Unilateral Conditions Research Articles

Applications of Conic Programming in Non-smooth Mechanics

In the field of nonlinear mechanics, many challenging problems (e.g., plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity condition, unilateral condition, etc.), which makes their numerical resolution through standard Newton methods quite difficult. Their formulation as conic programs alleviates this difficulty since large-scale conic optimization problems can now be solved in a very robust and efficient manner, thanks to the development of dedicated interior-point algorithms. In this contribution, we review old and novel formulations of various non-smooth mechanics problems including associated plasticity with nonlinear hardening, nonlinear membranes, minimal crack surfaces, and viscoplastic fluid flows.

Benefit of sequential bilateral cochlear implantation in children between 5 to 18 years old: A prospective cohort study.

To determine the benefit of sequential cochlear implantation after a long inter-implantation interval in children with bilateral deafness receiving their second implant between 5 and 18 years of age. Prospective cohort-study. Tertiary multicenter. 85 children with bilateral deafness and unilateral implantation receiving a contralateral cochlear implant at the age of 5 to 18 years. The primary outcomes were speech recognition in quiet and noise (CVC) scores. The secondary outcomes were language outcomes and subjective hearing abilities, all measured before and 12 months after sequential bilateral cochlear implantation. Medians of the paired data were compared using the Wilcoxon signed-rank test. Univariable linear regression analyses was used to analyze associations between variables and performance outcomes. A significant benefit was found for speech recognition in quiet (96% [89-98] vs 91% [85-96]; p < 0.01) and noise (65% [57-75] vs 54% [47-71]; p = 0.01) in the bilateral CI condition compared to unilateral (n = 75, excluded 10 non-users). No benefit was seen for language outcomes. The subjective sound quality score was statistically significant higher in bilateral compared to the unilateral CI condition. Pre-operative residual hearing level in the ear of the second implant, the inter-implant interval and age at time of second implantation was not significantly associated with performance scores. After 12 months of use, sequential bilateral cochlear implantation showed improved speech perception in quiet and noise and improved subjective sound quality outcomes in children despite a great inter-implantation interval (median of 8 years [range 1-16 years]).

Pain-Related Anxiety in Chronic Vulvar Pain Conditions Associated with Vulvodynia

ABSTRACT Introduction Chronic, idiopathic vulvar pain (vulvodynia) is often treated as a unilateral condition. However, there are likely multiple causes to vulvar pain, relating to nerves, muscles, hormones, and inflammation, as well as psychosocial factors. Pain-related anxiety is a known contributor to the cycle of chronic pain. Rates of pain-related anxiety have been explored in vulvodynia associated with hypertonic pelvic floor muscle dysfunction; however, the roles in other associated genitopelvic pain conditions are still unknown. Objective Evaluate pain-related anxiety in the context of chronic vulvar pain conditions associated with vulvodynia: pudendal neuralgia (PN), hypertonic pelvic floor dysfunction (PFD), provoked vestibulodynia (PVD), and lichen sclerosus (LS). Methods A retrospective chart review was conducted for all new patients presenting to two metropolitan gynecology clinics specializing in vulvar pain for one full year. Patients were evaluated by a vulvar pain specialist to receive a specific vulvar pain diagnosis based on history and physical examination. Pain-related anxiety scores were measured with the Pain Anxiety Symptoms Scale-20 (PASS-20) prior to evaluation. Adult women presenting with vulvar pain who completed the PASS-20 and received a diagnosis of hypertonic pelvic floor muscle dysfunction were included in the study. Patients with concomitant vulvovaginal infections were excluded. Patients were grouped according to diagnosis: pudendal neuralgia (PN), overactive pelvic floor dysfunction alone (PFD), provoked vestibulodynia (PVD), or vulvar lichen sclerosus (LS). Independent two-tailed t-tests and one-way ANOVAs were performed comparing the distributions and scores for each of the four aspects of the PASS-20. Results 126 patients were included in the analysis: PN (17), PFD (43), PVD (57), and LS (9). Pain-related anxiety was highest for those with PN (mean score=47.18, SD=24.66) with 76.5% scoring above the 30-point cutoff for maladaptive levels of pain-related anxiety. This was followed by those with PFD (mean=37.02, SD=18.91, 65.1% scored &amp;gt;30), PVD (mean=32.53, SD=17.60, 43.9% scored &amp;gt;30), and LS (mean=23.44, SD=19.98, 33.3% scored &amp;gt;30). The PN group scored highest in cognitive, fear, and physiological anxiety, while the PFD group scored higher in escape and avoidance. One-way ANOVAs with post-hoc analysis yielded significant differences between the cognitive anxiety scores of PN vs PFD (p=0.03), PN vs PVD (p&amp;lt;0.01), and PN vs LS (p&amp;lt;0.01); as well as with the physiological anxiety scores of PN vs PFD (p=0.02), PN vs PVD (p=0.01), and PN vs LS (p&amp;lt;0.01). Comparing PFD and PVD, those with PFD alone had significantly higher scores in cognitive anxiety (t(498) = 2.12, p&amp;lt;0.04) and fear of pain (t(495) = 2.76, p&amp;lt;0.006). Conclusions Vulvar pain conditions in addition to hypertonic PFD can differentially impact pain-related anxiety. Notably, patients with PN have higher cognitive, physiologic, and fear-related anxiety compared to patients with other distressing vulvar pain conditions. Differences in pain-related anxiety between the additional vulvar pain conditions and PFD alone may reflect the severity of hypertonic PFD, which was not delineated in this study. These findings highlight the importance of identifying all causes of genitopelvic pain in the evaluation of vulvodynia, as well as acknowledging and addressing the role of pain-related anxiety in chronic genitopelvic pain. Disclosure Any of the authors act as a consultant, employee or shareholder of an industry for: Consultant for Good Clean Love and Mahana Therapeutics; Consultant to SST, Ipsen, Amag, Lupin, an employee of Dare, and received research funding from Elen, Ipsen, En

