Single Hump Research Articles

Influence of laser energy on weld quality during blue laser spot-welding of electrical steel laminations

Blue laser spot welding electrical steel can improve material absorption, stabilise the molten pool and reduce heat input. The influence of process parameters on the welding quality of blue laser spot welding electrical steel is investigated. With the increase of laser power, a ‘single hump’ molten pool was generated. At the power of 1000 W, the melting mode changed, and the plume appeared above the molten pool. The maximum penetration depth was 0.75 mm (laser power 1000 W, pulse time 1 s). Higher laser energy led to a continuous increase in the proportion of columnar grains, exceeding 45% at 1000 J. Finally, higher laser power and pulse time enhanced the connection and bonded area of laminations.

Numerical Investigation on internal flow characteristics of a mixed-flow pump with Tandem malposed blades

Abstract Mixed-flow pump plays an important role in national major projects and national economic construction. In this paper, a mixed-flow pump is taken as the research object, and the internal flow characteristics and the distribution of turbulent kinetic energy in the pump under different malposed angles of blade are studied by using numerical simulation and blade modification method. The results show that the pump efficiency and head are higher when the tandem blade angles (α) are 15° and 45°, and the pump head is the largest at the α =15°, increasing by 4.37%. Meanwhile, the high-pressure area inside the impeller was large, which had a higher pressurization performance. Under the rated flow condition, the velocity curve of α =15° changes most gently, which is close to the prototype velocity curve, and the single hump zone is not obvious. The tandem malposed blades can restrain the velocity fluctuation and improve the flow field in the impeller. At α =45°, the turbulent kinetic energy dissipation and the velocity fluctuation were the smallest; the flow field was the most stable. The research results have reference significance for the optimal design and selection of mixed flow pump.

HIWIND Balloon and Antarctica Jang Bogo FPI High Latitude Conjugate Thermospheric Wind Observations and Simulations

AbstractUsing the High attitude Interferometer WIND observation balloon and Antarctic Jang Bogo station high latitude conjugate observations of the thermospheric winds we investigate the seasonal and hemispheric differences between the northern and southern hemispheres in June 2018. We found that the summer (northern) hemisphere dayside meridional winds have a double‐hump feature, whereas in the winter (southern) hemisphere the dayside meridional winds have a single hump feature. We attribute that to stronger summer, perhaps, northern hemisphere cusp heating. We also compared the observation with NCAR Thermosphere Ionosphere Electrodynamics General Circulation Model (TIEGCM) model. The TIEGCM reproduced the double‐hump feature because of added cusp heating. The summer hemisphere has stronger anti‐sunward winds. This is the first time we have very high latitude conjugate thermospheric wind observations.

Photovoltaic spatial gap solitons in biased photorefractive optical lattices

We investigate the existence and characteristics of spatially confined optical gap solitons within an optical lattice embedded in a biased bulk photovoltaic photorefractive crystal. The Floquet-Bloch theory is used to analyze the uniform lattice and derive the optical lattice band structure. In the photonic band gaps, which are typically opaque to light transmission, the photorefractive nonlinearity permits the formation of solitons. The paraxial Helmholtz equation is set up and solved thereby discovering single hump and double hump soliton states in both band gaps. Interestingly, we have not found any multi peak solitons to exist in this particular case. We examine the characteristics of these gap solitons, finding that the soliton width (an indicator of nonlinearity) and intensity depend on their location within the band gap. We find that the magnitude of the external electric field profoundly affects the gap soliton characteristics. Additionally, the Vakhitov-Kolokolov (VK) criterion, perturbation analysis and numerical techniques are used to analyze the stability of the various types of the spatial gap solitons in both the band gaps.

