Wall Excitation Research Articles

Long-range entanglement and topological excitations

Topological order comes in different forms, and its classification and detection is an important field of modern research. In this work, we show that the Disconnected Entanglement Entropy, a measure originally introduced to identify topological phases, is also able to unveil the long-range entanglement (LRE) carried by a single, fractionalized excitation. We show this by considering a quantum, delocalized domain wall excitation that can be introduced into a system by inducing geometric frustration in an antiferromagnetic spin chain. Furthermore, we show that the LRE of such systems is resilient against a quantum quench and the introduction of disorder, as it happens in traditional symmetry-protected topological phases. All these evidences establish the existence of a new phase induced by frustration with topological features despite not being of the usual type.

Three-Dimensional Vortex Gyration Dynamics Unraveled by Time-Resolved Soft X-ray Laminography with Freely Selectable Excitation Frequencies.

The imaging of magneto-dynamical processes has been, so far, mostly a two-dimensional business, also due to the constraints of the available experimental techniques. In this paper, building on the recent developments of soft X-ray magnetic laminography, we present an experimental setup where magneto-dynamical processes can be resolved in all three spatial dimensions and in time at arbitrary frequencies. We employ this setup to investigate two resonant dynamical modes of a CoFeB microstructure, namely, the fundamental vortex gyration mode and a magnetic field-induced domain wall excitation mode. For the former, we observe a large variation of the gyration dynamics across the thickness of the core, coexisting with a breathing mode of the vortex core. For the latter, we observe a uniform displacement of the domain walls across the thickness of the microstructure. The imaging of these two modes establishes the possibility to freely select the excitation frequency for soft X-ray time-resolved laminography, allowing for the investigation of resonant magneto-dynamical processes.

Relevance of two- and three-dimensional disturbance field explained with linear stability analysis of Orr-Sommerfeld equation by compound matrix method

Three-dimensional Orr-Sommerfeld equation is analyzed by compound-matrix method to explain the relevance of two- and three-dimensional wall excitations with respect to three-dimensional direct simulation results presented in Sharma and Sengupta, Effect of frequency and wavenumber on the three-dimensional routes of transition by wall excitation, Phys. Fluids, 31 (6), 064107 (2019). Physical variables are considered in a finite spanwise domain which allows us to consider spanwise wavenumber β as the higher harmonics of fundamental spanwise mode β0 defined by the spanwise domain. Linear stability analysis is performed for various cases with different spanwise wavenumber and neutral curves are generated in both spatial and temporal frameworks. Even though the neutral curves appear different, the critical Reynolds number remains same for all spanwise excitation wavenumbers. The significance of neutral curve in either spatial, or temporal or spatio-temporal frameworks is explained for both modal and non-modal component of the response field. It is shown that as spanwise wavenumber of input excitation increases, the critical Reynolds number increases, while the spatial amplification rate αi decreases. Thus, this establishes that increasing three-dimensionality of input excitation will shown enhanced stability of the flow, and helps one to understand the three-dimensional direct simulation of receptivity analysis for wall excitation reported very recently.

Vibrations of thick domain walls: How to avoid no-go theorem

The asymptotic properties of the stability potentials of kinks with power-law tails are discussed. In particular, in cosmology such kinks can describe “thick” domain walls. The discrete part of the domain wall excitation spectrum, the profile of which is described by a kink solution with one or both power-law asymptotics, cannot contain levels other than zero (translational) mode. Nevertheless, it can be shown that scenarios are quite possible when long-lived localized vibrations will be excited on the domain wall. This, in turn, can affect the processes of interaction of two or more domain walls.

Ultrahigh differential mobility and velocity of Néel domain walls in spin valves with planar-transverse polarizers and perpendicularly injected small currents

Transverse domain wall (TDW) dynamics in long and narrow spin valves with perpendicular current injection is theoretically investigated. We demonstrate that stable traveling-wave motion of TDWs with finite velocity survives for strong enough planar-transverse polarizers. For typical ferromagnetic materials (for example, Co) and achievable spin polarization ($P=0.6$), TDWs acquire a velocity of $10^3$ m/s under a current density below $10^7$ $\mathrm{A/cm^2}$. This efficiency is comparable with that of perpendicular polarizers. More importantly, in this case the wall has ultra-high "differential mobility" around the onset of stable wall excitation. Our results open new possibilities for developing magnetic nanodevices based on TDW propagation with low energy consumption. Also, analytics for parallel and perpendicular polarizers perfectly explains existing simulation findings. Finally, further boosting of TDWs by external uniform transverse magnetic fields is investigated and turns out to be efficient.

Design Parameters for a Small-Gauge Fragmatome.

