Weak Mode Research Articles

Laser ablation ignition modes in a cavity-based supersonic combustor

A numerical and experimental study was conducted to investigate the Laser Ablation (LA) ignition mode in an ethylene-fueled supersonic combustor with a cavity flameholder. The experiments were operated under a Mach number 2.92 supersonic inflow, with stagnation pressure of 2.4 MPa and stagnation temperature of 1600 K. Reynolds-averaged Navier-Stokes simulations were conducted to characterize the mixing process and flow field structure. This study identified four distinct LA ignition modes. Under the specified condition, laser ablation in zero and negative defocusing states manifested two distinct ignition modes termed Laser Ablation Direct Ignition (LADI) mode and Laser Ablation Re-Ignition (LARI) mode, correspondingly. LA ignition in a local small cavity, created by depressing the flow field regulator, could facilitate the ignition mode transforming from LARI mode to Laser Ablation Transition Ignition (LATI) mode. On the other hand, the elevation of the flow field regulator effectively inhibited the forward propagation of the initial flame kernel and reduced the dissipation of LA plasma, further enhancing the LADI mode. Based on these characteristics, the LADI mode was subdivided into strong (LADI-S) and weak (LADI-W) modes. Facilitating the transition of ignition modes through alterations in the local flow field could contribute to attaining a more effective and stable LA ignition.

Detection of Earth’s free oscillation and analysis of the non-synchronous oscillation phenomenon of normal modes

Earth’s free oscillation can provide essential constraints for refining Earth models, inverting seismic source mechanisms, and studying the deep internal structure of the Earth. Large earthquakes can simultaneously excite numerous normal modes. Due to the Earth’s ellipticity, rotation, and internal heterogeneities, these normal modes undergo splitting, with the frequencies of singlets of normal modes becoming very close (only a few µHz apart). This imposes greater demands on the detection of normal modes. This paper introduces a novel method for normal mode detection based on the normal time–frequency transform (NTFT). Compared to classical FT spectrum methods and recent optimal sequence estimation (OSE), the proposed method not only detects more weak normal modes but also reveals the spatial distribution of the phase of each normal mode. Taking the detection of 0S2 as an example, the phase measurements of each singlet are spatially inconsistent. This phenomenon can provide prior information for other methods, such as product spectrum analysis (PSA), spherical harmonic stacking (SHS), multistation experiments (MSE), and OSE. Additionally, understanding the phase distribution patterns contributes to further study of geological structures, offering crucial foundational data and observational support.

Mesoscopic modeling of interaction dynamics for two bubbles in the near-wall region

A nonorthogonal hybrid thermal lattice Boltzmann cavitation model is proposed in this study. The flow and density field are described by the pseudopotential model, while the temperature is realized by solving the macroscopic temperature function. The model is verified by simulating the Laplace law and a bubble evolves in the unbounded region. Furthermore, the interaction dynamics between two bubbles near the wall are investigated. The bubble collapse intensity is dominated by the initial bubble–bubble distance and bubble–wall distance. A pair of inclined reentrant jets are reported for the strong interaction modes, and splashing resulting from the jet collisions may lead to the bubble center shifting away from the wall or the axis of symmetry. For the weak interaction mode with dimensionless bubble-wall distance γ between 1 and 3.5, the maximum collapse pressure increases linearly. The maximum collapse pressure Pc_max decreases with increasing bubble spacing, and Pc_max for distance between two bubbles with d2=40lu increases by 9 % to 16.2 % compared to that of d2=30lu. The variation of the liquid film thickness h between adjacent cavitation bubbles is primarily governed by the expansion velocity of the bubble wall ḣ, and similarly, the thickness of the liquid film between the bubble wall follows the same principle with h∼ḣ−2. The bubble radius in the growth stage aligns closely with the theoretical analysis for the weak interaction mode, while discrepancies appear between the simulation and prediction due to the bubble losing its roundness in the collapse stage.