Realization of homogeneous dielectric barrier discharge in atmospheric pressure argon and the effect of beads on its characteristics

This paper describes the realization of a homogeneous dielectric barrier discharge (DBD) in argon at atmospheric pressure. The effect of the morphology of the dielectric surface (especially the dielectric surface covered by hollow ceramic beads (99% Al2O3) with different diameters) on discharge is investigated. With different dielectrics, the argon DBD presents two discharge modes: a filamentary mode and a homogeneous mode. Fast photography shows that the filamentary mode operates in a streamer discharge, and the homogeneous mode operates in a Townsend discharge regime. It is found that a homogeneous discharge can be generated within a certain voltage range. The voltage amplitude range decreases, and the breakdown voltage increases with the increase in the mean diameter of the ceramic beads. Waveforms of the total current and optical emission signal present stochastic pulses per half voltage cycle for the filamentary mode, whereas there is one single hump per half voltage cycle for the homogeneous mode. In the homogeneous mode, the intensity of the optical emission decreases with the mean diameter of the ceramic beads. The optical emission spectrum is mainly composed of atomic lines of argon and the second positive system of molecular nitrogen. It reveals that the electron density decreases with the increasing mean diameter of the ceramic beads. The vibrational temperature increases with the increasing mean diameter of the ceramic beads. It is believed that a large number of microdischarges are formed, and smaller ceramic beads have a larger activation surface area and more point discharge. Electrons liberated in the shallow well and electrons generated from microdischarges can increase the secondary electron emission coefficient of the cathode and provide initial electrons for discharge continuously. Therefore, the breakdown electric field is reduced, which contributes to easier generation of homogeneous discharge. This is confirmed by the simulation results.

Numerical Study of the Effect of Angle and Location of the First and Second Steps on the Performance of Planing Hull and Their Optimization Using the Taguchi Statistical Method

Providing steps at the bottom of a high‐speed craft could decrease the resistance and enhance the longitudinal stability by dividing a single pressure hump into several ones and extending the hydrodynamic pressure towards aft of the vessel. In the present paper, the effects of the fore and aft steps’ locations and angles on double‐stepped hulls are investigated systematically via a numerical approach. The parent model investigated in this study is a model of a high‐speed recreational craft called Cougar, with a 1 : 5 scale. The three‐dimensional analysis of the model is conducted via the finite volume method, and the free surface is tracked using the volume of the fluid technique. The computational domain is discretized by the overset technique, and the calculations are validated via experimental data. Overall, 27 numerical tests designed by the Taguchi experiment design method are simulated, and the resistance, trim, and rise‐up values are calculated at 8 to 10 m/s speeds. The findings support the notion that the resistance increases by increasing the distance between the fore step and vessel stern. In addition, increasing the distance between the aft step and vessel stern and the increase of the angle of the fore step leads to reducing the vessel resistance. However, the results showed that finding a sensible relationship between the angle of the aft step and resistance requires more investigation. The findings revealed that the interactional effects between the angles of the aft and fore steps are the most considerable among all studied interactional effects. Among the all studied configurations, the lowest resistance was experienced by the model with an aft step at 25% of the vessel’s length to the stern, having an angle of 150°, and a fore step at 40% of the vessel’s length to the stern, having an angle of 180°.

Effects of Specific Surface Area of Artificial Carriers on Carbon Metabolism Activity of Biofilm

Biofilm technology has been applied to polluted water treatment. The functional characteristics of biofilm play key roles in the decontamination efficiency and are affected by the physicochemical properties of the carrier surface. Previous studies reported that the larger the specific surface area of the artificial carrier, the more biofilms there are attached to its surface. However, the coupling relationship between the metabolic activity of biofilm and the specific surface area of carrier remained limitedly studied. Herein, five carriers with a gradient of specific surface areas were selected to incubate biofilms in two low-pollution rivers for 44 days, and a BIOLOG ECO microplate was used to analyze the metabolic activity of biofilm. Results demonstrated that the carbon metabolic capacity of biofilm fluctuates with the increase in the specific surface area. In Xuanwu Lake, the carbon metabolism rate of biofilm demonstrated a linear correlation with a specific surface area. In Donghu Lake, there was a trend of a single hump because of mass transfer limitation. In different water bodies, the carbon metabolic activity of biofilm demonstrated different trends with the change of specific surface area, and mass transfer limitation should be considered. For the classified carbon sources, there was a threshold (with Xuanwu Lack of 7500 m2/m3 and Donghu Lack of 5000 m2/m3) to make the biofilm achieve the best utilization ability of classified carbon sources. Nevertheless, the change of carriers’ specific surface area had little effect on the community structure of biofilm.

