Curvature Dependence Research Articles

Dependence of HAMR Transition Curvature on Bit Length

Transition curvature is a major contributor to transition broadening in current heat-assisted magnetic recording (HAMR) devices. In this article, in order to clarify HAMR performance versus bit length (BL), a detailed study of the dependence of HAMR transition curvature on BL is presented. With the help of micromagnetic simulations, HAMR bits with three different BLs (10.5, 15, and 21 nm) are written and transition curvatures are calculated. Both thermal exchange coupling composite (ECC) media and pure FePt media are tested. By tracking the change of transition curvature during the HAMR cooling process, an erase-after-write effect is observed. DC-erased media, introduction of intergranular exchange, and removal of dipole interactions are also examined for potential optimization of the HAMR system.

Stretch-Induced Cavitation: How Critical Cavity Radius and Barrier Energy, Radius, and Energy of a Stable Cavity Depend on the Stretching Factor.

Characteristics of tension-induced cavitation, such as free energy at the barrier for cavitation, the size of the critical (barrier) cavity, the stable cavity size, and the free energy of the stable cavity, depend on the amount of tension (stretch) and the initial size of the sample. In this work, we study how the characteristics of the cavitation mentioned above scale with the amount of applied tension. We consider two models characterizing the properties of cavitating liquid: (a) a simple model with a linear tension-strain relation and neglect of curvature dependence of cavity surface tension and (b) a more realistic model with a nonlinear tension-strain relation and curvature-dependent surface tension. For both models, we find the relevant scaling relations when we stretch the initial volume of the liquid sample in the interval between 1% and 20% of the initial volume. Specific numerical tests are performed for the case of liquid water when the initial volume of the sample is a sphere with a radius of 100 nm.

Quantum Gravity: A Fluctuating Point of View

In this contribution, we discuss the asymptotic safety scenario for quantum gravity with a functional renormalization group approach that disentangles dynamical metric fluctuations from the background metric. We review the state of the art in pure gravity and general gravity–matter systems. This includes the discussion of results on the existence and properties of the asymptotically safe ultraviolet fixed point, full ultraviolet-infrared trajectories with classical gravity in the infrared, and the curvature dependence of couplings also in gravity–matter systems. The results in gravity–matter systems concern the ultraviolet stability of the fixed point and the dominance of gravity fluctuations in minimally coupled gravity–matter systems. Furthermore, we discuss important physics properties such as locality of the theory, diffeomorphism invariance, background independence, unitarity, and access to observables, as well as open challenges.

Development of a method for geometric modeling of centrifugal compressor impellers

The practice of designing centrifugal compressors in which impellers are the main components shows that there are reserves for their further improvement. One of the main reserves consists in improving flow conditions for the compressed medium in the compressor setting and, above all, in the impeller. A method of geometric modeling settings of the impellers of centrifugal compressors was proposed which involves the construction of meridional boundaries of impellers and the blade profile on an involute of the cylindrical surface of the outer radius of the impeller. The blade is represented by ruled surfaces. The outer boundary of the impeller is described by a curve in natural parameterization using cubic dependence of curvature on the arc length. Dependences and length of the arc are determined in the process of modeling the boundary based on the set source data. The problem is solved by minimizing deviations of intermediate curves from the boundary endpoint. The inner boundary is obtained as an envelope of circles inscribed in the meridional channel of the impeller. Radii of the circles are determined taking into account the flow areas of the channel. The midline of the blade profile on an involute of the cylindrical surface of the outer radius of the impeller is modeled using a curve that is presented in natural parameterization with quadratic law of curvature distribution. A computer code was developed in the Fortran Power Station programming environment that visualizes the obtained numerical results graphically on a computer display in addition to digital information on the modeled boundaries and the blade profile. Graphical results were presented. They confirmed the efficiency of the proposed method of modeling the settings of centrifugal compressor impellers. The method can be useful to offices involved in the design of centrifugal compressors

U-duct turbulent-flow computation with the ST-VMS method and isogeometric discretization

The U-duct turbulent flow is a known benchmark problem with the computational challenges of high Reynolds number, high curvature and strong flow dependence on the inflow profile. We use this benchmark problem to test and evaluate the Space–Time Variational Multiscale (ST-VMS) method with ST isogeometric discretization. A fully-developed flow field in a straight duct with periodicity condition is used as the inflow profile. The ST-VMS serves as the core method. The ST framework provides higher-order accuracy in general, and the VMS feature of the ST-VMS addresses the computational challenges associated with the multiscale nature of the unsteady flow. The ST isogeometric discretization enables more accurate representation of the duct geometry and increased accuracy in the flow solution. In the straight-duct computations to obtain the inflow velocity, the periodicity condition is enforced with the ST Slip Interface method. All computations are carried out with quadratic NURBS meshes, which represent the circular arc of the duct exactly in the U-duct computations. We investigate how the results vary with the time-averaging range used in reporting the results, mesh refinement, and the Courant number. The results are compared to experimental data, showing that the ST-VMS with ST isogeometric discretization provides good accuracy in this class of flow problems.

