Regions Of Low Curvature Research Articles

Imaging Dissolution Dynamics of Individual NaCl Nanoparticles during Deliquescence with In Situ Transmission Electron Microscopy.

Water vapor condensation on hygroscopic aerosol particles plays an important role in cloud formation, climate change, secondary aerosol formation, and aerosol aging. Conventional understanding considers deliquescence of nanosized hygroscopic aerosol particles a nearly instantaneous solid to liquid phase transition. However, the nanoscale dynamics of water condensation and aerosol particle dissolution prior to and during deliquescence remain obscure due to a lack of high spatial and temporal resolution single particle measurements. Here we use real time in situ transmission electron microscopy (TEM) imaging of individual sodium chloride (NaCl) nanoparticles to demonstrate that water adsorption and aerosol particle dissolution prior to and during deliquescence is a multistep dynamic process. Water condensation and aerosol particle dissolution was investigated for lab generated NaCl aerosols and found to occur in three distinct stages as a function of increasing relative humidity (RH). First, a < 100 nm water layer adsorbed on the NaCl cubes and caused sharp corners to dissolve and truncate. The water layer grew to several hundred nanometers with increasing RH and was rapidly saturated with solute, as evidenced by halting of particle dissolution. Adjacent cube corners displayed second-scale curvature fluctuations with no net particle dissolution or water layer thickness change. We propose that droplet solute concentration fluctuations drove NaCl transport from regions of high local curvature to regions of low curvature. Finally, we observed coexistence of a liquid water droplet and aerosol particle immediately prior to deliquescence. Particles dissolved discretely along single crystallographic directions, separated by few second lag times with no dissolution. This work demonstrates that deliquescence of simple pure salt particles with sizes in the range of 100 nm to several microns is not an instantaneous phase transition and instead involves a range of complex dissolution and water condensation dynamics.

Direct numerical simulations of methane, ammonia-hydrogen and hydrogen turbulent premixed flames

Three turbulent premixed flames with the same unstretched laminar flame speeds and thicknesses are analyzed and compared using 3D Direct Numerical Simulation (DNS) in a slot burner configuration at atmospheric conditions: a CH4/air flame at ϕ=1, an NH3−H2/air (46% vol. H2) at ϕ=1 and an H2/air flame at ϕ=0.45.While both stoichiometric methane and ammonia-hydrogen flames behave similarly, the lean hydrogen flame brush is twice as short with less flame surface, and exhibits significant alteration of its local flame structure: for the H2 flame, the thickness of flamelets decreases significantly while burning rates increase drastically. This is observed for flame elements convexly curved with respect to fresh reactants (positive curvature) because of preferential diffusion, where thermo-diffusive instabilities generate long-tail structures that continuously head toward the fresh gases, and also for near-flat flame elements because of local strain effects. Opposite behaviors are observed for flame elements concavely curved (negative curvature) where fuel depletion caused by unfocusing of hydrogen and strain effects are unable to increase the consumption, even leading to near-extinction of the flame. The turbulent methane and ammonia-hydrogen flames studied in this work do not exhibit the instabilities seen in the pure hydrogen flame. However, local flame-flame interactions are observed in the cusp regions of all three flames, which significantly increase the displacement speed as well as flame surface destruction.A 1D-3D comparison indicates that strain effects in regions of low curvature and preferential diffusion effects in regions of positive curvature can be modeled using counterflow flamelets to account for stretch effects on the turbulent hydrogen flame propagation in addition to turbulent wrinkling.

The θ-formulation of the two-dimensional elastica: buckling and boundary layer theory

The equations of a planar elastica under pressure can be rewritten in a useful form by parameterizing the variables in terms of the local orientation angle, θ , instead of the arc length. This ‘ θ -formulation’ lends itself to a particularly easy boundary layer analysis in the limit of weak bending stiffness. Within this parameterization, boundary layers are located at inflection points, where θ is extremum, and they connect regions of low and large curvature. A simple composite solution is derived without resorting to elliptic functions and integrals. This approximation can be used as an elementary building block to describe complex shapes. Applying this theory to the study of an elastic ring under uniform pressure and subject to a set of point forces, we discover a snapping instability. This instability is confirmed by numerical simulations. Finally, we carry out experiments and find good agreement of the theory with the experimental shape of the deformed elastica.