Travelling Wave Solutions of Nonlinear Evolution Problem Arising in Mathematical Physics through (G′/G)-Expansion Scheme

This article deals with the application of well-known (G′/G)-expansion to investigate the travelling wave solutions of nonlinear evolution problems including the Boussinesq equation, Klein–Gordon equation, and sine-Gordon equation as these problems appear frequently in mathematical physics. The beauty of the suggested method is to transform the highly nonlinear evolution equation into a system of nonlinear algebraic equations by means of trial solution and auxiliary equation. It is found that the presented approach is simple, efficient, has a less computational cost, and produced rational trigonometric solutions. In order to investigate the novel results, various simulations have been executed. It is renowned that all solutions are in the form of soliton with a single hump and singular which is travelling as time increases gradually. It travels as time travel with the same shape. Moreover, as A2 decreases the amplitude of the solutions decreases. A comparative study illustrates that some of the obtained solution matches with the existing results against particular values of parameters and various new travelling wave solution attained the first time. The method seems more appropriate by means of a computational work. It can also be extended to demonstrate the behavior of other physical models of physical nature.

Study of the Cross-Section for the 122Te(γ, n)121Te Reaction by the Activation Method

Relevance. The study of photonuclear reactions plays a defining role in the formation of modern ideas about highlocalized collective excitations in nuclei of the giant resonance type. The giant dipole E1-resonance (GR) is the main feature in γ-quantum absorption cross-sections of nuclei. The presence of isotopes with multiple isotopes makes it possible to trace the evolution of GR characteristics from changes in the number of neutrons in the nuclei. One such element is tellurium. Purpose. The purpose of this research is an experimental and theoretical study of the cross-section of 122Te(γ, n)121Te reaction in the region of giant E1-resonance energies. Methods. The study of the cross-section of (γ, n) reaction on 122Te isotope was performed on the bremsstrahlung γ-beam of the M-30 microtron of the Institute of Electronic Physics of the National Academy of Sciences of Ukraine. The yield curves were measured in the range of maximum gamma-quantum energies Eγmax=10-18 MeV. The reaction cross-section was calculated by the inverse matrix method. When registering the reaction products, an activation technique was used, while the gamma activity of the products was recorded by the spectrometric method. The theoretical calculations of the cross-section for the 122Te(γ, n)121Te reaction were performed using the TALYS-1.9 software package. Results. The measured experimental yield ratios of the 122Te(γ, n)121Te і 130Te(γ, n)129Te d= Yn121 /Yn129 = f (E max) reactions allowed the experimental cross-section for the 122Te(γ, n)121Te reaction to be calculated. The cross-section has a single hump shape with a maximum at an energy of ~ 15.3 MeV. It was approximated by the Lorentz curve with the parameters δ0 =(274.1±2.1) MB, Е0 (15.27±0.10) MeV, Г0 =(4.76±0.08) MeV. The cross-section obtained was compared with similar cross-sections for 126Te and 130Te isotopes, as well as with theoretical calculations according to the TALYS-1.9 program. Conclusions. The obtained cross-section for the 122Te(γ, n)121Te reaction is consistent with the evolution of the parameters of (γ, n) reaction cross-section on tellurium isotopes 130Te(γ, n)129Te with a change in the number of neutrons. The theoretical approaches used are satisfactorily consistent with the experimental data. This agreement indicates the main contribution of the statistical mechanism to the cross-section of the considered (γ, n) reaction and a relatively small contribution of semi-direct processes

Improvement of Rear Seat Vibrations of Passenger Bus by Tuning Damper Characteristics