Effects of wind turbine dimensions on the collision risk of raptors: A simulation approach based on flight height distributions

Wind energy development is a key component of climate change mitigation. However, birds collide with wind turbines, and this additional mortality may negatively impact populations. Collision risk could be reduced by informed selection of turbine dimensions, but the effects of turbine dimensions are still unknown for many species.As analyses of mortality data have several limitations, we applied a simulation approach based on flight height distributions of six European raptor species. To obtain accurate flight height data, we used high-frequency GPS tracking (GPS tags deployed on 275 individuals). The effects of ground clearance and rotor diameter of wind turbines on collision risk were studied using the Band collision risk model.Five species had a unimodal flight height distribution, with a mode below 25 m above ground level, while Short-toed Eagle showed a more uniform distribution with a weak mode between 120 and 260 m. The proportion of positions within 32–200 m ranged from 11 % in Marsh Harrier to 54 % in Red Kite.With increasing ground clearance (from 20 to 100 m), collision risk decreased in the species with low mode (−56 to −66 %), but increased in Short-toed Eagle (+38 %). With increasing rotor diameter (from 50 to 160 m) at fixed ground clearance, the collision risk per turbine increased in all species (+151 to +558 %), while the collision risk per MW decreased in the species with low mode (−50 % to −57 %).These results underpin that wind turbine dimensions can have substantial effects on the collision risk of raptors. As the effects varied between species, wind energy planning should consider the composition of the local bird community to optimise wind turbine dimensions. For species with a low mode of flight height, the collision risk for a given total power capacity could be reduced by increasing ground clearance, and using fewer turbines with larger diameter.

Combustion modes of kerosene spray in a scramjet combustor with different injection schemes

Combustion modes of kerosene spray in a scramjet combustor condition with different injection schemes are experimentally investigated at Mach 2.52. The study is based on two single injectors with nozzle diameters of 0.79 and 1.14 mm and two dual injectors with nozzle diameters of 0.56 and 0.72 mm, respectively. The results show that the weak combustion mode has little effect on the flow field, while the intensive combustion mode has the opposite effect. The dual injector can promote evaporation and mixing of the kerosene spray. Compared with the dual injector, intensive combustion cannot occur when a single injector is used, and the flame stability range is also narrower. As the nozzle diameter of the injector increases, the distribution and oscillation of kerosene spray change significantly, transition from the weak to intensive combustion mode occurs at a higher equivalence ratio, and the flame stability range increases. However, change in the nozzle diameter does not affect the overall process of combustion mode transition. For the single injector, intensive combustion still cannot occur when the nozzle diameter changes. In addition, change in the nozzle diameter has little effect on combustion heat release when the combustion mode remains unchanged.

Study of the isoscalar scalar bcu¯d¯ tetraquark Tbc with lattice QCD

We present a lattice QCD study of the elastic S-wave DB¯ scattering in search of tetraquark candidates with explicitly exotic flavor content bcu¯d¯ in the isospin I=0 and JP=0+ channel. We use four lattice QCD ensembles with dynamical u/d, s, and c quark fields generated by the MILC collaboration. A nonrelativistic QCD Hamiltonian, including improvement coefficients up to O(αsv4), is utilized for the bottom quarks. For the rest of the valence quarks we employ a relativistic overlap action. Five different valence quark masses are utilized to study the light quark mass dependence of the DB¯ scattering amplitude. The finite volume energy spectra are extracted following a variational approach. The elastic DB¯ scattering amplitudes are extracted employing Lüscher’s prescription. The light quark mass dependence of the continuum extrapolated amplitudes suggests an attractive interaction between the B¯ and D mesons. At the physical pseudoscalar meson mass (Mps=Mπ) the DB¯ scattering amplitude has a subthreshold pole corresponding to a binding energy of −39(−6+4)(−18+8) MeV with respect to the DB¯ threshold. The critical Mps at which the DB¯ scattering length diverges and the system becomes unbound corresponds to Mps*=2.94(15)(5) GeV. This result can hold significant experimental relevance in the search for a bound scalar Tbc tetraquark, which could well be the next “doubly heavy” bound tetraquark to be discovered with only weak decay modes. Published by the American Physical Society 2024

Label-free detection of inclusion body formation in E. coli with application of terahertz