Shift-curvature, SGD, and generalization

A longstanding debate surrounds the related hypotheses that low-curvature minima generalize better, and that stochastic gradient descent (SGD) discourages curvature. We offer a more complete and nuanced view in support of both hypotheses. First, we show that curvature harms test performance through two new mechanisms, the shift-curvature and bias-curvature, in addition to a known parameter-covariance mechanism. The shift refers to the difference between train and test local minima, and the bias and covariance are those of the parameter distribution. These three curvature-mediated contributions to test performance are reparametrization-invariant even though curvature itself is not. Although the shift is unknown at training time, the shift-curvature as well as the other mechanisms can still be mitigated by minimizing overall curvature. Second, we derive a new, explicit SGD steady-state distribution showing that SGD optimizes an effective potential related to but different from train loss, and that SGD noise mediates a trade-off between low-loss versus low-curvature regions of this effective potential. Third, combining our test performance analysis with the SGD steady state shows that for small SGD noise, the shift-curvature is the dominant of the three mechanisms. Our experiments demonstrate the significant impact of shift-curvature on test loss, and further explore the relationship between SGD noise and curvature.

Quantum corrected polymer black hole thermodynamics: mass relations and logarithmic entropy correction

In this paper, we continue the analysis of the effective model of quantum Schwarz­schild black holes recently proposed by some of the authors in [1,2]. In the resulting quantum-corrected spacetime the central singularity is resolved by a black-to-white hole bounce, quantum effects become relevant at a unique mass-independent curvature scale, while they become negligible in the low curvature region near the horizon and classical Schwarzschild geometry is approached asymptotically. This is the case independently of the relation between the black and white hole masses, which are thus freely specifiable independent observables. A natural question then arises about the phenomenological implications of the resulting non-singular effective spacetime and whether some specific relation between the masses can be singled out from a phenomenological perspective. Here we focus on the thermodynamic properties of the effective polymer black hole and analyze the corresponding quantum corrections as functions of black and white hole masses. The study of the relevant thermodynamic quantities such as temperature, specific heat, and horizon entropy reveals that the effective spacetime generically admits an extremal minimal-sized configuration of quantum-gravitational nature characterized by vanishing temperature and entropy. For large masses, the classically expected results are recovered at leading order and quantum corrections are negligible, thus providing us with a further consistency check of the model. The explicit form of the corrections depends on the specific relationship among the masses. In particular, a first-order logarithmic correction to the black hole entropy is obtained for a quadratic mass relation. The latter corresponds to the case of proper finite-length effects which turn out to be compatible with a minimal length generalized uncertainty principle associated with an extremal Planck-sized black hole.

Reconstruction of the three-dimensional beat pattern underlying swimming behaviors of sperm

The eukaryotic flagellum propels sperm cells and simultaneously detects physical and chemical cues that modulate the waveform of the flagellar beat. Most previous studies have characterized the flagellar beat and swimming trajectories in two space dimensions (2D) at a water/glass interface. Here, using refined holographic imaging methods, we report high-quality recordings of three-dimensional (3D) flagellar bending waves. As predicted by theory, we observed that an asymmetric and planar flagellar beat results in a circular swimming path, whereas a symmetric and non-planar flagellar beat results in a twisted-ribbon swimming path. During swimming in 3D, human sperm flagella exhibit torsion waves characterized by maxima at the low curvature regions of the flagellar wave. We suggest that these torsion waves are common in nature and that they are an intrinsic property of beating axonemes. We discuss how 3D beat patterns result in twisted-ribbon swimming paths. This study provides new insight into the axoneme dynamics, the 3D flagellar beat, and the resulting swimming behavior.Graphic abstract

2-D and 3-D measurements of flame stretch and turbulence–flame interactions in turbulent premixed flames using DNS

Abstract

Unitarity from a smooth horizon?

Under semiclassical evolution, black holes retain a smooth horizon but fail to return information. Yet, the Ryu-Takayanagi prescription computes the boundary entropy expected from unitary CFT evolution. We demonstrate this in a novel setting with an asymptotic bulk detector, eliminating an assumption about the entanglement wedge of auxiliary systems. We consider three interpretations of this result. (i) At face value, information is lost in the bulk but not in the CFT. This conflicts with the AdS/CFT dictionary. (ii) No unique QFT state (pure or mixed) governs all detector responses to the bulk Hawking radiation. This conflicts with the existence of an S-matrix. (iii) Nonlocal couplings to the black hole interior cause asymptotic detectors to respond as though the radiation was pure, even though it is naively thermal. This invalidates the standard interpretation of the semiclassical state, including its smoothness at the horizon. We conclude that unitary boundary evolution requires asymptotic bulk detectors to become unambiguously pure at late times. We ask whether the RT prescription can still reproduce the boundary entropy in this bulk scenario. We find that this requires a substantial failure of semiclassical gravity in a low-curvature region, such as a firewall that purifies the Hawking radiation. Finally, we allow that the dual to semiclassical gravity may be an ensemble of unitary theories. This appears to relax the tensions we found: the ensemble average of out-states would be mixed, but the ensemble average of final entropies would vanish.