Different Types of Mastoid Process Vibrations Affect Dynamic Margin of Stability Differently.

The vestibular system is critical for human locomotion. Any deteriorated vestibular system leads to gait instability. In the past decades, these alternations in gait patterns have been majorly measured by the spatial-temporal gait parameters and respective variabilities. However, measuring gait characteristics cannot capture the full aspect of motor controls. Thus, to further understand the effects of deteriorated vestibular system on gait performance, additional measurement needs to be taken into consideration. This study proposed using the margin of stability (MOS) to identify the patterns of dynamic control under different types of mastoid vibrations in walking. This study hypothesized that (1) using the MOS method could facilitate the understanding of another aspect of motor control induced by different types of mastoid vibrations, and (2) applying the mastoid vibrations could induce the asymmetric MOS. Twenty healthy young adults were recruited. Two electromechanical vibrotactile transducers were placed on the bilateral mastoid process to apply different types of vestibular vibrations (bilateral, unilateral, and no vibration). A motion capture system with eight cameras was used to measure the MOSap (margin of stability in the anterior-posterior direction), MOSml (margin of stability in the medial-lateral direction), and respective variabilities. The results were in line with the hypotheses that both bilateral and unilateral mastoid vibrations significantly increased MOSap (p = 0.036, p < 0.001), MOSml (p = 0.012, p < 0.001), and respective variabilities p = 0.001, p < 0.001; p = 0.001, p < 0.01 when compared to the no vibration condition. Also, significantly larger MOSml (p = 0.001), MOSml variability (p < 0.023), MOSap (p < 0.001), and MOSap variability (p = 0.002) were observed under the unilateral vibration condition than that observed under the bilateral vibration condition. The above-mentioned result found that different types of mastoid vibrations affected the MOS differently, suggesting different patterns of control mechanisms under different sensory-conflicted situations. Besides, a significant difference between the dominant and non-dominant legs was observed in MOSml. Moreover, applying the unilateral mastoid vibrations induced a greater symmetric index of MOSml, suggesting that more active control in balance was needed in the medial-lateral than in the anterior-posterior direction.

