Gravity induced from quantum spacetime

Classical differential geometry can be encoded in spectral data, such as Connes' spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes' non-commutative spin geometry encompassing non-commutative Riemannian, symplectic, complex-Hermitian and (Hyper-)Kaehler geometry. A general framework for non-commutative geometry is developed from the point of view of supersymmetry and illustrated in terms of examples. In particular, the non-commutative torus and the non-commutative 3-sphere are studied in some detail.

Noncommutative Riemannian geometry on graphs

We overview a new mechanism whereby classical Riemannian geometry emerges out of the differential structure on quantum spacetime, as extension data for the classical algebra of differential forms. Outcomes for physics include a new formula for the standard Levi-Civita connection, a new point of view of the cosmological constant as a very small mass for the graviton of around $10^{-33}$ev, and a weakening of metric-compatibility in the presence of torsion. The same mechanism also provides a new construction for quantum bimodule connections on quantum spacetimes and a new approach to the quantum Ricci tensor.

This study aimed to investigate the irrigation dynamics of the positive pressure side-vented (SV) needle, EndoVac (micropores) needle and modified apical negative pressure (mANP) open-ended needle using computational fluid dynamics (CFD). A simulation of a prepared root canal (conical frustum) of 15 mm length with an apical diameter of 0.40 mm following Protaper F4 apical preparation was created using three-dimensional (3D) CAD software. The 3D simulated needle of SV 30G needle, EndoVac with micropores needle and mANP, 30G flat open-ended needle were also created. The irrigation dynamics were evaluated through transient CFD simulations. In addition, the irrigation dynamics of mANP at 0.2 mm, 0.5 mm, and 1.0 mm short from the working length were also assessed. The EndoVac and mANP showed negative apical static pressure and streamline patterns able to reach the apical region, thus indicating negligible extrusion. Meanwhile, SV showed positive apical static pressure and almost nonexistent streamlines beyond the needle tip. The SV showed the highest wall shear stress (WSS) magnitude of 1030Pa whereas Endovac (161 Pa) and mANP1 (258 Pa). However, SV revealed lower average WSS (10 Pa) compared to mANP1 (13 Pa) and mANP2 (11 Pa). This is due to SV developed a localised maximum WSS opposite the open vent area only therefore, uneven distribution of WSS. The EndoVac system developed a localised maximum WSS in the pair of micropores furthest away from the apical. CFD analysis of the EndoVac, mANP and SV showed different technique approach, needle design and needle depths insertion affect the irrigation dynamics pattern and magnitude.

Mechanical insufflation-exsufflation (MI-E) uses positive and negative pressures to assist weak cough and to help clear airway secretions. Laryngeal visualization during MI-E has revealed that inappropriate upper airway responses can impede its efficacy. However, the dynamics of pressure transmission in the upper airways during MI-E are unclear, as are the relationships among anatomic structure, pressure, and airflow. Can airflow resistance through the upper airway and the larynx feasibly be calculated during MI-E, and if so, how are the pressures transmitted to the trachea? Cross-sectional study of 10 healthy adults, where MI-E was provided with and without active cough using pressure settings+20/-40cm H2O and ± 40cm H2O. Airflow and pressure at the level of the facemask were measured using a pneumotachograph, whereas pressure transducers (positioned via transnasal fiber-optic laryngoscopy) recorded pressures above the larynx and within the trachea. Upper airway resistance (Ruaw) and translaryngeal resistance (Rtl) were calculated (in centimeters of water per liter per second) and were compared with direct observations via laryngoscopy. Positive pressures reached the trachea effectively, whereas negative tracheal pressures during exsufflation were approximately one-half of the intended settings. Insufflation pressure increased slightly when passing through the larynx. Participant effort influenced tracheal pressures and the resistances, with findings consistent with laryngoscopic observations. During MI-E, resistance seems to be dynamic, with Ruaw exceeding Rtl. Inappropriate laryngeal closure increased Rtl during both positive and negative pressures. We found that Ruaw and Rtl can be calculated feasibly during MI-E. The findings indicate different transmission dynamics for positive and negative pressures and that resistances are influenced by participant effort. The findings support using lower insufflation pressures and higher negative pressures in clinical practice.