<div class="section abstract"><div class="htmlview paragraph">Passenger vehicles are used as one of the frequently used and versatile mode of transport. Commercial buses cater to short to long distance travel for city as well as highway applications. Thus, passenger ride comfort becomes paramount for the salability of the vehicle. Generally, it is observed that the rear seat experiences the worst ride comfort characteristics due to rear overhang and pitching characteristics of buses. Therefore the objective of this project is to improve the rear seat vibrations of passenger bus by tuning damper characteristics. Shock absorbers, being a low cost and easily interchangeable component is tuned first before optimizing other suspension parameters. The methodology is as follows: first, a 4 degree of freedom mathematical model is created on MATLAB Simulink R2015a environment. Time domain data is obtained by road load data analysis and used as an input for the mathematical model. An experimentation was carried out on the bus at speeds of 20 km/h over a single hump to obtain actual acceleration time domain data. The model is then correlated with actual test over a single hump.</div><div class="htmlview paragraph">After setting up baseline results, tuning of damper is carried out. First low speed compression range is tuned to obtain better ride comfort characteristics over Class A road and results are observed. This is done by varying the damping force from 5kgf to 100kgf in speeds between 0.05 m/s to 0.25 m/s in compression. Thereafter, high speed rebound range is tuned over a single hump by varying the damping force between 1000 kgf to 4000 kgf in speeds between 1m/s to 3 m/s in rebound travel and results are obtained. Finally, fitment of data in Ride Comfort Index is carried out as per ISO 2631. Therefore a comprehensive and parametric damper tuning sheet is prepared considering the natural frequency, critical damping coefficient and damping ratio.</div></div>

Simulation of Zinc-diffused InAs cells for low temperature thermophotovoltaic systems

We simulated zinc-diffused InAs cells which used in the low-temperature thermophotovoltaic system under 600–1200 °C blackbody radiation. By analyzing some important parameters, such as surface recombination speed or thickness of different InAs cells, we achieve the optimal cell structure. The Zn diffusion process was experimented at Zn–In alloy sources at different temperatures for 2 h and a box-shaped Zn profile with a single hump was obtained. We also performed a simulation for optimized GaSb structure. Unlike InAs cells, the GaSb cells have been investigated for a long time under various temperatures, from which we have obtained a better structure and a maximal efficiency of 30%. However, the output power density of InAs cells is greater than that of GaSb cells when applied under low temperature heat source below 1200 °C. Its open circuit voltage and short circuit current density were measured as 0.1157 V and 3.786 A, and the output power density was 0.2222 W/cm2, which is better than 0.098 W/cm2 of GaSb cell under a blackbody temperature of 800 °C with anti-reflection coating and 13.7% grid area. The improved performance can be attributed to its lower bandgap and better quantum efficiency (QE) curves.

One-dimensional quantum droplets under space-periodic nonlinear management

Quantum droplets have recently emerged as a novel liquid state of matter in a mixture of two-component ultracold Bose gases under the equilibrium condition between the competing attractive inter- and repulsive intraspecies forces. Quantum droplets represent a self-bound liquid state in purely nonlinear systems and as such there is not any management applied to their study up to now. We here introduce the nonlinear management via space-periodic Feshbach resonance technique to a binary Bose–Einstein condensate and investigate theoretically the structure, property and dynamics of the one-dimensional quantum droplets therein, three findings are made: small droplets with single hump (solitonlike), moderate droplets composed of two solitons, large droplets feature a modulated flat-top shape. Particularly, by means of linear-stability and direct perturbed simulations, we prove that the droplets have a much wider stable region than their counterparts without taking the nonlinear management. The variational approximation is adopted and validated with numerical results in terms of small droplets. The results predicted here may be realized in the frontier ultracold atoms experiments aided by Feshbach-resonance, opening up a new channel to the quantum droplets studies.

Force-Time Waveform Shape Reveals Countermovement Jump Strategies of Collegiate Athletes.