A new class of history-dependent quasi variational–hemivariational inequalities with constraints

In this paper we consider an abstract class of time-dependent quasi variational–hemivariational inequalities which involves history-dependent operators and a set of unilateral constraints. First, we establish the existence and uniqueness of solution by using a recent result for elliptic variational–hemivariational inequalities in reflexive Banach spaces combined with a fixed-point principle for history-dependent operators. Then, we apply the abstract result to show the unique weak solvability to a quasistatic viscoelastic frictional contact problem. The contact law involves a unilateral Signorini-type condition for the normal velocity and the nonmonotone normal damped response condition while the friction condition is a version of the Coulomb law of dry friction in which the friction bound depends on the accumulated slip.

Plasticity damage self-consistent model incorporating stress triaxiality and shear controlled fracture mechanisms – Model formulation

A model for plasticity and damage, developed in the context of continuum damage mechanics and consistent with micromechanisms of void nucleation, growth, and coalescence, is presented. The damage dissipation potential has been formulated specifically to account for different damage contributions due to intervoid necking, shearing, and sheeting under arbitrary stress states. The existence of a cut-off for the negative stress triaxiality was questioned and unilateral conditions for ductile damage have been reformulated accordingly, considering the combination of stress triaxiality and Lode parameter. The model allows the derivation, although in implicit form, of the fracture locus for the whole range of stress triaxiality. An example application to Al2024-T351 and Al6061-T6 is presented. The proposed formulation represents an attempt to reconcile CDM theoretical framework with the ductile fracture specific mechanisms and their sequential progression under general loading conditions, making advantages of micromechanical modeling to establish correlations between void evolution and continuum scale physical quantities. Finite element model implementation and plasticity model formulation will be discussed in a forthcoming companion paper.

Plasticity damage self-consistent model incorporating stress triaxiality and shear controlled fracture mechanisms – Model verification and validation

The plasticity damage self-consistent (PDSC) model is a damage model developed in the context of continuum damage mechanics in which the damage dissipation potential is formulated to account for damage contributions due to intervoid necking, shearing, and sheeting for an arbitrary stress state. The synergic action of different micromechanisms contributing to ductile fracture is accounted for by their dependence on the plastic deformation, stress triaxiality, third invariant of the deviatoric of the stress tensor, and unilateral conditions. In this work, the PDSC has been implemented in the commercial finite element code MSC MARC via user subroutines and used to predict ductile failure response under different stress state conditions. Firstly, the model implementation has been verified by comparing calculated damage evolution as a function of plastic strain, for prescribed combinations of stress triaxiality and Lode parameter under proportional loading, with an analytical solution. Successively, the model has been validated in predicting ductile fracture for Al6061-T6 in different specimen geometries and comparing with experiment results. Model capability to anticipate fracture initiation conditions, together with specimen global response, and ductile crack propagation also for complex load paths, is demonstrated.

Different implant diameters and their effect on stress distribution pattern in 2-implant mandibular overdentures: A 3D finite element analysis study

Statement of problemThe edentulous mandible is commonly treated with a 2-implant overdenture. A change in diameter of the implants may affect the biomechanical behavior of the overdenture, but information on these effects is lacking. PurposeThe purpose of this 3D finite element analysis study was to evaluate the biomechanical behavior of 2-implant mandibular overdentures (2IMO) and their individual components by using implants of different diameters. Material and methodsA 3D mandibular model was obtained from the cone beam computed tomography (CBCT) images of a 59-year-old edentulous man, and a 3D denture model was developed from intraoral scanning files in the Mimics software program. A 3D model of different diameters of implants (2.5 mm, 3.0 mm, 3.5 mm, and 4.0 mm) with a LOCATOR attachment was developed in the Solidworks software program. Two same-sized implants were inserted in the mandibular model at 10 mm from the midline in the 3Matics software program. A vertical load of 100 N was applied on the first molar region on the right side or both sides in the ANSYS software program. The maximum von Mises stresses and strains were recorded and analyzed. ResultsStresses within the implants decreased with an increase in diameter (from 2.5 mm to 3 mm, 3.5 mm, and 4.0 mm) of the implants. The highest stresses were observed with 2.5-mm-diameter implants (0.949 MPa under unilateral and 0.915 MPa under bilateral loading) and the lowest with Ø4-mm implants (0.710 MPa under unilateral and 0.703 MPa under bilateral loading). The strains on the implants ranged between 0.0000056 and 0.0000097, and those on the mandible ranged between 0.0000513 and 0.0000566 across all diameters of the implants without following a specific trend. ConclusionsIn 2IMO, the stresses in the implants and mandible decreased with an increase in the diameter of the implants. The implants of lesser diameter (2.5 mm) exhibited the highest stresses and strains, and the implants of the largest diameter (4 mm) exhibited the lowest stresses and strains under unilateral and bilateral loading conditions.