We study general relativity in the framework of non-commutative differential geometry. As a prerequisite we develop the basic notions of non-commutative Riemannian geometry, including analogues of Riemannian metric, curvature and scalar curvature. This enables us to introduce a generalized Einstein-Hilbert action for non-commutative Riemannian spaces. As an example we study a space-time which is the product of a four dimensional manifold by a two-point space, using the tools of non-commutative Riemannian geometry, and derive its generalized Einstein-Hilbert action. In the simplest situation, where the Riemannian metric is taken to be the same on the two copies of the manifold, one obtains a model of a scalar field coupled to Einstein gravity. This field is geometrically interpreted as describing the distance between the two points in the internal space.

Middle ear pressure changes have been thought to cause sensori-neural loss as well as conductive hearing loss. To clarify the degree and mechanism, we used electrocochleography in guinea pigs to investigate electrophysiological changes in the inner ear while positive or negative pressure changes were applied only to the middle ear cavity (middle ear group), or to the external auditory canal and middle ear cavity simultaneously (external-middle ear group).1) Significant reductions in action potential (AP) amplitude were found in the middle ear group receiving either positive or negative pressure, but there was no significant difference between the two groups. No significant reductions were found in the external-middle ear group regardless of whether positive or negative pressure was applied.2) Significant reductions in summating potential (SP) amplitude and SP/AP ratio were found in the middle ear group receiving positive pressure. There was wide variation in the changes observed in the middle ear group receiving negative pressure. The external-middle ear group receiving negative pressure showed greater reductions in SP amplitude and SP/AP ratio than the group receiving positive pressure, implying a difference in the changes in stiffness of the inner ear windows between the two groups.3) Rebound phenomenon in SP amplitude and SP/AP ratio was found in the middle ear group when positive pressure in the middle ear cavity was released, implying secondary effects on hearing due to inner ear pressure changes.

Linear brakes are devices used to restrict relative linear motions between two points. The use of soft robotic technology has enabled the fabrication of lightweight linear brakes making use of frictional forces generated by a vacuum on jamming layers. This kind of device has significant potential for wearable devices as they are lightweight yet produce significant linear tensions which can be used to transfer loads or to selectively prevent certain motions of the body. However, vacuum-based devices have limitations in terms of maximum pressure and due to the decreasing frictional forces as the jamming layers decrease in contact area as they separate during the motion. This article introduces a positive and negative pressure linear brake where both positive and negative pressure is applied to jamming layers located inside of a pouch motor which is pressurized using positive pressures. This results in a soft linear brake capable of large braking forces and of adjusting its behavior through the variation of both positive and negative pressures. The proposed brake could sustain a linear tensile force approaching 500 N even at lower pressures and was implemented as a lower back support device intended for factory and healthcare workers.

Hochschild homology (along with cyclic and periodic cyclic homologies) plays in the non-commutative geometry the role which de Rham cohomology plays in the classical geometry. It is defined for any associative algebra. The Hochschild chains over the algebra \(\mathcal {A}\) are not localised and the operations with the chains over the algebra \(\mathcal {A}\) are not commutative. If the algebra were the algebra of differentiable functions over a topological manifold M, the corresponding Hochschild chains would be differentiable functions over MN. Cyclic/periodic cyclic homology of the \(\mathcal {A}\) were introduced to extend the Chern–Weil characteristic classes to idempotents over \(\mathcal {A}\). Cyclic/periodic cyclic homology represents the minimal algebraic structure for which the Chern–Weil construction works. The cyclic/periodic cyclic homology of the algebra of differentiable functions constitutes the link between the classical differential geometry and non-commutative geometry.