Extensive production of recombinant protein is essential for use in various fields. Bacterial cells, especially the Escherichia coli (E. coli) expression system, are widely used for the production of recombinant proteins due to their advantages in time and cost. However, the formation of inclusion bodies (IBs) caused by the production of recombinant protein is a significant issue. Therefore, a precise tool for the detection of IBs is in high demand. In this study, we demonstrated a label-free and rapid sensing platform for the detection of IBs formation in E. coli using terahertz-time domain spectroscopy (THz-TDS) system and terahertz metamaterials. The detection was based on the local polarity difference between E. coli samples with induced (positive) and non-induced (negative) protein overexpression. The formation of IBs in positive samples resulted in a decrease in local polarity compared to negative samples. This local polarity difference, strongly related to intermolecular interactions, influenced THz absorption as the THz regime involves weak intermolecular vibrational modes. Experimental results showed that the THz transmittance (ΔT) and resonance frequency shift (Δf) were significantly different between positive and negative samples, confirming the effectiveness of our method. Specifically, positive samples exhibited a ΔT value of 26.57% and a Δf value of 0.12 THz, while negative samples showed a ΔT value of 31.83% and a Δf value of 0.14 THz. These results highlight the capability of our platform to detect IBs rapidly and accurately.

Bayesian-guided operational modal identification of a highway bridge considering non-uniform sampling

During the structural health monitoring of bridges, it has been observed that the vibration data collected can sometimes be randomly lost or sampled non-uniformly. This leads to a low signal-to-noise ratio in the spectral functions of the measured data, making it difficult to identify weak modes. To address this issue, a framework for operational modal identification is proposed in this study. It utilizes the fast Bayesian fast Fourier transform (FFT) method to estimate the modal parameters of highway bridges considering the non-uniform monitoring data. The initial frequency parameters for the fast Bayesian FFT approach are automatically determined using the proposed autoregressive (AR) power spectral density (PSD)-guided peak picking method. This overcomes the challenge of capturing initial frequencies related to weakly contributed modes. Additionally, the bandwidth parameter for each mode is determined using the modal assurance criterion (MAC) of the first left singular vectors of PSD matrices. Furthermore, when analyzing non-uniform vibration data, it is recommended to use the non-uniform FFT (NUFFT) for calculating PSD functions in order to improve identification accuracy. The proposed method is validated using acceleration data from both a numerical model and a real-world bridge. The results demonstrate that the identification uncertainty of modal parameters increases with higher non-uniform levels.

High-cadence monitoring of the emission properties of magnetar XTE J1810−197 with the Stockert radio telescope

Context. Since the detection of a burst resembling a fast radio burst (FRB) from the Galactic magnetar SGR 1935+2154, magnetars have joined the set of favourable candidates for FRB progenitors. However, the emission mechanism of magnetars remains poorly understood. Aims. Observations of magnetars with a high cadence over extended timescales have allowed for their emission properties to be determined, in particular, their temporal variations. In this work, we present the results of the long-term monitoring campaign of the magnetar XTE J1810−197 since its second observed active phase from December 2018 until November 2021, with the Stockert 25 m radio telescope. Methods. We present a single pulse search method, improving on commonly used neural network classifiers thanks to the filtering of radio frequency interference based on its spectral variance and the magnetar’s rotation. Results. With this approach, we were able to lower the signal to noise ratio (S/N) detection threshold from 8 to 5. This allowed us to find over 115 000 spiky single pulses – compared to 56 000 from the neutral network approach. Here, we present the temporal variation of the overall profile and single pulses. Two distinct phases of different single pulse activity can be identified: phase 1 from December 2018 to mid-2019, with a few single pulses per hour, and phase 2 from September 2020 with hundreds of single pulses per hour (with a comparable average flux density). We find that the single pulse properties and folded profile in phase 2 exhibit a change around mid-March 2021. Before this date, the folded profile consists of a single peak and single pulses, with fluences of up to 1000 Jyms and a single-peaked width distribution at around 10 ms. After mid-March 2021, the profile consists of a two peaks and the single pulse population shows a bimodal width distribution with a second peak at 1 ms and fluences of up to 500 Jyms. We also present asymmetries in the phase-resolved single pulse width distributions beginning to appear in 2020, where the pulses arriving earlier in the rotational phase appear wider than those appearing later. This asymmetry persists despite the temporal evolution of the other single pulse and emission properties. Conclusions. We argue that a drift in the emission region in the magnetosphere may explain this observed behaviour. Additionally, we find that the fluence of the detected single pulses depends on the rotational phase and the highest fluence is found in the centre of the peaks in the profile. While the majority of the emission can be linked to the detected single pulses, we cannot exclude another weak mode of emission. In contrast to the pulses from SGR 1935+2154, we have not found any spectral feature or bursts with energies in the order of magnitude of an FRB during our observational campaign. Therefore, the question of whether this magnetar is capable of emitting such highly energetic bursts remains open.