Study of surface evolution via Modified Ion Beam Sputtering Semi-Empirical Model (MIBSEM)

An Ion Beam Sputtering Monte Carlo Model (IBSM) was modified to study the effect of different surface diffusion mechanics on the surface height and surface roughness of materials when bombarded with energetic ions. The extension was done by incorporating Seahet al.’s semi-empirical ion sputtering equations into the sputter erosion algorithm of the MC model and by enforcing curvature dependence of sputter yield. Also, TRansport of Ions in Matter (TRIM) software, was used to calculate the sputter yield and the values obtained were compared with those obtained from Seahet al.’s semi-empirical model and the sputter yield obtained from sputtering experiments. Our studies show that the surface diffusion mechanics that occurs during a sputtering process controls the substrate surface height and its roughness while curvature dependence of sputter yield has little or no contribution to the target surface height and its roughness. Our comparison of the calculated sputter yield values of TRIM and Seahet al.’s model with experimental sputter yield values show that Seahet al.’s model gives sputter yield values closer to experimental values than TRIM at a normal angle of incidence while TRIM gives sputter yield values closer to experimental values at 60°angle of incidence.

Band structure of MoSTe Janus nanotubes

Nanotubes generated by rolling up transition metal dichalcogenide Janus monolayers are a new class of low-dimensional materials, which are expected to display unique electronic properties compared to their parent two- and three-dimensional structures. Here, we investigate the band structure of $1H$-MoSTe Janus armchair and zigzag nanotubes, which were recently hypothesized to be stable as single-walled structures with radii of only a few nanometers. We first investigate the most stable nanotube sizes and assess the influence of quantum confinement and curvature on the band structures, showing that these are heavily modified by curvature while confinement effects are negligible. The curvature dependence is then further studied by analyzing the band gap dependence on the nanotube radius, where band gap changes as large as 0.5 eV are observed. By investigating the band edge positions and orbital projected density of states for different tube sizes, we find that this high sensitivity is mainly attributed to the Mo $d$ states in the conduction band.

Direct measurement of curvature-dependent surface tension of an alcohol nanomeniscus.

Surface tension is a key parameter for understanding nucleation in the very initial stage of phase transformation. Although surface tension has been predicted to vary with the curvature of the liquid-vapor interface, particularly at the large curvature of, e.g., the subnanometric critical nucleus, experimental study still remains challenging due to inaccessibility to such a small cluster. Here, by directly measuring the critical size of a single capillary-condensed nanomeniscus using atomic force microscopy, we address the curvature dependence of surface tension of alcohols and observe that the surface tension is doubled for ethanol and n-propanol with a radius-of-curvature of ∼-0.46 nm. We also find that the interface of larger negative (positive) curvature exhibits larger (smaller) surface tension, which evidently governs nucleation at the ∼1 nm scale and below, indicating more facilitated nucleation than normally expected. Such well characterized curvature effects contribute to better understanding and accurate analysis of nucleation occurring in various fields including materials science and atmospheric science.

저시간 분해능으로 인한 화염 속도 분석의 불확실성

This paper analyzes the effect of low temporal resolution on the accuracy of determining the local flame speed for experimental measurements and simulations. Flame speed measurement of moving flames requires the evaluation of a temporal derivative of flame front motion. Measurements have limited temporal resolution, which can lead to a bias error in the calculation of flame speed. The error associated with the temporal resolution was derived in the leading order effect on sampling time. In order to demonstrate the error term, we employed numerical examples. Artificial flame solutions are generated by solving the G-equation with prescribed flow fields and fine spatial/temporal resolutions. By varying the sampling time step, we demonstrated the error can lead to negative values of the measured flame speed. Furthermore, when coarse sampling time steps are used, the calculated flame speed also exhibits a spurious curvature dependency. Lastly, the associated error can be estimated by spatial gradients of the flame front for convection dominated flows.