PurposeManufacturers of surgical instrumentation have increasingly sought to decrease the size of ophthalmic surgical instruments. We have used finite element modeling to model the stress and strain present in a fragmatome as a function of driving frequency and fragmatome dimensions.MethodsFinite element calculations using the COMSOL Multiphysics system v3.5 were used to elucidate the influence of wall thickness, length, and excitation frequency on a titanium fragmatome tube with outer diameters of 20, 23, 25, and 27 gauge.ResultsBy coupling structural mechanics, fluid mechanics, and acoustical physics, we were able to determine the eigenfrequencies (resonant frequencies) as well as parameters in which the von Mises stress in a fragmatome tube exceeds the yield strength, leading to destruction of the instrument.ConclusionSolid fragmatomes have far fewer possible failure modes than fragmatomes with a standard wall thickness. Eigenfrequency analysis and finite element calculations can be critical in predicting potentially catastrophic designs in modern surgical instruments.Translational RelevanceInstruments developed for microsurgical applications cannot always simply be scaled down versions of conventional instruments. Such an approach can lead to potentially dangerous intraoperative failures, such as a fragmatome shattering inside the eye. Modern engineering techniques are increasingly necessary to investigate potential instrument failure mechanisms and to optimize device performance in a design in silico before in vivo testing.

Effect of frequency and wavenumber on the three-dimensional routes of transition by wall excitation

Three-dimensional (3D) routes of transition affected by the frequency of monochromatic wall excitation started impulsively are studied by performing direct numerical simulation. The computed results for the two frequencies of excitation reported here resemble the experimental setup of Klebanoff et al. [“The three-dimensional nature of boundary-layer instability,” J. Fluid Mech. 12(1), 1–34 (1962)], where a two-dimensional boundary layer is excited using 3D disturbances. Such a monochromatic wall excitation creates three-component disturbance field: a near-field followed by the Tollmien-Schlichting wave-packet and a spatiotemporal wave-front (STWF), which is responsible for eventual transition. It is noted that the case of moderate frequency of excitation shows a complete noninteracting nature of the near-field solution and the STWF. We report another route of transition computationally for a lower frequency of excitation. This case shows an interacting nature of the near-field solution and the STWF. While both frequency of excitations can cause transition for moderate spanwise wavelength (λz) disturbances, dependence of transition on λz is reported here for the first time. It is noted that doubling the spanwise wavenumber leads to the disappearance of STWF and no transition of the flow. We use the recently developed disturbance enstrophy transport equation in Sengupta et al. [“An enstrophy based linear and nonlinear receptivity theory,” Phys. Fluids 30, 054106 (2018)] for a better quantitative method to trace the evolution of disturbance field of the imposed 3D disturbances.

Is Tollmien-Schlichting wave necessary for transition of zero pressure gradient boundary layer flow?

Comprehensive understanding of the routes of instability and transition for many flows is not complete yet. For a zero pressure gradient (ZPG) boundary layer, linear spatial theory predicted Tollmien-Schlichting (TS) waves, which have been experimentally verified by vortically exciting the flow by a monochromatic source. This is the well-known frequency response of dynamical system theory. Natural transition in real flows occurs due to polychromatic excitation, and to simulate such transition, the ZPG boundary layer has been excited via an impulse response in some of our recent direct numerical simulations. Such impulse responses cause transition even when TS waves are not excited. In the present exercise, we show the theoretical basis of natural transition by spatiotemporal stability analysis, as used in the work of Sengupta et al. [“Spatiotemporal growing wave fronts in spatially stable boundary layers,” Phys. Rev. Lett. 96(22), 224504 (2006)], by invoking finite start-up of the frequency response to wall excitation. There appear to be different instability mechanisms active for the frequency and the impulse responses to localized wall excitation. Here, we show that in both the frequency and impulse responses, the spatiotemporal wave-front (STWF) is the common element. Additionally, we also consider cases, where following different start-ups, the wall excitation remains constant, which also show the presence of the STWF. The presented results for the ZPG boundary layer show that the TS wave is not necessary for transition to turbulence and help us to re-evaluate our understanding of the transition mechanism for this canonical flow.