Differing Bilateral Benefits for Spatial Release From Masking and Sound Localization Accuracy Using Bone Conduction Devices.

Objectives:Normal binaural hearing facilitates spatial hearing and therefore many everyday listening tasks, such as understanding speech against a backdrop of competing sounds originating from various locations, and localization of sounds. For stimulation with bone conduction hearing devices (BCD), used to alleviate conductive hearing losses, limited transcranial attenuation results in cross-stimulation so that both cochleae are stimulated from the position of the bone conduction transducer. As such, interaural time and level differences, hallmarks of binaural hearing, are unpredictable at the level of the inner ears. The aim of this study was to compare spatial hearing by unilateral and bilateral BCD stimulation in normal-hearing listeners with simulated bilateral conductive hearing loss.Design:Bilateral conductive hearing loss was reversibly induced in 25 subjects (mean age = 28.5 years) with air conduction and bone conduction (BC) pure-tone averages across 0.5, 1, 2, and 4 kHz (PTA4) <5 dB HL. The mean (SD) PTA4 for the simulated conductive hearing loss was 48.2 dB (3.8 dB). Subjects participated in a speech-in-speech task and a horizontal sound localization task in a within-subject repeated measures design (unilateral and bilateral bone conduction stimulation) using Baha 5 clinical sound processors on a softband. For the speech-in-speech task, the main outcome measure was the threshold for 40% correct speech recognition when masking speech and target speech were both colocated (0°) and spatially and symmetrically separated (target 0°, maskers ±30° and ±150°). Spatial release from masking was quantified as the difference between colocated and separated masking and target speech thresholds. For the localization task, the main outcome measure was the overall variance in localization accuracy quantified as an error index (0.0 = perfect performance; 1.0 = random performance). Four stimuli providing various spatial cues were used in the sound localization task.Results:The bilateral BCD benefit for recognition thresholds of speech in competing speech was statistically significant but small regardless if the masking speech signals were colocated with, or spatially and symmetrically separated from, the target speech. Spatial release from masking was identical for unilateral and bilateral conditions, and significantly different from zero. A distinct bilateral BCD sound localization benefit existed but varied in magnitude across stimuli. The smallest benefit occurred for a low-frequency stimulus (octave-filtered noise, CF = 0.5 kHz), and the largest benefit occurred for unmodulated broadband and narrowband (octave-filtered noise, CF = 4.0 kHz) stimuli. Sound localization by unilateral BCD was poor across stimuli.Conclusions:Results suggest that the well-known transcranial transmission of BC sound affects bilateral BCD benefits for spatial processing of sound in differing ways. Results further suggest that patients with bilateral conductive hearing loss and BC thresholds within the normal range may benefit from a bilateral fitting of BCD, particularly for horizontal localization of sounds.

Finite element analysis of class II mandibular unilateral distal extension partial dentures

The current paper aims to investigate the stress distribution developed in Kennedy Class II mandibular distal extension removable partial dentures due to applying a unilateral load condition in both vertical and lateral oblique directions. 3D models of mandible bone and RPD framework were first built based on actual patient data and later exported to ANSYS software to implement the numerical analysis. For realistic analysis, the model considered the frictional contact between the RPD retainers with the teeth and mucosa with the resin denture base by applying the feature of small sliding. To ensure maximum longevity and suitability of restoration, two different metallic RPDs constructed from commercially pure titanium (CP Ti) and cobalt–chromium (Co-Cr) base materials were investigated within the proposed model. It was found that the highest stress value was seen within the Co-Cr framework followed by the titanium framework, particularly within the bar clasp under both loading directions. The principle abutment of the distal extension side carried the highest stress value under both RPD models in both loading cases. Also, it was found that the captured von Mises stress levels within the titanium bar clasps were lower than that in Co-Cr demonstrating both long durability and high flexibility of Ti clasps.