Real-time safety risk assessment of floating offshore platforms based on on-site monitoring

Real-time safety risk assessment of in-service marine engineering structures is one of the key components for the intelligent development of marine resources. Floating platforms typically have weak modes and time-varying characteristics, and hence, traditional structural damage identification and safety assessment methods cannot be directly applied to floating platforms. The objective of this study was to achieve the real-time safety risk assessment of in-service floating platforms. First, a structural damage identification method for floating platforms was proposed based on virtual loads, and the physical parameters of the platforms were obtained through inversion of measurable data. The identification result was verified based on the lengths and stiffnesses of polyester cables, which affected the dynamic response of the floating platform. The results showed that the proposed method effectively detected the parameter changes of the platform during long-term service. Then, the neural network was used to construct a load–stress surrogate model at key positions of the floating offshore platform. This model could calculate the stresses at key positions in real time, thereby evaluating the safety risks of the platform. Lastly, a real-time safety risk assessment method for floating offshore platforms was proposed, which provides a technical solution for ensuring the safety of offshore platforms.

How does the uncut chip thickness affect the deformation states within the primary shear zone during metal cutting?

The deformation states within the primary shear zone (PSZ) significantly affect material removal during machining. Uncut chip thickness (UCT) is an important factor that influences the material deformation states. However, the specific mechanism by which UCT influences the deformation states within PSZ remains unknown. This study aims to investigate the relationship between the deformation states in PSZ and UCTs via in-situ measurement and microscopic characterization techniques. Using the digital image correlation (DIC) technique, strain and strain rate distributions were derived to reveal the discrepant deformation in PSZ with increasing UCT. Furthermore, velocity vector fields and Electron Back-Scattered Diffraction (EBSD) characterizations were employed to examine the heterogeneity of deformation modes. To determine the specific deformation information, a deformation extraction framework based on the deformation gradient tensor theory was developed. Thus, strong and weak shear modes within PSZ were revealed based on the full-field deformation information of compression and extension. As the UCT increased, the transition of deformation states from a strong shear state to a hybrid shear state was determined. This work presents a new understanding of the deformation mechanism within PSZ in a ductile material of pure iron. A critical UCT was proposed to guide the cutting process to avoid inefficient weak shear mode.

Seismic performance loss evaluation of reinforced concrete frame structure based on updatable damage model

AbstractAs structural seismic damage develops, the internal force transfer and damage weight relationship of component are constantly changing, and the fixed weighted coefficient is adopted by the traditional weighted method, which cannot reflect the changes in the structural damage state. The structure is a network formed by connecting a large number of components, and the network state undergoes complex changes with the development of component damage. In this paper, a novel method for component damage transfer to structural seismic performance loss is proposed using network shortest paths. First, a directed weighted complex network based on force transfer direction and component stiffness is constructed for reinforced concrete (RC) frame structures. Then, the component damage is calculated by the degradation of its stiffness and is used to update the weight distribution of the damage network. Finally, the structural performance loss is evaluated by the degradation of damage network efficiency. Results show that the proposed method with an updated component weight relationship is able to reflect the true loss of structural performance according to the finite element dynamic elastic‐plastic analysis of RC frame structures. For the structural performance loss degree (none, slight, moderate, severe, complete), the proposed method and the weighted method both exhibit high accuracy (number correctly classified/total number of samples) when structural performance loss is none, severe, or complete loss. The accuracy of the proposed method is significantly higher than that of the weighted method when structural performance loss is slight and moderate loss, with 58.1% and 84.2% improvement, respectively. For structural typical damage modes (global, local, and weak layer damage mode), the proposed method and the weighted method both exhibit high accuracy when structures exhibit global damage mode. The accuracy of the proposed method is significantly higher than that of the weighted method when structures exhibit local and weak layer damage mode. The accuracy of the proposed method is stable at 95.2%, while the accuracy of the weighted method is 76.2% and 70.2%, respectively. Overall, the weighted method exhibits high accuracy when structural performance loss is less than slight loss or greater than moderate loss, while the proposed method exhibits high accuracy throughout the entire process of structural performance loss, especially in moderate loss.