Surface Curvature Effects on Film Cooling Performance for Shaped Holes on a Model Turbine Blade

Abstract Surface curvature has been shown to have significant effects on the film cooling performance of round holes, but the literature include few studies of its effects on shaped holes despite their prevalence in gas turbines. Experiments were performed using two rows of holes placed on the suction side of a scaled-up turbine blade in a low Mach number linear cascade wind tunnel with low freestream turbulence. The rows were placed in regions of high and low convex surface curvature. Geometries and flow conditions for the rows were matched to those from previous flat plate studies. Comparison of the adiabatic effectiveness results from the high curvature and flat plate rows revealed the same trends as those in the literature using round holes, with increased performance for the high curvature row at lower blowing ratios and the opposite at higher ones. The low curvature row had similar performance to the flat plate row at lower blowing ratios, suggesting the mild convex curvature had little beneficial effect. At higher blowing ratios, the low curvature row had inferior performance, which was attributed to the local freestream adverse pressure gradient that generated additional turbulence, promoting jet-to-mainstream mixing and decreasing performance.

Quantum geometry and effective dynamics of Janis-Newman-Winicour singularities

Inspired by the recent proposal for the quantum effective dynamics of the Schwarzschild spacetime given in \cite{AOS1}, we investigate the effective dynamics of the loop quantized Janis-Newman-Winicour (JNW) spacetime which is an extension of the Schwarzschild spacetime with an extra minimally coupled massless scalar field. Two parameters are introduced in order to regularize the Hamiltonian constraint in the quantum effective dynamics. These two parameters are assumed to be Dirac observables when the effective dynamics is solved. By carefully choosing appropriate conditions for these two parameters, we completely determine them, and the resulted new effective description of the JNW spacetime leads to a well behaved quantum dynamics which on one hand resolves the classical singularities, and on the other hand, agrees with the classical dynamics in the low curvature region.

Effective quantum extended spacetime of polymer Schwarzschild black hole

The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches. In the context of loop quantum gravity (LQG), one of the major candidates for a non-perturbative background-independent quantisation of general relativity, considerable effort has been devoted to construct effective models in which these questions can be studied. In these models, classical singularities are replaced by a ‘bounce’ induced by quantum geometry corrections. Undesirable features may arise however depending on the details of the model. In this paper, we focus on Schwarzschild black holes and propose a new effective quantum theory based on polymerisation of new canonical phase space variables inspired by those successful in loop quantum cosmology. The quantum corrected spacetime resulting from the solutions of the effective dynamics is characterised by infinitely many pairs of trapped and anti-trapped regions connected via a space-like transition surface replacing the central singularity. Quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon. The effective quantum metric describes also the exterior regions and asymptotically classical Schwarzschild geometry is recovered. We however find that physically acceptable solutions require us to select a certain subset of initial conditions, corresponding to a specific mass (de-)amplification after the bounce. We also sketch the corresponding quantum theory and explicitly compute the kernel of the Hamiltonian constraint operator.

Topology of Disordered 3D Graphene Networks.

Disordered carbons comprise graphene fragments assembled into three-dimensional networks. It has long been debated whether these networks contain positive curvature, as seen in fullerenes, negative curvature, as proposed for the schwarzite structures, or zero curvature, as in ribbons. We present a mesh-based approach to analyze the topology of a set of nanoporous and glassy carbon models that accurately reproduce experimental properties. Although all three topological elements are present, negatively curved structures dominate. At the atomic level, analysis of local environments shows that sp- and sp^{3}-bonded atoms are associated with line defects and screw dislocations that resolve topological complexities such as termination of free edges and stacking of low curvature regions into ribbons. These results provide insight into the synthesis of porous carbon materials, glassy carbon and the graphitizability of carbon materials.