The purpose of this study was to relate the shape of countermovement jump (CMJ) vertical ground reaction force waveforms to discrete parameters and determine if waveform shape could enhance CMJ analysis. Vertical ground reaction forces during CMJs were collected for 394 male and female collegiate athletes competing at the National Collegiate Athletic Association (NCAA) Division 1 and National Association of Intercollegiate Athletics (NAIA) levels. Jump parameters were calculated for each athlete and principal component analysis (PCA) was performed on normalized force-time waveforms consisting of the eccentric braking and concentric phases. A K-means clustering of PCA scores placed athletes into three groups based on their waveform shape. The overall average waveforms of all athletes in each cluster produced three distinct vertical ground reaction force waveform patterns. There were significant differences across clusters for all calculated jump parameters. Athletes with a rounded single hump shape jumped highest and quickest. Athletes with a plateau at the transition between the eccentric braking and concentric phase (amortization) followed by a peak in force near the end of the concentric phase had the lowest jump height and slowest jump time. Analysis of force-time waveform shape can identify differences in CMJ strategies in collegiate athletes.

STABILITY AND INSTABILITY IN ONE DIMENSIONAL POPULATION MODELS

One dimensional difference equations are widely used in population biol- ogy. These seemingly simple models can show a variety of behaviors from stability to chaos. (see Cull, Yorke, May, Feigenbaum) We show how the enveloping technique can be used to demonstrate global and semi-global stability. We discuss the issue of whether local stability implies global stability. We give some examples of more com- plicated behavior which can co-exist with local stability. We show that local stability implies global stability even for models slightly more complicated than the usual mod- els. We address the issue of how complicated a model must be to have local without global stability, and we describe our candidates for the simplest such models. 1 Introduction Populations wax and wane. To understand these changes in population, we often use simple models. In this paper, we will study difference equation (10) models of population growth. Often these models have a single equilibrium point and for some values of the param- eters this equilibrium is stable. Biological modelers have often checked for stability with respect to small perturbations and then treated the equilibrium as being stable with re- spect to large perturbations. Remarkably, this logical jump never caused any difficulties. Eventually, a number of mathematical papers (4, 34, 32) showed that for some of the usual population models local stability implies global stability. These papers used a variety of methods including Lyapunov functions (23, 18, 19) Schwartzian derivative (34), and some ad hoc techniques (34, 1, 2, 4, 3, 5, 32). But, one uniform technique applicable to all usual population models was lacking. In particular, it was unclear whether the single hump of population models was sufficient to derive global stability from local stability. Finally, Cull and Chaffee (9, 8) were able to show that the usual population models were bounded by linear fractional functions and that this bounding was enough to show global stability from local stability. One aspect of the above approaches is the assumption that the models were three times continuously differentiable. Huang (22) pointed out that for some of these arguments, the continuously differentiable assumption was essential. It was also unclear whether biological modelers really wanted to make such an assumption about their models. Cull (13) showed that bounding (enveloping) by linear fractionals did not depend on differentiability, and, in fact, such enveloping could apply to discontinuous multi-functions. In contrast to such stability May (25, 26) and others have shown that without local stability, population models can show complicated behavior including chaos (24, 14). But, is more complicated behavior possible for population models when local stability is assumed? We investigate some generalizations of the usual population models and show that YES, more complicated behavior is possible even with local stability. How much more complicated does a population model have to be to allow more complicated behavior? We show that

On the influence of two-dimensional hump roughness on laminar–turbulent transition