Unusual Corneal Sarcoidosis Manifestations

ABSTRACT Aim To document atypical presenting forms of ocular sarcoidosis at the corneal level. Methods Case report. Results A 63-year-old woman presented multiple uncommon unilateral primary corneal conditions as manifestation of ocular sarcoidosis, including peripheral ulcerative keratitis, sterile corneal infiltrate (corneal granuloma), and sterile infiltrates related to a corneal foreign body, requiring medical and surgical management to control the inflammatory symptoms and to preserve the integrity of the eyeball. An excisional biopsy of a nodule in the temporal conjunctiva was performed under topical anesthesia. Histological analysis revealed a non-caseating granuloma, confirming the diagnosis of ocular sarcoidosis. Conclusion When thinking of ocular involvement in patients with ocular sarcoidosis, it is essential to remember that manifestations such as peripheral ulcerative keratitis, sterile corneal infiltrate, and sterile foreign body-related infiltrates may be presentations of this disease.

On Harmonic Balance Method-based Lagrangian contact formulations for vibro-impact problems

This article assesses two Harmonic Balance Method-based numerical Lagrangian strategies for the characterization of the periodic response of a mechanical system subject to unilateral contact constraints. The model used for evaluation is an academic rod model facing an obstacle that is firstly considered as equivalent to a stiffness (flexible) and then as a rigid obstacle. Nonlinear frequency response curves are obtained through an arc-length continuation procedure and confronted to the corresponding time integration simulations. An in-depth comparative analysis is conducted on the time signals obtained through both frequency domain strategies: (1) linear complementarity problem (LCP-HBM) and (2) dynamic Lagrangian frequency time (DLFT-HBM). The unilateral contact conditions are thoroughly investigated in the time domain and compared with the reference time integration simulations. Particular attention is paid to the relation between both methods and it is shown that the DLFT-HBM is asymptotically equivalent to the LCP-HBM. This study also shows that the oversampling of time signals inside alternating frequency–time procedures generates non-physical high harmonics. Finally, a convergence analysis is conducted in order to assess the influence of the different numerical parameters on the respect of the unilateral contact laws.

Do Adults with Stroke have Altered Interhemispheric Inhibition? A Systematic Review with Meta-Analysis

ObjectiveInterhemispheric inhibition is an important cortical mechanism to support motor control. Altered interhemispheric inhibition has been the target of neuromodulation interventions. This systematic review investigated the evidence for altered interhemispheric inhibition in adults with unilateral neurological conditions: stroke, amyotrophic lateral sclerosis, cerebral palsy, complex regional pain syndrome, traumatic brain injury, and cerebral palsy MethodsWe pre-registered the protocol and followed PRISMA guidelines. Five databases were systematically searched to identify studies reporting interhemispheric inhibition measures in unilateral neurological conditions and healthy controls. Data were grouped according to the measure (ipsilateral silent period and dual-coil), stimulated hemisphere, and stage of the condition (subacute and chronic). Results1372 studies were identified, of which 14 were included (n = 226 adults with stroke and 161 age-matched controls). Ipsilateral silent period-duration was longer in people with stroke than in controls (stimulation of dominant hemisphere) regardless of stroke stage. Motor evoked potential was less suppressed in people with sub-acute stroke (stimulation of the unaffected hemisphere) than controls (stimulation of dominant hemisphere) and this reversed in chronic stroke. ConclusionDetection of altered interhemispheric inhibition appears to be dependent on the measure of interhemispheric inhibition and the stage of recovery. SignificanceRebalancing interhemispheric inhibition using neuromodulation is considered a promising line of treatment for stroke rehabilitation. Our results did not find compelling evidence to support consistent alterations in interhemispheric inhibition in adults with stroke.