The three-dimensional impulse response of a boundary layer to different types of wall excitation

Here we report a study of the physical mechanism behind the creation of perturbation of a boundary layer by direct numerical simulation (DNS) of an incompressible Navier-Stokes equation (NSE) that leads to eventual three-dimensional (3D) transition. By considering two different types of impulsive wall-excitations which are similar to dip-slip and strike-slip events in the seismological terminology for a zero pressure gradient (ZPG) boundary layer, we show that initial events and the evolution of the resultant wave-packet bear a close resemblance with the physical mechanism for the creation of tsunamis. This is due to the significant differences in the characteristics and dynamics of the wall-bounded and oceanic boundary layer at deep-ocean. Here we particularly seek out the impulse response of a ZPG boundary layer as demonstrated recently in the work of S. Bhaumik and T. K. Sengupta [“Impulse response and spatio-temporal wave-packets: The common feature of rogue waves, tsunami, and transition to turbulence,” Phys. Fluids 29, 124103 (2017)], by considering a specific boundary motion similar to dip-slip events for the creation of tsunamis. The precursor of flow transition, noted as the spatiotemporal wave front, has been shown to be very effectively created by the dip-slip type of boundary motion, first reported in the work of Sengupta et al. [“Spatiotemporal growing wave-fronts in spatially stable boundary layers,” Phys. Rev. Lett. 96, 224504 (2006)], from both linear and nonlinear analyses of NSE. In this study, receptivity of the boundary layer to these two types of subduction motions is contrasted. This is performed for the first time using 3D DNS of NSE. It is shown that the dip-slip event displays stronger receptivity than the strike-slip event.

Three-dimensional transition of zero-pressure-gradient boundary layer by impulsively and nonimpulsively started harmonic wall excitation

A three-dimensional (3D) transition route for zero-pressure-gradient boundary layer over a flat plate is computationally investigated, for impulsive and nonimpulsive startup of harmonic wall excitation. A monochromatic frequency of excitation is chosen to perturb the boundary layer. The exciter placed near the leading edge of the flat plate is stapled in the spanwise direction, as in the classical experiment by Klebanoff, Tidstrom, and Sargent [J. Fluid Mech. 12, 1 (1962)]. The computational domain includes the leading edge and the 3D Navier-Stokes equation is solved first for the equilibrium flow without any excitation. This is followed by computing the disturbed flow with the exciter started in either an impulsive or in a nonimpulsive manner. Detailed description of the transition process is provided for the startup cases, which shows that the transition is essentially caused by the spatiotemporal wave front for the moderate frequency of excitation. The present investigation follows the formulation and methodology given by Bhaumik and Sengupta [Phys. Rev. E 89, 043018 (2014)], which specifically reported only the impulsive startup of harmonic wall Gaussian circular patch excitation for a moderate frequency that led to the aligned pattern of $\mathrm{\ensuremath{\Lambda}}$ vortices.

Excitations of interface pinned domain walls in constrained geometries

We report a theoretical investigation of the equilibrium pattern and the spectra of head-to-head and Neel domain walls of flat Fe and Py stripes, exchange coupled with a vicinal antiferromagnetic substrate. We show that the domain wall excitation spectrum is tunable by the strength of the interface field. Furthermore, strong interface coupling favors localized wall excitations.

Impulse response and spatio-temporal wave-packets: The common feature of rogue waves, tsunami, and transition to turbulence

Here, we present the impulse response of the canonical zero pressure gradient boundary layer from the dynamical system approach. The fundamental physical mechanism of the impulse response is in creation of a spatio-temporal wave-front (STWF) by a localized, time-impulsive wall excitation of the boundary layer. The present research is undertaken to explain the unit process of diverse phenomena in geophysical fluid flows and basic hydrodynamics. Creation of a tsunami has been attributed to localized events in the ocean-bed caused by earthquakes, landslides, or volcanic eruptions, whose manifestation is in the run up to the coast by surface waves of massive amplitude but of very finite fetch. Similarly rogue waves have often been noted; a coherent account of the same is yet to appear, although some explanations have been proposed. Our studies in both two- and three-dimensional frameworks in Sengupta and Bhaumik [“Onset of turbulence from the receptivity stage of fluid flows,” Phys. Rev. Lett. 107(15), 154501 (2011)] and Bhaumik and Sengupta [“Precursor of transition to turbulence: Spatiotemporal wave front,” Phys. Rev. E 89(4), 043018 (2014)] have shown that the STWF provides the central role for causing transition to turbulence by reproducing carefully conducted transition experiments. Here, we furthermore relax the condition of time behavior and use a Dirac-delta wall excitation for the impulse response. The present approach is not based on any simplification of the governing Navier-Stokes equation (NSE), which is unlike solving a nonlinear shallow water equation and/or nonlinear Schrödinger equation. The full nonlinear Navier-Stokes equation (NSE) is solved here using high accuracy dispersion relation preserving numerical schemes and using appropriate formulation of the NSE which minimizes error. The adopted numerical methods and formulation have been extensively validated with respect to various external and internal 2D and 3D flow problems. We also present results from the Orr-Sommerfeld equation to show that the origin of the STWF is via a linear mechanism. Nonlinearity and nonparallelism play the central role in causing these phenomena of geophysics and transition to turbulence.