The presence of large surface irregularities such as humps, where the height is similar to the local boundary-layer (BL) displacement thickness, introduces regions of localized strong streamwise gradients in the base flow quantities. These large gradients can significantly modify the spatial development of incoming disturbances that lead to laminar–turbulent transition in wall-bounded flows [e.g., Tollmien–Schlichting (TS) waves]. Techniques such as Parabolized Stability Equations (PSE) are not suited for BL instability analysis in such regions: their formulation assumes that streamwise variations of base flow and disturbance quantities are small, allowing a marching procedure for their resolution. On the other hand, the Adaptive Harmonic Linearized Navier–Stokes (AHLNS) equations can handle these large streamwise gradients by using a fully elliptic system of equations, similar to Linearized Navier–Stokes (LNS), Harmonic LNS (HLNS), or Direct Numerical Simulation (DNS). Moreover, in AHLNS (as in PSE), a wave-like character of the instabilities is assumed, leading to a significant reduction in the number of streamwise grid points required compared with LNS, HLNS, or DNS computations. In the present study, an efficient combination of PSE and AHLNS is used to investigate the effect of height, length, and shape of a single hump placed on a flat plate in a two-dimensional flow field at Ma∞ = 0.5 without pressure gradient. The effect of this hump on the spatial evolution of TS waves, in terms of N-factors, is presented. An expected laminar–turbulent transition onset, via the eN methodology, is also described. It is shown that the shape of the surface irregularity, together with the height and length, plays an important role for the location of laminar–turbulent transition onset in convectively unstable flows.

Time-frequency analysis for two cases of boundary-layer transition induced by random distributed roughness

The boundary layer transition induced by distributed surface roughness has great practical relevance, but remains poorly understood. In this experimental work, we investigate the transition in a flat-plate boundary layer downstream of a localized strip of random distributed roughness. The boundary layer exhibits different temporal and spectral behaviour in two (roughness-) Reynolds-number regimes separated by a critical value. In the “sub-critical” regime, the velocity signals show presence of “turbulent spots”, whereas in the “super-critical” regime, no distinct turbulent spots are observed. Two boundary-layer profiles, one each from the sub-critical and super-critical regimes, are chosen for comparison. The sub-critical case exhibits a bi-modal power spectrum having two humps in frequency ranges differing by an order of magnitude, whereas the super-critical case has a uni-modal spectrum with a single hump in the high-frequency range. The wavelet analysis shows that the energy distribution is intermittent in time for both the cases at all frequencies. However, for the sub-critical case, the energy in the high-frequency range appears as clusters, which are seen as turbulent spots in the velocity signal. On the other hand, for the super-critical case there is no such clustering, consistent with the absence of spots in the velocity signal. We conjecture that, for the sub-critical case, the motions corresponding to the low-frequency spectral hump (possibly the streamwise streaks) could be responsible for imparting organization to the high-frequency motions in the form of turbulent spots. We also detect “events” in the wavelet-energy time series. For the sub-critical case, the events in the high-frequency range have a higher degree of time-localization, which increases with frequency. For the super-critical case, however, the time-localization is independent of frequency over nearly the entire frequency range. These findings present two different scenarios for the late stages of transition, having distinct time-frequency behaviour. This could have implications towards modelling roughness-induced transition.

Global dynamics of a nonlinear state-dependent feedback control ecological model with a multiple-hump discrete map

An ecological model with nonlinear state-dependent feedback control is proposed and studied. The Poincaré map defined in the phase set integrates the properties of continuous, discrete and impulsive dynamical systems. The map has complex behavior including single hump and multiple-hump functions and multiple discontinuous points. The properties of various cases of the Poincaré map are systematically studied including monotonicity, continuity and the existence of a fixed point and a transcritical bifurcation, which correspond to the existence and global stability of the order-1 periodic solutions or limit cycles of the proposed model. Moreover, the conditions under which the discontinuity occurs and the number of discontinuous points are discussed, which can result in the coexistence of multiple order-1 periodic solutions and complex dynamics. Furthermore, some sufficient conditions for the global stability of the fixed point (order-1 limit cycle) have been provided even when there are multiple peaks and valleys or multiple discontinuous points for the Poincaré map.