A framework for computing directivities for ultrasonic sources in generally anisotropic, multi-layered media

The knowledge of the directivity of ultrasonic sources is an important element in the design of non-destructive evaluation inspection. The commonly used directivity model of piezoelectric devices is the superposition of out-of-plane force monopoles on the stress-free surface of an isotropic elastic half-space. However, this does not cover a growing range of ultrasonic generation scenarios, as new ultrasonic technologies such as laser ultrasound (LU) emerges, and the need for inspection of materials such as carbon fibre reinforced polymers (CFRPs) rises. A directivity calculation framework based on the reciprocity theorem is developed in the current paper, which accommodates various combinations of source types, material properties, and boundary conditions, for example, a localised heating under a surface layer over an anisotropic half-space. The calculation is applicable to materials with weak anisotropy or wave modes that do not have cuspoidal wavefronts, and was validated with finite element models on key representative cases. The analytical solution for LU excitation in a CFRP sample also shows a good fit to the experimentally measured directivity of the quasi-longitudinal wave mode.

The relational states of the given object: intensionality and extensionality. Some examples from physics, mathematics and everyday life

The author examines the reality of an object in a situation. Such a given is due to the corresponding actual (intentional) property that forms the situation with the studied object in the act of attention. In a situation, an object has its own way of being – a mode. Modes are conditionally divided into strong and weak. In epistemological terms, the reality of an object in a situation has two states relative to each other, depending on the position of the cognizing subject in relation to this object. In accordance with this, the object is known either intensionally or extensionally. A phenomenological approach is used. The difference between internal and external observers in the constituted situation is shown. Such a distinction does not occur at all, but depends on the actual property in the situation. The act of cognition introduces asymmetry into the reality of its relational states: one of them will be relevant (with a strong mode), the other – only possible (with a weak mode) in the same situation. This asymmetry, in particular, manifests itself in wave-particle dualism and is expressed through the principles of complementarity and uncertainty. In particular, it is shown that the complementarity principle indicates the duality of the given object, expressed through its relational states, and the uncertainty principle indicates the difference of modes (strong and weak) of these states in the same situation. In support of what has been said, some other examples from physics, as well as from mathematics and everyday life are given.

Ignition Delay and Reaction Time Measurements of Hydrogen–Air Mixtures at High Temperatures

Induction and reaction times of hydrogen–air mixtures (ϕ = 0.5–2) have been measured behind reflected shock waves at temperatures of 1000–1600 K, pressures of 0.1, 0.3, 0.6 MPa in the domain of the extended second explosion limit. The measurements were performed in the shock tube with a completely transparent test section of 0.5 m long, which provides pressure, ion current, OH and high-speed chemiluminescence observations. The experimental induction time plots demonstrate a clear increasing of the global activation energy from high- to low temperature post-shock conditions. This trend is strongly pronounced at higher post-shock pressures. For a high-temperature range of T > 1200 K, induction time measurements show an activation energy for the global reaction rate of hydrogen oxidation of 64–83 kJ/mole. Detected reaction times exhibit a big scatter and a weak temperature dependence. The minimum reaction time value was nearly 2 µs. Obtained induction time data were compared with calculations carried out in accordance with the known kinetic mechanisms. For current and former shock-tube experiments within a pressure range of 0.1–2 MPa, critical temperatures required for strong (1000–1100 K), transient and weak auto-ignition modes behind reflected shock waves were identified by means of the pressure and ion-probe measurements in stoichiometric hydrogen-air mixture. The transfer from the strong volumetric self-ignition near the reflecting wall to the hot spot ignition (transient) was established and visualized below <1200 K with a post-shock temperature decreasing.

Hourglasslike spin excitation in a doped Mott insulator

We examine the dynamical magnetic response in a two-component resonating-valence-bond (RVB) description of the doped Mott insulator. The half-filled antiferromagnetic phase described by the Schwinger-boson mean-field theory will evolve into a bosonic-RVB state in the superconducting phase upon doping, where the doped holes introduce another fermionic itinerant spinon which forms a BCS-like RVB order. The spin excitations are thus composed of a resonance-like mode from the former and a weak dispersive mode from the itinerant component at the mean-field level. These two-component spinons are shown to give rise to an hourglasslike spin excitation at the random-phase approximation level via an antiferromagnetic coupling between the two modes, which provides an unconventional explanation of the experimental observations in the cuprate. In particular, we also discuss an instability towards an incommensurate magnetic order in this theoretical framework. Published by the American Physical Society 2024

Ultrasensitive measurement of tactile force based on a PDMS-embedded microfiber Mach-Zehnder interferometer.