Receptivity to Harmonic Excitation Following Nonimpulsive Start for Boundary-Layer Flows

It has been shown in recent times that transition to turbulence occurs following two- and three-dimensional routes primarily by what is called the spatiotemporal wave front, for the canonical problem of a zero-pressure gradient boundary layer excited harmonically at the wall following an impulsive start. This paper shows that this onset process of disturbance growth continues also for a varying range of nonimpulsive wall excitation onset that is switched on smoothly. This is important because this will dispel any idea that a spatiotemporal wave front is totally due to impulsive start of wall excitation. This paper distinguishes between high- and low-frequency excitation cases to follow qualitatively different transition routes.

이차원 푸리에 필터링을 이용한 수중음향 펄스 튜브에서의 평면파 반사계수 결정

ABSTRACT: Complex acoustic signals can be formed in a water-filled acoustic pulse tube under some exciting conditions. It makes difficult to measure plane-wave reflection coefficient with the pulse tube for low frequency bands. In this study, using COMSOL Multiphysics we show that the tube wall excitation generates complex acoustic field of nonplanar mode as well as planar one. From such field incident or reflected planar mode can be decomposed respectively with a modal decomposition method, two-dimensional Fourier filtering. It makes possible to more accurately determine the plane-wave reflection coefficient of acoustic specimen with time gating.Keywords: P ulse tube, Mode decomposition, Two-dimensional Fourier filtering, Plane-wave reflection coefficient PACS numbers: 43.30.Xm, 43.20.Mv, 43.20.Ye, 43.58.Bh†Corresponding author: Suk Wang Yoon (swyoon@skku.ac.kr) Department of Physics, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon 16419, Republic of Korea(Tel: 82-31-290-7043, Fax: 82-31-290-7055)

Role of Time Integration in Computing Transitional Flows Caused by Wall Excitation

Numerical investigation of receptivity and flow transition in spatio-temporal framework have shown the central role of spatio-temporal wave-front (STWF) created by wall excitation for transition of a two-dimensional (2D) zero pressure gradient boundary layer (ZPGBL) in Sengupta and Bhaumik (Phys Rev Lett 107:154501, 2011). Although the STWF is created by linear mechanism, it is the later nonlinear stage of evolution revealed by the solution of Navier---Stokes equation (NSE), which causes formation of turbulent spots merging together to create fully developed turbulent flow. Thus, computing STWF for ZPGBL from NSE is of prime importance, which has been reported by the present authors following earlier theoretical investigation. Similar computational efforts using NSE by other researchers do not report finding the STWF. In the present investigation we identify the main reason for other researchers to miss STWF, as due to taking a very short computational domain. Secondly, we show that even one takes a long enough domain and detect STWF, use of traditional low accuracy method will not produce the correct dynamics as reported by Sengupta and Bhaumik (2011). The role of time integration plays a very strong role in the dynamics of transitional flows. We have shown here that implicit methods are more error prone, as compared to explicit time integration methods during flow transition. For the present problem, it is noted that the classical Crank---Nicolson method is unstable for 2D NSE. Same error-prone nature will also be noted for hybrid implicit---explicit time integration methods (known as the IMEX methods). One of the main feature of present analysis is to highlight the accuracy of computations by compact schemes used by the present investigators over a significantly longer domain and over unlimited time, as opposed to those reported earlier in the literature for the wall excitation problem. A consequence of taking long streamwise domain enables one to detect special properties of STWF and its nonlinear growth. The main focus of the present research is to highlight the importance of STWF, which is a new class of spatio-temporal solution obtained from the linear receptivity by solving Orr---Sommerfeld equation and nonlinear analysis of NSE.

Precursor of transition to turbulence: spatiotemporal wave front.

To understand transition to turbulence via 3D disturbance growth, we report here results obtained from the solution of Navier-Stokes equation (NSE) to reproduce experimental results obtained by minimizing background disturbances and imposing deterministic excitation inside the shear layer. A similar approach was adopted in Sengupta and Bhaumik [Phys. Rev. Lett. 107, 154501 (2011)], where a route of transition from receptivity to fully developed turbulent stage was explained for 2D flow in terms of the spatio-temporal wave-front (STWF). The STWF was identified as the unit process of 2D turbulence creation for low amplitude wall excitation. Theoretical prediction of STWF for boundary layer was established earlier in Sengupta, Rao, and Venkatasubbaiah [Phys. Rev. Lett. 96, 224504 (2006)] from the Orr-Sommerfeld equation as due to spatiotemporal instability. Here, the same unit process of the STWF during transition is shown to be present for 3D disturbance field from the solution of governing NSE.