Equivalence between condensation and boiling in a Lennard-Jones fluid.

Condensation and boiling are phase transitions highly relevant to industry, geology, and atmospheric science. These phase transitions are initiated by the nucleation of a drop in a supersaturated vapor and of a bubble in an overstretched liquid, respectively. The surface tension between both phases, liquid and vapor, is a key parameter in the development of such nucleation stage. Whereas the surface tension can be readily measured for a flat interface, there are technical and conceptual limitations to obtain it for the curved interface of the nucleus. On the technical side, it is quite difficult to observe a critical nucleus in experiments. From a conceptual point of view, the interfacial free energy depends on the choice of the dividing surface, being the surface of tension the one relevant for nucleation. We bypass the technical limitation by performing simulations of a Lennard-Jones fluid where we equilibrate critical nuclei (both drops and bubbles). Regarding the conceptual hurdle, we find the relevant cluster size by searching the radius that correctly predicts nucleation rates and nucleation free energy barriers when combined with Classical Nucleation Theory. With such definition of the cluster size we find the same value of the surface tension for drops and bubbles of a given radius. Thus, condensation and boiling can be viewed as two sides of the same coin. Finally, we combine the data coming from drops and bubbles to obtain, via two different routes, estimates of the Tolman length, a parameter that allows describing the curvature dependence of the surface tension in a theoretical framework.

Full field dependence of primary aberrations in perturbed double-plane symmetric systems with a circular pupil.

This paper deals with the theory of primary aberrations for perturbed double-plane symmetric optical systems consisting of a combination of tilted and decentered surfaces and a circular pupil. First, the analytical expressions describing the full field behavior of Zernike polynomials are derived from the fourth-order wavefront aberration function for this class of optical systems. Then, such expressions are combined to retrieve the full field dependence of primary coma, primary astigmatism, and field curvature. They are described by an elliptical conic-shaped surface with a variable apex location over the field of view, by a binodal surface with two nodes over the field of view, and by a general elliptical surface with one node. The proposed analytical expressions provide a better understanding of the primary aberration behavior for these systems and can be of great use in their optical design and aberration correction. An optical system constituted by a pair of tilted and decentered biconic lenses is studied to validate the proposed expressions.

Assessment of absorbed power density and temperature rise for nonplanar body model under electromagnetic exposure above 6 GHz

The averaged absorbed power density (APD) and temperature rise in body models with nonplanar surfaces were computed for electromagnetic exposure above 6 GHz. Different calculation schemes for the averaged APD were investigated. Additionally, a novel compensation method for correcting the heat convection rate on the air/skin interface in voxel human models was proposed and validated. The compensation method can be easily incorporated into bioheat calculations and does not require information regarding the normal direction of the boundary voxels, in contrast to a previously proposed method. The APD and temperature rise were evaluated using models of a two-dimensional cylinder and a three-dimensional partial forearm. The heating factor, which was defined as the ratio of the temperature rise to the APD, was calculated using different APD averaging schemes. Our computational results revealed different frequency and curvature dependences. For body models with curvature radii of >30 mm and at frequencies of >20 GHz, the differences in the heating factors among the APD schemes were small.

Magnetic domain wall curvature induced by wire edge pinning

In this study, we report on the analysis of the magnetic domain wall (DW) curvature due to magnetic field induced motion in Ta/CoFeB/MgO and Pt/Co/Pt wires with perpendicular magnetic anisotropy. In wires of 20 μm and 25 μm, a large edge pinning potential produces the anchoring of the DW ends to the wire edges, which is evidenced as a significant curvature of the DW front as it propagates. As the driving magnetic field is increased, the curvature reduces as a result of the system moving away from the creep regime of DW motion, which implies a weaker dependence of the DW dynamics on the interaction between the DW and the wire edge defects. A simple model is derived to describe the dependence of the DW curvature on the driving magnetic field and allows us to extract the parameter σE, which accounts for the strength of the edge pinning potential. The model describes well the systems with both weak and strong bulk pinning potentials like Ta/CoFeB/MgO and Pt/Co/Pt, respectively. This provides a means to quantify the effect of edge pinning induced DW curvature on magnetic DW dynamics.