Band gap bowing for high In content InAlN films

The InAlN alloy system has bandgap energies that span the entire visible range and is a promising candidate for bandgap engineering. To facilitate bandgap engineering, the bandgap bowing for the entire composition range must be well characterized. In rich InxAl1−xN (x &amp;gt; 0.60), films were grown via plasma assisted molecular beam epitaxy on freestanding GaN substrates. The InxAl1−xN film compositions were determined using high resolution X-ray diffraction. On-axis 0002 ω-2θ scans were used to determine the c spacing of the films, reciprocal space maps of the 1¯015 peaks were used to determine that the films were completely relaxed, and the film compositions were calculated from that information assuming Vegard's law. The bandgaps were independently measured using absorbance spectroscopy and fitting to the linear region of a Tauc plot (dependence of α2 hν on hν) as determined by interpolating the second derivative of the data and selecting a region of low curvature. Compared with the literature, the data were fit to a composition-independent bandgap bowing model, and a bowing parameter of b = 4.0 ± 0.2 eV was calculated, which is consistent with previous results.

Emergent Shape Sensing of Dynamic Membranes

For cells to divide or branch, they need to be able to sense their own shape, localizing proteins to regions of high or low curvature. Curved proteins prefer to bind to curved membranes, which can explain some of this shape sensitivity. However, when the membrane has curvature on the micron scale, and proteins are on the nanometer scale, single-protein sensing may be challenging. Shape sensing can also arise from the collective action of many proteins even if single proteins don’t sense curvature - i.e. the shape sensing is emergent. In particular, it is known that the motion of traveling waves arising from reaction-diffusion processes on a curved surface is altered by surface curvature. Common biochemical reactions that distinguish the cell front from rear (Rho GTPase polarity, modeled by a “wave-pinning” mechanism) also sense shape, with the cell front pointing toward the narrow end of an elongated cell. However, it is not completely clear what aspects of the cell geometry the wave-pinning reaction senses. Does the cell front localize to high mean or Gaussian curvature, or a different shape feature altogether? Is this shape sensing disrupted by the membrane fluctuations? We address these questions with a combination of detailed simulation of reaction-diffusion on a curved membrane surface and a phenomenological theory that allows us to construct an energy landscape to predict where these domains localize. This landscape theory allows us to develop a coarse-grained model of how regions of high Rho signaling will diffuse on a fluctuating membrane.

Quantum extension of the Kruskal spacetime

A new description of macroscopic Kruskal black holes that incorporates the quantum geometry corrections of loop quantum gravity is presented. It encompasses both the `interior' region that contains classical singularities and the `exterior' asymptotic region. Singularities are naturally resolved by the quantum geometry effects of loop quantum gravity. The resulting quantum extension of space-time has the following features: (i) It admits an infinite number of trapped, anti-trapped and asymptotic regions; (ii) All curvature scalars have uniform (i.e., mass independent) upper bounds; (iii) In the large mass limit, all asymptotic regions of the extension have the same ADM mass; (iv) In the low curvature region (e.g., near horizons) quantum effects are negligible, as one would physically expect; and (v) Final results are insensitive to the fiducial structures that have to be introduced to construct the classical phase space description (as they must be). Previous effective theories [1-10] shared some but not all of these features. We compare and contrast our results with those of these effective theories and also with expectations based on the AdS/CFT conjecture [11]. We conclude with a discussion of limitations of our framework, especially for the analysis of evaporating black holes.

Existence, lifespan, and transfer rate of Ricci flows on manifolds with small Ricci curvature

We show that in dimension 4 and above, the lifespan of Ricci flows depends on the relative smallness of the Ricci curvature compared to the Riemann curvature on the initial manifold. We can generalize this lifespan estimate to the local Ricci flow, using which we prove the short-time existence of Ricci flow solutions on noncompact Riemannian manifolds with at most quadratic curvature growth, whose Ricci curvature and its first two derivatives are sufficiently small in regions where the Riemann curvature is large. Those Ricci flow solutions may have unbounded curvature. Moreover, our method implies that, under some appropriate assumptions, the spatial transfer rate (the rate at which high curvature regions affect low curvature regions) of the Ricci flow resembles that of the heat equation.