Bilateral deficit magnitude increases with velocity during a half-squat exercise

ABSTRACT Movement velocity has been viewed as one of the bilateral deficit (BLD) determinants. This research tested the velocity effect on BLD during a half-squat exercise. The role of muscle excitation in BLD was also assessed. BLD amplitude was assessed in 12 male soccer players while performing a half-squat exercise with incremental load. During the exercise’s pushing phase, the average force and velocity were measured in bilateral and unilateral conditions to provide the bilateral index (BI) at each interpolated velocity. The vastus lateralis and medialis excitation was assessed during the exercise by calculating the surface electromyography signal root mean square (sEMGRMS). The BI for sEMGRMS (sEMG BI) was calculated. The theoretical maximum force (F0) and velocity (v0) were also determined. F0 was +43 (28)% in bilateral compared with unilateral conditions (p < 0.001), whereas v0 was similar in both conditions (p = 0.386). The BI magnitude rose with the increase in velocity from −34 (7)% at 50%v0 to −70 (17)% at 90%v0 (p 0.03-<0.001), whereas no sEMG BI occurred (p: 0.07-0.991 in both muscles). The study reported velocity-dependent changes in the BLD amplitude, with the largest BLD amplitudes occurring at the highest velocities. This behaviour could provide useful information for setting specific contraction velocities to exploit/limit the BLD amplitude as a possible training stimulus.

The Effect of Breathing Laterality on Hip Roll Kinematics in Submaximal Front Crawl Swimming.

The purpose of this study was to determine the effect of breathing laterality on hip roll kinematics in submaximal front crawl swimming. Eighteen elite competitive swimmers performed three 100 m front crawl trials at a consistent sub-maximal speed (70% of seasonal best time) in a 25 m pool. Each trial was performed with one of three different breathing conditions: (1) unilateral breathing (preferred side), (2) bilateral breathing (alternating left/right-side every 3 strokes) and (3) simulated non-breathing using a swim snorkel. A waist-mounted triaxial accelerometer was used to determine continuous hip roll angle throughout the trial, from which peak hip roll angles (Ө) and average angular velocities (ω) were calculated. Two-way repeated measures ANOVAs were used to identify significant main effects for laterality (preferred vs. non-preferred breathing sides) and condition (unilateral, bilateral and snorkel breathing) for both Ө and ω. Peak hip roll to the preferred side was significantly greater (p < 0.001) in the unilateral condition, while ω to the non-preferred side was significantly greater in the unilateral (p < 0.01) and bilateral (p < 0.04) conditions. Significant same-side differences were also found between the different breathing conditions. The results demonstrate that breathing laterality affects hip roll kinematics at submaximal speeds, and that unilateral and snorkel breathing are associated with the least and most symmetric hip roll kinematics, respectively. The findings show that a snorkel effectively balances and controls bilateral hip rotation at submaximal speeds that are consistent with training, which may help to minimize and/or correct roll asymmetries that are the result of unilateral breathing.

ACUTE EFFECTS OF BILATERAL AND UNILATERAL WHOLE BODY VIBRATION TRAINING ON JUMPING ABILITY, ASYMMETRY, AND BILATERAL DEFICIT ON FORMER ARTISTIC GYMNASTS

Whole-body vibration (WBV) has been used to improve jumping ability, muscle strength, power, and performance in various sports. Bilateral deficit (BLD) is defined as the difference in the magnitude of the maximum force during single or double support. The present study investigated the effect of unilateral and bilateral whole-body vibration (WBV) exercise on jumping ability, asymmetry and BLD on former artistic gymnasts. Twenty-eight former artistic gymnasts volunteered to participate in this study. Participants performed 4 experimental protocols on nonconsecutive days in a random order. Each protocol included a 3-min-warm-up running on the treadmill at 2.22 m.s -1, followed by a 2-min rest. The intervention protocols were: a) WBV with feet [bipedal] (WBVB), b) WBV with single foot [unilateral] (WBVU), c) WBVB with the device turn-off (NWBVB), and d) WBVU with the device turn-off (NWBVU). The dependent variables were the squat jump (SJ) and counter movement jump (CMJ) with both feet (bilateral) and with single leg (unilateral). Results showed a significant interaction effect between the condition and time on SJ on both condition (bilateral and unilateral) and CMJ, whereas significant main effect was found for the condition and for time on SJ. Conclusively, the WBV unilateral condition improves significantly lower limbs symmetry during SJ performance. Further, bilateral WBV (WBV B) was the most effective condition on bilateral and unilateral SJ and CMJ performance.