This study investigates the utilization of an in-fiber interferometer embedded in polydimethylsiloxane (PDMS) to develop a highly sensitive tactile sensor. The tapered mode-field mismatch structure is more conducive to stimulating strong high order modes to promote the sensitivity of the sensor. Experimental investigations are conducted to study the sensing performance of the sensor, resulting in a sensitivity of 23.636 nm/N and a detection limit of 0.746 mN. The experiments demonstrate that employing fast Fourier transform (FFT) and inverse FFT (IFFT) methods to filter weak high order modes significantly improves the repeatability of the sensor, resulting in a repeatability error of less than 1%.

Boosting effect of strong western pole of the Indian Ocean Dipole on the decay of El Niño events

The Indian Ocean Basin (IOB) mode is believed to favor the decay of El Niño via modulating the zonal wind anomalies in the western equatorial Pacific, while the contribution of the Indian Ocean Dipole (IOD) mode to the following year’s El Niño remains highly controversial. In this study, we use the evolution of fast and slow decaying El Niño events during 1950–2020 to demonstrate that the positive IOD with a strong western pole prompts the termination of El Niño, whereas a weak western pole has no significant effect. The strong western pole of a positive IOD leads to a strong IOB pattern peaking in the late winter (earlier than normal), enhancing local convection and causing anomalous rising motions over the tropical Indian Ocean and sinking motions over the western tropical Pacific. The surface equatorial easterly wind anomalies on the western flank of the sinking motions stimulate oceanic equatorial upwelling Kelvin waves, which shoal the thermocline in the eastern equatorial Pacific and rapidly terminate the equatorial warming during El Niño. However, a weak western pole of the IOD induces a weak IOB mode that peaks in the late spring, and the above-mentioned cross-basin physical processes do not occur.

Giant optical absorption of a PtSe2-on-silicon waveguide in mid-infrared wavelengths.

Low-dimensional platinum diselenide (PtSe2) is a promising candidate for high-performance optoelectronics in the short-wavelength mid-infrared band due to its high carrier mobility, excellent stability, and tunable bandgap. However, light usually interacts moderately with low-dimensional PtSe2, limiting the optoelectronic responses of PtSe2-based devices. Here we demonstrated a giant optical absorption of a PtSe2-on-silicon waveguide by integrating a ten-layer PtSe2 film on an ultra-thin silicon waveguide. The weak mode confinement in the ultra-thin waveguide dramatically increases the waveguide mode overlap with the PtSe2 film. Our experimental results show that the absorption coefficient of the PtSe2-on-silicon waveguide is in the range of 0.0648 dB μm-1 to 0.0704 dB μm-1 in a spectral region of 2200 nm to 2300 nm wavelengths. Furthermore, we also studied the optical absorption in an ultra-thin silicon microring resonator. Our study provides a promising approach to developing PtSe2-on-silicon hybrid optoelectronic integrated circuits.

CO2 ultrathin film growth on a monolayer of CO2 adsorbed on the NaCl(100) surface: sticking coefficient and IR-optical signatures in the ν3 region.

CO2 ultrathin molecular films were grown onto a preadsorbed monolayer NaCl(100)/p(2 × 1)-CO2 at 40 K. Polarization infrared spectroscopy (PIRS) reveals that so-prepared films have better quality than directly grown films. A sticking probability of 0.74 ± 0.1 was deduced from the integrated IR absorption. The presence of the monolayer doublet in the film spectra suggests a Stranski-Krastanov film growth with locally varying film thicknesses on the surface. In the region of the ν3(12C16O2) band, fine structure was observed between the well-known transverse-optical (TO) and longitudinal optical (LO) bands. Two independent computational models were applied to analyze the nature of the observed fine structure. Both pair potential calculations in combination with a vibrational exciton model as well as plane-wave density functional theory (DFT) in combination with phonon calculations of IR intensities at the Γ-point reveal that a weak mode visible in s-polarization and p-polarization originates from a vibrational film excitation located near the substrate interface. A series of p-polarized weak bands appearing and partly disappearing upon film-growth is assigned to film stacks of unique local thickness.