Phase field modeling of sintering: Role of grain orientation and anisotropic properties

The influence of anisotropic properties of powder particles on microstructural evolution during solid-state sintering processes is analyzed. Two types of anisotropy studied in the current work are direction-dependent interface diffusion anisotropy, and grain orientation dependent grain boundary energy anisotropy. A phase field modeling approach is utilized to assess how the individual anisotropic characteristics influence morphological changes during sintering. In addition, a novel approach for updating grain orientation after rigid-body rotation of particles during powder compaction accompanying the sintering process is developed. It is observed that conventional isotropic microstructural analysis over-simplifies the material behavior and demonstrates faster microstructural evolution. Direction-dependent diffusion produces gradual shape change of the particles by mass transfer from high curvature region to low curvature region along the particle surface, and delays the onset of the grain growth process. Depending on the grain boundary misorientation and inclination, anisotropic grain boundary energy may induce faster or slower grain boundary migration rate. Orientation update during the process plays a critical role in the consolidation kinetics, as well as in the final microstructural configuration. Variation in grain orientation and its evolution during the sintering process can produce different grain morphologies for the same initial condition.

Nucleotide-dependent Conformational Dynamics and Energetics of Tubulin

Microtubules (MTs) are key components of the cytoskeleton and play a central role in cell division and development. They undergo stochastic switching between phases of growth and shrinkage driven by GTP hydrolysis in αβ-tubulin dimers. MT assembly requires that tubulin adopts a straight conformation in the lattice, while during disassembly it adopts a kinked conformation that is incompatible with the MT geometry. The mechanism by which GTP binding renders individual tubulin dimers polymerization-competent is still poorly understood. In particular, two models of MT assembly are being controversially discussed: in the allosteric model, GTP binding directly promotes tubulin straightening, whereas in the lattice model tubulin is kinked regardless of its nucleotide state, and it is the assembling MT itself that forces tubulin into a straight conformation. In order to distinguish between these two hypotheses, we have characterized the conformational dynamics and energetics of free tubulin in solution using atomistic molecular dynamics simulations and free energy calculations. Unexpectedly, and contradictory to the above models, we find that GTP-tubulin samples a broad range of intrinsic curvatures all of which are almost isoenergetic. In contrast, GDP-tubulin is confined to low-curvature regions of the conformational space. Furthermore, an additional energy barrier is seen in all simulated tubulin ensembles that is associated with collective rearrangements in the β-subunit of tubulin but not with the nucleotide state. This barrier separates different bending modi and may be related to the inhibitory mechanism of MT-associated proteins such as stathmin which suppresses tubulin polymerization in a nucleotide-independent manner. Overall, our results suggest a new combined conformational selection / induced fit model in which GTP binding renders tubulin more flexible at the intadimer interface and allows a specific type of tubulin bending that facilitates MT assembly.

Quantum fluctuating geometries and the information paradox

We study Hawking radiation on the quantum space-time of a collapsing null shell. We use the geometric optics approximation as in Hawking’s original papers to treat the radiation. The quantum space-time is constructed by superposing the classical geometries associated with collapsing shells with uncertainty in their position and mass. We show that there are departures from thermality in the radiation even though we are not considering a back reaction. One recovers the usual profile for the Hawking radiation as a function of frequency in the limit where the space-time is classical. However, when quantum corrections are taken into account, the profile of the Hawking radiation as a function of time contains information about the initial state of the collapsing shell. More work will be needed to determine whether all the information can be recovered. The calculations show that non-trivial quantum effects can occur in regions of low curvature when horizons are involved, as is proposed in the firewall scenario, for instance.

Optimization and analysis of hypersonic leading edge geometries

An aerothermal optimization study of two-dimensional hypersonic leading edge geometries has been performed using both genetic algorithm and particle swarm optimization. The accuracy of a simplified model and a reduced order numerical model was assessed through comparison to simulations of the compressible Navier–Stokes equations performed in OpenFOAM. Specifically, the estimated surface pressure and laminar convective heating distributions have been compared. The simplified model was found to have compromised accuracy in regions of high and low surface curvature. The reduced order numerical model was found to give accurate results with significantly reduced computational cost compared to complete Navier–Stokes simulations. Optimizations were then performed using the simplified analysis technique, and the reduced order numerical model. The performance of the optimized hypersonic leading edge geometries was analyzed using OpenFOAM. The results show that both methods achieve a similar geometric result. However, the quality of the optimization is improved by using the reduced order numerical model. An analysis was performed in the design space immediately surrounding the optimized geometry to assess the impact of small geometric changes on aerothermal performance. The results show that even small changes in leading edge geometry can have a significant influence on aerothermal performance.