Dynamic viscoelastic unilateral constrained contact problems with thermal effects

A new model that describes a dynamic frictional contact between a viscoelastic body and an obstacle is investigated in this paper. We consider a nonlinear viscoelastic constitutive law which involves a convex subdifferential inclusion term and thermal effects. The contact condition is modeled with unilateral constraint condition for a version of normal velocity. The boundary conditions that describe the contact, friction and heat flux are govern by the generalized Clarke multivalued subdifferential. We derive a coupled system of two nonlinear first order evolution inclusions problems, which consists of a parabolic variational-hemivariational inequality for the displacement and a hemivariational inequality of parabolic type for the temperature. Then, the unique weak solvability of the contact problem is obtained by virtue of a fixed point theorem and the surjectivity result of multivalued maps. Finally, we deliver a continuous dependence result on a coupled system when the data are subjected to perturbations.

Correlation Between Unilateral Free End Edentulous and Morphological Variations of Condyle Using Panoramic Radiographs

Background: Unilateral free end edentulous can cause a habit of one side chewing which will affect the condition of the temporomandibular joint (TMJ) mechanism. The TMJ is a complex joint consisting of the glenoid fossa, mandibular condyle and disc articular. No previous studies have examined the correlation between free end edentulous and morphological variations in the mandibular condyles. Purpose: to determine the correlation between unilateral free end edentulous and morphological variations of condyle using panoramic radiographs at South Sumatera RSKGM. Methods: This analytic observational study was using 68 samples of panoramic radiographs at RSKGM South Sumatra in September 2019 - March 2020. The sample was divided into 34 unilateral free end edentulous and 34 complete teeth. The condyle morphology of each sample was traced, and the data obtained were analyzed using the Chi-square method in the SPSS application. Results: Morphological abnormalities of the condyles were more frequently seen in patients with unilateral free end edentulous conditions, that is 41.18%. While in patients with complete teeth, the visible abnormalities of the condyles was only 5.88%. There was a significant correlation between unilateral free end edentulous and morphological variations of mandibular condyles (p&lt;0.005). Conclusion: There is a correlation between unilateral free end edentulous and morphological variations of condyle using panoramic radiographs in Dental Hospital of South Sumatera Province.

A multiscale method for the heterogeneous Signorini problem

In this paper, we develop a multiscale method for solving the Signorini problem with a heterogeneous field. The Signorini problem is encountered in many applications, such as hydrostatics, thermics, and solid mechanics. It is well-known that numerically solving this problem requires a fine computational mesh, which can lead to a large number of degrees of freedom. The aim of this work is to develop a new hybrid multiscale method based on the framework of the generalized multiscale finite element method (GMsFEM). The construction of multiscale basis functions requires local spectral decomposition. Additional multiscale basis functions related to the contact boundary are required so that our method can handle the unilateral condition of the Signorini type naturally. A complete analysis of the proposed method is provided and a result of the spectral convergence is shown. Numerical results are provided to validate our theoretical findings.

Sensitivity Analysis of a Scalar Mechanical Contact Problem with Perturbation of the Tresca’s Friction Law

This paper investigates the sensitivity analysis of a scalar mechanical contact problem described by a boundary value problem involving the Tresca’s friction law. The sensitivity analysis is performed with respect to right-hand source and boundary terms perturbations. In particular, the friction threshold involved in the Tresca’s friction law is perturbed, which constitutes the main novelty of the present work with respect to the existing literature. Hence, we introduce a parameterized Tresca friction problem and its solution is characterized by using the proximal operator associated with the corresponding perturbed nonsmooth convex Tresca friction functional. Then, by invoking the extended notion of twice epi-differentiability depending on a parameter, we prove the differentiability of the solution to the parameterized Tresca friction problem, characterizing its derivative as the solution to a boundary value problem involving Signorini unilateral conditions. Finally, numerical simulations are provided in order to illustrate our main result.