Topping Failure Analysis of Anti-Dip Bedding Rock Slopes Subjected to Crest Loads

Crest loads are often encountered in hydropower, highway, open-pit and other engineering rock slopes. Toppling failure is one of the most common deformation failure types of anti-dip bedding rock slopes. Analysis on such failure of anti-dip bedding rock slopes subjected to crest loads has an important influence on engineering practice. Based on the step-by-step analysis approach proposed by Goodman and Bray, a geo-mechanical model was developed, and the related analysis approach was proposed for the toppling failure of anti-dip bedding rock slopes subjected to crest loads. Using the transfer coefficient method, a formulation was derived for calculating the residual thrust of slope toe and the support force required to meet the requirements of the slope stability under crest loads, which provided a scientific reference to design and support for such slopes. Through slope examples, the influence of crest loads on the residual thrust and sliding ratio coefficient was investigated for cases of different block widths and slope cut angles. The results show that there exists a critical block width for such slope. The influence of crest loads on the residual thrust is non-negligible when the block thickness is smaller than the critical value. Moreover, the influence of crest loads on the slope stability increases with the slope cut angle and the sliding ratio coefficient of anti-dip bedding rock slopes increases with the crest loads. Finally, the theoretical solutions and numerical simulations using Universal Distinct Element Code (UDEC) were compared, in which the consistent results show the applicability of both approaches.

The Design of Broadband 8x2 Phased Array 5G Antenna MIMO 28 GHz for Base Station

This paper proposed a design of 16 elements, 8x2 linear fed patch antenna array with 16 ports, for 28 GHz, mm-wave band 5G for base station. The phased array covers along the azimuth plane to provide the coverage to the users in omnidirectional. The proposed antenna is designed RT Duroid 5880 substrate with the overall size of 85x35.6x0.787 mm3. The array is operating from 27.43 GHz to 28.34 GHz with a 910 MHz impedance bandwidth. The gain of the array is 18.3 dB, while the suppression of the side lobes is -1.0 dB. The main lobe direction of the array is 15 deg. The array shows a high array gain throughout the impedance bandwidth with overall of VSWR is below 1.12. The design will be proposed in single element and 16 elements antenna.

Investigation on Behavior of Fixed-Ended Reinforced Concrete Deep Beams

Reinforced Concrete (RC) deep beams are special structural elements because of their geometry and behavior under loads. For example, assumption of strain- stress distribution is not linear in the cross section. These types of beams may have simple supports or fixed supports. A lot of research works have been conducted on simply supported deep beams, but little study has been done in the fixed-end RC deep beams behavior. Recently, using of fixed-ended deep beams has been widely increased in structures. In this study, the behavior of fixed-ended deep beams is investigated, and the important parameters in capacity of this type of beams are mentioned.

Investigation of Some Flotation Parameters and the Role of Dispersants in the Flotation of Chalcopyrite

A suitable choice of flotation parameters and reagents have a strong effect on the effectiveness of flotation process. The objective of this paper is to give an overview of the flotation of chalcopyrite with the different conditions and dispersants. Flotation parameters such as grinding time, pH, type, and dosage of dispersant were investigated. In order to understand the interaction of some dispersants, sodium silicate, sodium hexametaphosphate and sodium polyphosphate were used. The optimum results were obtained at a pH of 11.5 and a grinding time of 10 minutes. A copper concentrate was produced assaying 29.85% CuFeS2 and 65.97% flotation recovery under optimum rougher flotation conditions with sodium silicate.

Effect of Core Puncture Diameter on Bio-Char Kiln Efficiency

Biochar has been used as a soil amendment since it has high porous structure and has proper nutrients and chemical properties for plants. Product yields produced from biochar kiln are dependent on process parameters and kiln types used. The objective of this research is to investigate the effect of core puncture diameter on biochar kiln efficiency, i.e., yields of biochar and produced gas. Corncobs were used as raw material to produce biochar. Briquettes from agricultural wastes were used as fuel. Each treatment was performed by changing the core puncture diameter. From the experiment, it is revealed that the yield of biochar at the core puncture diameter of 3.18 mm, 4.76 mm, and 6.35 mm was 10.62 wt. %, 24.12 wt. %, and 12.24 wt. %, of total solid yields, respectively. The yield of produced gas increased with increasing the core puncture diameter. The maximum percentage by weight of the yield of produced gas was 81.53 wt. % which was found at the core puncture diameter of 6.35 mm. The core puncture diameter was furthermore found to affect the temperature distribution inside the kiln and its thermal efficiency. In conclusion, the high efficient biochar kiln can be designed and constructed by using the proper core puncture diameter.

