consistent with these software simulations over a large range of signal-to-noise ratios. Most importantly, our physical emulation of Poisson chemical dynamics does not involve any inherently sequential processes and updates such that, unlike prior exact simulation approaches, they are parallelizable, asynchronous, and enable even more speedup for larger-size networks.

Tumor Cell Dynamics: Microenvironmental Stiffness of 3D Polymeric Structures to Study Invasive Rates of Cancer Cells (Adv. Healthcare Mater. 22/2017)

Three-dimensional cage-like microscaffolds with tailored Young's modulus are used to induce different invasive behaviours of cancer cells according to structural stiffness by Enrico Domenico Lemma, Ferruccio Pisanello, and co-workers in article number 1700888. Tumor cells invasion is boosted by softer architectures and by the presence of stiffness “weak spots” within overall rigid scaffolds, enabling more detailed analysis on mechanical interactions between tumor cells and the extracellular matrix.

LASSIE: simulating large-scale models of biochemical systems on GPUs

BackgroundMathematical modeling and in silico analysis are widely acknowledged as complementary tools to biological laboratory methods, to achieve a thorough understanding of emergent behaviors of cellular processes in both physiological and perturbed conditions. Though, the simulation of large-scale models—consisting in hundreds or thousands of reactions and molecular species—can rapidly overtake the capabilities of Central Processing Units (CPUs). The purpose of this work is to exploit alternative high-performance computing solutions, such as Graphics Processing Units (GPUs), to allow the investigation of these models at reduced computational costs.ResultsLASSIE is a “black-box” GPU-accelerated deterministic simulator, specifically designed for large-scale models and not requiring any expertise in mathematical modeling, simulation algorithms or GPU programming. Given a reaction-based model of a cellular process, LASSIE automatically generates the corresponding system of Ordinary Differential Equations (ODEs), assuming mass-action kinetics. The numerical solution of the ODEs is obtained by automatically switching between the Runge-Kutta-Fehlberg method in the absence of stiffness, and the Backward Differentiation Formulae of first order in presence of stiffness. The computational performance of LASSIE are assessed using a set of randomly generated synthetic reaction-based models of increasing size, ranging from 64 to 8192 reactions and species, and compared to a CPU-implementation of the LSODA numerical integration algorithm.ConclusionsLASSIE adopts a novel fine-grained parallelization strategy to distribute on the GPU cores all the calculations required to solve the system of ODEs. By virtue of this implementation, LASSIE achieves up to 92× speed-up with respect to LSODA, therefore reducing the running time from approximately 1 month down to 8 h to simulate models consisting in, for instance, four thousands of reactions and species. Notably, thanks to its smaller memory footprint, LASSIE is able to perform fast simulations of even larger models, whereby the tested CPU-implementation of LSODA failed to reach termination. LASSIE is therefore expected to make an important breakthrough in Systems Biology applications, for the execution of faster and in-depth computational analyses of large-scale models of complex biological systems.

Variational-based energy–momentum schemes of higher-order for elastic fiber-reinforced continua

This paper contributes to the improvement of recently published higher-order accurate energy–momentum schemes for an anisotropic hyperelastic material formulation based on the concept of structural tensors. These Galerkin-based energy–momentum schemes are developed by means of time finite elements with the focus on improving numerical stability and robustness in the presence of stiffness and large rotations. They show advantages over conventional time stepping schemes in combination with anisotropic materials formulated with polyconvex strain energy density functions. In this paper, higher-order energy–momentum schemes are developed by using a differential variational principle in order to remedy the drawbacks of these Galerkin-based schemes, namely a variationally inconsistent time approximation of the strains in the higher-order case, no coordinate free superimposed stress tensor and an unseparated time approximation of the fibers and the matrix material. These new structure-preserving time integrators preserve all conservation laws of a free flying hyperelastic anisotropic continuum, namely the total linear and the total angular momentum conservation as well as the total energy conservation. Numerical examples demonstrate dynamic behavior of anisotropic continua, discrete conservation properties of flying continua and the effect of higher-order accuracy subject to transient loads.