Depth of Ellerman Burst Derived from High-resolution Hα and Ca ii 8542 Å Spectra

Abstract High-resolution spectra of an Ellerman burst (EB) sampling the Hα and the Ca ii 8542 Å lines obtained with the Fast Imaging Solar Spectrograph (FISS) installed on the 1.6 m Goode Solar Telescope at the Big Bear Solar Observatory are compared with synthetic line profiles constructed using the RH code for nonlocal thermodynamical equilibrium radiative transfer. The EB heating is modeled by a local temperature hump above the quiet-Sun temperature. Our first finding is that FISS Hα and Ca ii 8542 Å intensity profiles cannot be reproduced simultaneously by a single hump model as far as the hump is thicker than ≥100 km. Simultaneous reproduction of both line profiles is possible when the EB temperature enhancement is confined to a layer as thin as ≤20 km in the photosphere where the Hα wing response is high and that of the Ca ii 8542 Å is not. Moreover, when we examine the EB spectra at different times, we find that the EB at a time of weaker appearance is located at lower heights, ∼50 km, and moves upward to ∼120 km at the time of maximum intensity. Complementary calculations of the Na i D1 and Mg i b2 lines as well as that of UV continuum at 1600 and 1700 Å with the deduced EB atmosphere are also performed to test the result, which allows us to discuss the shortcomings of this plane–parallel static model atmosphere for understanding the physical properties of EBs.

Iris and knot configuration after Single Pass Four Throw (SFT) pupilloplasty as imaged by the spectral-domain optical coherence tomography.

Purpose:To analyze the morphological changes in the iris-knot complex configuration using spectral-domain optical coherence tomography (SD-OCT) following the single pass four throw (SFT) pupilloplasty.Methods:In this retrospective case series, eyes with SFT pupilloplasty were examined by SD-OCT (Optovue). Iris morphology compared to the normal iris, presence of specific patterns (single hump, double humps, peaks and valleys, tethering), prolene suture, knot complex (length and orientation), and intraocular lens (IOL) vault were evaluated.Results:Overall, 41 knots of 26 patients with a mean time duration of 3.1 ± 2 months from surgery were analyzed. Iris configurations seen were single hump (n = 28, 63.8%), double humps (n = 7, 17%), loop (n = 2, 4.8%), flat (n = 3, 7.3%), and mulberry (n = 1, 2.4%). The mean length and the height of the knot complex was 784.1 ± 433.7 μm and 317.7 ± 110.4 μm, respectively. Knot positions were at 3 clock hours in 9 eyes (21.9%), 9 in 8 eyes (19.5%), and others in 24 eyes (58.5%). Cut end of the prolene suture was detectable in 26 eyes (63.4%) as hyper-reflective line, and the mean cut length was 465.8 ± 321.1 μm. The suture was predominantly vertically oriented (80.6%) to the iris with a mean distance of 3.6 ± 0.3 mm (2.6–4 mm) away from corneal endothelium. The mean distance from the knot complex and the IOL was 289.2 ± 146 μm and the mean anterior chamber depth was 4.1 ± 0.1 mm.Conclusion:A significant change in iris configuration was noted after SFT pupilloplasty, and vertically oriented retained prolene suture was predominant with good endothelial vault.

Generalized multi-hump wave solutions of Kdv-Kdv system of Boussinesq equations

The KdV-KdV system of Boussinesq equations belongs to the class of Boussinesq equations modeling two-way propagation of small-amplitude long waves on the surface of an ideal fluid. It has been numerically shown that this system possesses solutions with two humps which tend to a periodic solution with much smaller amplitude at infinity (called generalized two-hump wave solutions). This paper presents the first rigorous proof. The traveling form of this system can be formulated into a dynamical system with dimension 4. The classical dynamical system approach provides the existence of a solution with an exponentially decaying part and an oscillatory part (small-amplitude periodic solution) at positive infinity, which has a single hump at the origin and is reversible near negative infinity if some free constants, such as the amplitude and the phase shit of the periodic solution, are activated. This eventually yields a generalized two-hump wave solution. The method here can be applied to obtain generalized $2^k$-hump wave solutions for any positive integer $k$.