Quantum disorder and local modes of the fully-frustrated transverse field Ising model on a diamond chain

We investigate the transverse field Ising model on a diamond chain using series expansions about the high-field limit and exact diagonalizations. For the unfrustrated case we accurately determine the quantum critical point and its expected 2d Ising universality separating the polarized and the Z2 symmetry broken phase. In contrast, we find strong evidences for a disorder by disorder scenario for the fully-frustrated transverse field Ising model, i.e. except for the pure Ising model, having an extensive number of ground states, the system is always in a quantum disordered polarized phase. The low-energy excitations in this polarized phase are understood in terms of exact local modes of the model. Furthermore, an effective low-energy description for an infinitesimal transverse field allows to pinpoint the quantum disordered nature of the ground state via mapping to an effective transverse field Ising chain and to determine the induced gap to the elementary effective domain wall excitation very accurately.

Direct numerical simulation of transitional mixed convection flows: Viscous and inviscid instability mechanisms

Receptivity studies using direct numerical simulation require computations of equilibrium flow and its response to deterministic excitation. Equivalent flow problem, without heat interaction for zero-pressure gradient boundary layer, has been studied with respect to wall-excitation by a finite difference high accuracy method based on the solution of Navier-Stokes equation in Sengupta and Bhaumik [Phys. Rev. Lett.107, 154501 (2011)] and Sengupta et al. [Phys. Rev. E85, 026308 (2012)]. One of the key features of this study has been that the same methodology is used for computing the equilibrium flow and the disturbance field. Computation of equilibrium flow was performed by solving Navier-Stokes equation to include the leading edge of the plate, so that the effects of leading edge singularity and the growth of the boundary layer is included in the nonlinear framework. When the same methodology is attempted for mixed convection flows past horizontal plate (with Boussinesq approximation to model heat transfer effects) some of the equilibrium flow features could not be explained with linear viscous instability theory results. For horizontal hot flat plate with adiabatic wall conditions, the equilibrium flow could be computed and its receptivity could be correlated with linear spatial theory for lower buoyancy parameter. Here, we focus on receptivity of mixed convection flows to wall excitation for the following cases which do not allow computing the equilibrium flows from the solution of Navier-Stokes equation: (i) Aadiabatic horizontal flat plate cooled significantly at the leading edge only and (ii) strongly heated isothermal wedge flow for a wedge angle of 60°. The cold plate case is particularly interesting as the linear spatial theory indicates enhanced stabilization for higher magnitude of the buoyancy parameter. Results presented for the cold plate case indicates disturbance growth outside the shear layer. This prompted us to re-investigate various mechanisms of instability present for mixed convection flows. There is no definitive study for inviscid mechanism in this respect and the present effort not only fills this void, but also explains the relative roles of viscous and inviscid mechanisms for strong heat transfer effects, within the Boussinesq approximation.

Dynamic Oscillations of Coupled Domain Walls

In domain wall (DW) excitation experiments, nonlinearity (NL) intrinsic to the DW dynamics is often hard to distinguish from perturbation due to the confining potential or DW distortion. Here we numerically investigate the dynamic oscillations of magnetostatically coupled DWs: a system well understood in the quasistatic limit. NL is observed, even for a harmonic potential, due to the intrinsic DW motion. This behavior is principally dependent on terms normally associated with the DW canonical momentum and is in contrast with a NL restoring potential. This NL is not observable in quasistatic measurements, relatively insensitive to the confining potential, and may be tuned by the nanowire parameters. The shown NLs are present in any DW restoring potential and must be accounted for when probing DW potential landscapes.

Metastable magnetic domain wall dynamics

The dynamics of metastable magnetic domain walls in straight ferromagnetic nanowires under spin waves, external magnetic fields and current-induced spin-transfer torque are studied by means of micromagnetic simulations. It is found that in contrast to a stable wall, it is possible to displace a metastable domain wall in the absence of external excitation. In addition, independent of the domain wall excitation method, the velocity of a metastable wall is much smaller than that of a stable wall and its displacement direction could be different from that of the stable wall depending on the structure of metastable walls. Under current-induced spin-transfer torque excitation, the direction of domain wall displacement is directly related to the intensity of non-adiabatic spin-transfer torque. In a rough nanowire, it is found that the displacement of a metastable wall could happen much below the critical excitation of a stable wall. Furthermore, we show that it is possible to have either a forward or a backward displacement of a metastable domain wall by changing the pulse width of the excitation.