Applicability of extrapolation relations for curvature and stretch rate dependences of displacement speed for statistically planar turbulent premixed flames

A three-dimensional Direct Numerical Simulation (DNS) database of statistically planar turbulent premixed flames covering the wrinkled/corrugated flamelets and the thin reaction zones regimes of premixed turbulent combustion has been utilised to assess the performances of the extrapolation relations, which approximate the stretch rate and curvature dependences of density-weighted displacement speed . It has been found that remains negatively correlated with curvature and exhibits a significantly non-linear relation with stretch rate for all cases considered here. As a result of these behaviours, an extrapolation relation, which assumes a linear stretch rate dependence of density-weighted displacement speed has been found to be inadequate. However, an alternative extrapolation relation which assumes a linear curvature dependence of has been found to be more successful in capturing local behaviour of the density-weighted displacement speed because it allows for a non-linear stretch rate dependence of . The extrapolation relations, which express as non-linear functions of either curvature or stretch rate, have been found to perform better than the linear extrapolation relations. The Markstein length for all the extrapolation relations except for the one, which assumes a linear stretch rate dependence of , has been found to be in good agreement with an analytical expression for . An extrapolation relation which involves solving a non-linear equation in terms of stretch rate has been found to be sensitive to the initial guess and an alternative high-order polynomial-based extrapolation relation gives rise to overshoots and undershoots and thus the goodness of fit of these relations suffers for high turbulence intensities. An alternative extrapolation relation has been proposed in this analysis, which explicitly accounts for the non-linear curvature dependence of the combined reaction and normal diffusion components of and satisfactorily captures the statistical behaviours of for all cases considered here.

Weyl anomaly induced Fermi condensation and holography

Recently it is found that, due to Weyl anomaly, a background scalar field induces a non-trivial Fermi condensation for theories with Yukawa couplings. For simplicity, the paper consider only scalar type Yukawa coupling and, in the BCFT case, only for a specific boundary condition. In these cases, the Weyl anomaly takes on a simple special form. In this paper, we generalize the results to more general situations. First, we obtain general expressions of Weyl anomaly due to a background scalar and pseudo scalar field in general 4d BCFTs. Then, we derive the general form of Fermi condensation from the Weyl anomaly. It is remarkable that, in general, Fermi condensation is non-zero even if there was not a non-vanishing scalar field background. Finally, we verify our results with free BCFT with Yukawa coupling to scalar and pseudo-scalar background potential with general chiral bag boundary condition and with holographic BCFT. In particular, we obtain the shape and curvature dependence of the Fermi condensate from the holographic one point function.

Lewis Number Effects on Flame Speed Statistics in Spherical Turbulent Premixed Flames

The influences of characteristic Lewis number hbox{Le} on the statistics of density-weighted displacement speed and consumption speed in spherically expanding turbulent premixed flames have been analysed using three-dimensional direct numerical simulations data for hbox{Le} = 0.8 , 1.0 and 1.2 under statistically similar flow conditions. It has been found that the extents of flame wrinkling and burning increase with decreasing hbox{Le} , which is reflected in increasing trends of mean and most probable values of both density-weighted displacement and consumption speed. Moreover, in all cases the marginal probability density functions of density-weighted displacement speed show finite probabilities of obtaining negative values, whereas consumption speed remains deterministically positive. The strain rate and curvature dependences of scalar gradient and temperature have been found to be strongly dependent on hbox{Le} , and these statistics, along with the interrelation between strain rate and curvature, influence the local strain rate and curvature responses of consumption speed and both reaction and normal diffusion components of density-weighted displacement speed. Density-weighted displacement speed and curvature have been found to be negatively correlated, whereas positive correlations are obtained between density-weighted displacement speed and tangential strain rate for all flames considered here. The positive correlation between temperature and curvature arising from differential diffusion of heat and mass in the hbox{Le} = 0.8 case induces a positive correlation between consumption speed and curvature, whereas these correlations are negative in the hbox{Le} = 1.2 flame. The statistical behaviour of density-weighted displacement speed has been utilised to demonstrate that Damköhler’s first hypothesis does not strictly hold for spherically expanding turbulent premixed flames.