Effect of counterparts on the friction and wear behavior of polyelectrolyte multilayers

Polyelectrolyte multilayers (PEMs) were prepared on Si substrates by alternative deposition of poly(sodium 4-styrenesulfonate) (PSS) as polyanion and poly (diallyldimethylammonium chloride) (PDDA) as polycation. The PEM film was characterized by means of ultraviolet-visible light absorption spectrometry and atomic force microscopy. The friction and wear behavior of the polymer film sliding against brass, 440C stainless steel, Si 3N 4 and WC balls was evaluated on a microtribometer. It was found that the multilayer film was uniform and compact, and it registered a lowered friction coefficient and extended antiwear life while sliding against soft counterparts, in particular, a brass ball. This could be because the polymeric transfer film had an enhanced adhesion on the soft metallic counterpart in the presence of inter-transferred metallic debris. Contrary to the above, the PEM film had a higher friction coefficient and shorter antiwear life while sliding against Si 3N 4 and WC balls, possibly owing to a higher shearing stress in the presence of stiff and hardly deformable hard counterparts. In other words, the polymeric transfer film on the hard couterparts, if any, would be easily scaled off, leading to decreased antiwear life. Moreover, the differences in the friction and wear behavior of the PEM film sliding against different counterparts were closely related to the differences in the chemical and crystallographic structure of the counterparts (ceramics Si 3N 4 and WC, and metals brass and stainless steel).

A Robust Approximation Scheme for the LQG Control of an Undamped Flexible Beam with a Tip Mass

This work deals with the LQG control problem of a flexible beam clamped at one end and with a point mass at the free end, where a boundary control force can be applied. A class of finite-dimensional control laws is proposed here, derived on the basis of the EulerBernoulli infinite-dimensional beam model. By means of this approach it is possible to take into account also the higher order modes that are indeed neglected in the more usual methods based on a finite-dimensional model of the beam. The main motivation for the approach followed here is that it naturally allows to overcome the phenomenon of spillover, occurring when unmodeled modes are excited by the control law itself. The finite-dimensional control law here proposed is derived by a Galerkin approximation of the solution of the LQG control problem, in a proper Hilbert space setting. In particular, the novelty of the approach is the definition of an implementable Galerkin approximation scheme based on generalized eigenfunctions of the Euler-Bernoulli model instead of the usual splines. It is here proved that, for any given finite time horizon, the evolution of the system state driven by the proposed control input converges, in L2 norm, to the optimal LQG evolution, as the order of the approximation scheme increases. The strong stability of the closed loop system is guaranteed for any order of the approximation scheme. Moreover, it is proved that the proposed compensator guarantees modal stability of the closed loop system also in the presence of stiffness/ inertia parameters uncertainties.

Conservation properties of a time FE method. Part IV: Higher order energy and momentum conserving schemes

In the present paper a systematic development of higher order accurate time stepping schemes which exactly conserve total energy as well as momentum maps of underlying finite-dimensional Hamiltonian systems with symmetry is shown. The result of this development is the enhanced Galerkin (eG) finite element method in time. The conservation of the eG method is generally related to its collocation property. Total energy conservation, in particular, is obtained by a new projection technique. The eG method is, moreover, based on objective time discretization of the used strain measure. This paper is concerned with particle dynamics and semi-discrete non-linear elastodynamics. The related numerical examples show good performance in presence of stiffness as well as for calculating large-strain motions. Copyright © 2005 John Wiley & Sons, Ltd.

Computing in the past with forward integration

Using existing, forward-in-time integration schemes, we demonstrate that under certain conditions it is possible to compute the solution at earlier times, even in the presence of stiffness (for which reverse integration is unstable). This technique can be used when a reverse integrator is not available—for example, when all one has is a forward-in-time legacy code. It can also be used for the “reverse coarse” integration of the macroscopic closure of a system defined by a microscopic model which itself is naturally forward in time (e.g., a particle model of a gas). The method proposed has stability properties that enable it to converge to stationary points of unstable stiff systems.