Exercise increases muscle microvascular flow via vasodilation from both endothelial dependent and independent mechanisms. Altered transmural pressure also affects blood flow in muscle. For example, lower body negative pressure decreases and lower body positive pressure increases blood flow. PURPOSE: To determine muscle microvascular blood flow (MBF) during post-exercise hyperemia at negative and positive lower body pressure (LBP). It was hypothesized that the post-exercise hyperemic response would not be present at increased levels of positive LBP. METHODS: Eight healthy subjects (6 male, 2 female; ages 21–41) were placed supine in a LBP chamber that was sealed at the waist. Photoplethysmography was used to noninvasively measure MBF of the tibialis anterior muscle and skin microvascular blood flow (SBF) of overlying skin during exposure to a series of LBP levels (−30, −20, −10, 0, 10, 20, 30mmHg) with and without dorsiflexion exercise. At each pressure level MBF was allowed to stabilize for one minute prior to a one minute baseline data collection. Subjects then performed a one minute isometric dorsiflexion at a resistance of 41N and MBF was recorded for one minute following dorsiflexion. Subjects were given a 5 minute rest period between pressure levels to ensure MBF return to baseline. All microvascular flow data were normalized to the control value obtained at ambient pressure without exercise and presented as percentages (mean±SE) to compare between conditions. Data were analyzed using two-way repeated measures ANOVA to determine exercise effect and pressure effect on MBF. RESULTS: MBF and SBF increased at all LBP levels with exercise compared to no exercise (p=0.001 and p=0.005). MBF significantly decreased with negative pressure and increased with positive pressure (p=0.003 and p<0.001). The lowest MBF was at −30mmHg (52±9% w/o exercise, 61±9% w/ exercise) and the highest was at 10mmHg (137±15% w/o exercise, 145±12% w/ exercise). CONCLUSION: Post exercise hyperemia occurs at all lower body pressure levels studied. Elevation of microvascular flow after isometric exercise adds to changes measured at different levels of LBP. Regimens for exercise training and post-injury rehabilitation may benefit from exercise at low levels of positive LBP. Supported by NIH Training Grant 2 T32AR07484-22 to GCM.

Water hammer is a transient flow in pipes that was created by sudden changesof velocity in pipe lines. This phenomenon can cause strong positive and negative pressures in water conveyance pipes and usually it poses pipeline to danger. Overall, water hammer creates by rapidly closing valves, shutting off or suddenly restarting pumps. It has destructive hydrodynamic effects in pressurized pipelines. In this study, governing equations of water hammer is numerically simulated using MATLAB software. Then, the sensitivity analysis in negative and positive pressures by changing some variables such as pipe diameter, pipe length and also wave velocity in pipewas investigated. Numerical simulation is based on characteristic method. Sensitivity analysis help designers to have well understand of water hammer phenomenon.

We introduce a class of metrics on the tangent bundle of a Riemannian manifold and find the Levi-Civita connections of these metrics. Then by using the Levi-Civita connection, we study the conformal vector fields on the tangent bundle of the Riemannian ma

To compare using computational fluid dynamics (CFD) the flow pattern, irrigant velocity, apical pressure and shear stress produced by negative (MiC) and positive pressure with different types of needles (side-vented (SV), front-vented (FV) and notched (N)) at two insertion depths in the apical ramification of oval root canals. The micro-CT of a mandibular molar with an oval root canal with an apical ramification was used for computational analysis after preparation and geometric reconstruction. Geometries with the needles in two positions (1 and 3mm from WL) were created to run the simulations. Key parameters of irrigation were displayed with CFD and compared. The penetration depth of the needle in the root canal strongly influenced shear stress and apical pressure. The three needles revealed that the highest shear stress, velocity and apical pressure were 1mm from the WL and generated medium velocities. In N simulations, the fluid flow did not reach the apical ramification and the lowest shear stress values for positive pressure needles were found. The predominant axial component for FV revealed a different pattern of irrigation with high shear stress values and higher apical pressures than those exerted by other needles. SV simulations had generalized fluid flow in most of the main canal, the highest shear stress values and lower apical pressure than the threshold determined for risk of extrusion. MiC was associated with low velocity, shear stress and apical pressure. The SV needle demonstrated a combination of low positive pressure and high shear stress; while N had the lowest shear stress and FV the highest apical pressure. MiC generated fluid flow in part of the apical ramification with negative apical pressure values but low shear stress and velocity.

Working within the recent formalism of Poisson–Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order . Here λ is the deformation parameter, plausibly the Planck scale. We find that are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace–Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson–Riemannian geometry we show that it deforms to□f+λ2ωαβ(Ricγα−Sγ;α)(∇^βdf)γ+O(λ2)in terms of the classical Levi-Civita connection , the contorsion tensor S, the Poisson-bivector ω and the Ricci curvature of the Poisson-connection that controls the quantum differential structure. The Majid–Ruegg spacetime with its standard calculus and unique quantum metric provides an example with nontrivial correction to the Laplacian at order λ.

Asymmetric nanochannels for efficient saltwater transport diodes