The Quantum Coherence Induced by Geometric Curvature of Gauge Field in Non-equilibrium Quantum Dynamics

The study of non-equilibrium quantum dynamics receives attentions recently. However, the nature and effects of nonequilibirumness such as detailed-balance breaking and the relationship to the underlying intrinsic geometry is still unclear. In this study, we uncover that a gauge field will be induced by the nonequilibriumness in the coherence representation and furthermore its internal geometrical curvature is directly related to the degree of detailed balance breaking. The nonequilibriumness of the quantum system induces an intrinsic geometric curvature which can enhance the quantum coherence, leading to the possibility of the space time origin for the non-local quantum correlations or the possibility of curved space time emergence from nonequilibrium quantum dynamics. We also uncovered that the internal curvature of the gauge field provides a bridge to connect the generalized quantum fluctuation dissipation theorem to the fluctuation theorem and time irreversibility of the quantum dynamics. The quantum time irreversibility is due to the path dependent factor along any particular path in an internal curved space, which is analogous to the Wilson lines (or Wilson loops) in Abelian gauge theory. We also found that the steady state quantum coherence disappears when the non-trivial internal curvature vanishes for the quantum system coupled with environments. When the curvature is relatively small indicating weak detailed balance breaking, the coherence increases as curvature increases. The internal curvature can provide a general and direct quantitative measure of the detail-balance breaking for any quantum/classical non-equilibrium systems, even without knowing the underlying steady state distribution or the steady state flux. Using an example of two harmonic oscillators coupled to two environments with different temperatures, we explicitly show the dependence of the internal curvature and quantum coherence.

Curvature Corrections Remove the Inconsistencies of Binary Classical Nucleation Theory.

The study of nucleation in fluid mixtures exposes challenges beyond those of pure systems. A striking example is homogeneous condensation in highly surface-active water-alcohol mixtures, where classical nucleation theory yields an unphysical, negative number of water molecules in the critical embryo. This flaw has rendered multicomponent nucleation theory useless for many industrial and scientific applications. Here, we show that this inconsistency is removed by properly incorporating the curvature dependence of the surface tension of the mixture into classical nucleation theory for multicomponent systems. The Gibbs adsorption equation is used to explain the origin of the inconsistency by linking the molecules adsorbed at the interface to the curvature corrections of the surface tension. The Tolman length and rigidity constant are determined for several water-alcohol mixtures and used to show that the corrected theory is free of physical inconsistencies and provides accurate predictions of the nucleation rates. In particular, for the ethanol-water and propanol-water mixtures, the average error in the predicted nucleation rates is reduced from 11-15 orders of magnitude to below 1.5. The curvature-corrected nucleation theory opens the door to reliable predictions of nucleation rates in multicomponent systems, which are crucial for applications ranging from atmospheric science to research on volcanos.

Curvature-sensitive trans-assembly of human Atg8-family proteins in autophagy-related membrane tethering.

In macroautophagy, de novo formation of the double membrane-bound organelles, termed autophagosomes, is essential for engulfing and sequestering the cytoplasmic contents to be degraded in the lytic compartments such as vacuoles and lysosomes. Atg8-family proteins have been known to be responsible for autophagosome formation via membrane tethering and fusion events of precursor membrane structures. Nevertheless, how Atg8 proteins act directly upon autophagosome formation still remains enigmatic. Here, to further gain molecular insights into Atg8-mediated autophagic membrane dynamics, we study the two representative human Atg8 orthologs, LC3B and GATE-16, by quantitatively evaluating their intrinsic potency to physically tether lipid membranes in a chemically defined reconstitution system using purified Atg8 proteins and synthetic liposomes. Both LC3B and GATE-16 retained the capacities to trigger efficient membrane tethering at the protein-to-lipid molar ratios ranging from 1:100 to 1:5,000. These human Atg8-mediated membrane-tethering reactions require trans-assembly between the membrane-anchored forms of LC3B and GATE-16 and can be reversibly and strictly controlled by the membrane attachment and detachment cycles. Strikingly, we further uncovered distinct membrane curvature dependences of LC3B- and GATE-16-mediated membrane tethering reactions: LC3B can drive tethering more efficiently than GATE-16 for highly curved small vesicles (e.g., 50 nm in diameter), although GATE-16 turns out to be a more potent tether than LC3B for flatter large vesicles (e.g., 200 and 400 nm in diameter). Our findings establish curvature-sensitive trans-assembly of human Atg8-family proteins in reconstituted membrane tethering, which recapitulates an essential subreaction of the biogenesis of autophagosomes in vivo.

Plasma Waves in 2D Crystals with Rashba Splitting

A dispersion relation for plasma waves in two-dimensional structures with Rashba splitting is considered. The effect high-frequency electromagnetic radiation has on the energy of plasmons is studied. It is shown that break points can emerge in the functional dependence of the curvature of the line of dispersion on the Fermi energy, and on the intensity of high-frequency radiation.