Real Time Object Tracking in H.264/ AVC Using Polar Vector Median and Block Coding Modes

This paper presents a real time video surveillance system which is capable of tracking multiple real time objects using Polar Vector Median (PVM) and Block Coding Modes (BCM) with Global Motion Compensation (GMC). This strategy works in the packed area and furthermore utilizes the movement vectors and BCM from the compressed bit stream to perform real time object tracking. We propose to do this in view of the neighboring Motion Vectors (MVs) using a method called PVM. Since GM adds to the object’s native motion, for accurate tracking, it is important to remove GM from the MV field prior to further processing. The proposed method is tested on a number of standard sequences and the results show its advantages over some of the current modern methods.

The Main Steamline Break Transient Analysis for Advanced Boiling Water Reactor Using TRACE, PARCS, and SNAP Codes

To confirm the reactor and containment integrity of the Advanced Boiling Water Reactor (ABWR), we perform the analysis of main steamline break (MSLB) transient by using the TRACE, PARCS, and SNAP codes. The process of the research has four steps. First, the ABWR nuclear power plant (NPP) model is developed by using the above codes. Second, the steady state analysis is performed by using this model. Third, the ABWR model is used to run the analysis of MSLB transient. Fourth, the predictions of TRACE and PARCS are compared with the data of FSAR. The results of TRACE/PARCS and FSAR are similar. According to the TRACE/PARCS results, the reactor and containment integrity of ABWR can be maintained in a safe condition for MSLB.

Bioleaching of Metals Contained in Spent Catalysts by Acidithiobacillus thiooxidans DSM 26636

Spent catalysts are considered as hazardous residues of major concern, mainly due to the simultaneous presence of several metals in elevated concentrations. Although hydrometallurgical, pyrometallurgical and chelating agent methods are available to remove and recover some metals contained in spent catalysts; these procedures generate potentially hazardous wastes and the emission of harmful gases. Thus, biotechnological treatments are currently gaining importance to avoid the negative impacts of chemical technologies. To this end, diverse microorganisms have been used to assess the removal of metals from spent catalysts, comprising bacteria, archaea and fungi, whose resistance and metal uptake capabilities differ depending on the microorganism tested. Acidophilic sulfur oxidizing bacteria have been used to investigate the biotreatment and extraction of valuable metals from spent catalysts, namely Acidithiobacillus thiooxidans and Acidithiobacillus ferroxidans, as they present the ability to produce leaching agents such as sulfuric acid and sulfur oxidation intermediates. In the present work, the ability of A. thiooxidans DSM 26636 for the bioleaching of metals contained in five different spent catalysts was assessed by growing the culture in modified Starkey mineral medium (with elemental sulfur at 1%, w/v), and 1% (w/v) pulp density of each residue for up to 21 days at 30 °C and 150 rpm. Sulfur-oxidizing activity was periodically evaluated by determining sulfate concentration in the supernatants according to the NMX-k-436-1977 method. The production of sulfuric acid was assessed in the supernatants as well, by a titration procedure using NaOH 0.5 M with bromothymol blue as acid-base indicator, and by measuring pH using a digital potentiometer. On the other hand, Inductively Coupled Plasma - Optical Emission Spectrometry was used to analyze metal removal from the five different spent catalysts by A. thiooxidans DSM 26636. Results obtained show that, as could be expected, sulfuric acid production is directly related to the diminish of pH, and also to highest metal removal efficiencies. It was observed that Al and Fe are recurrently removed from refinery spent catalysts regardless of their origin and previous usage, although these removals may vary from 9.5 ± 2.2 to 439 ± 3.9 mg/kg for Al, and from 7.13 ± 0.31 to 368.4 ± 47.8 mg/kg for Fe, depending on the spent catalyst proven. Besides, bioleaching of metals like Mg, Ni, and Si was also obtained from automotive spent catalysts, which removals were of up to 66 ± 2.2, 6.2±0.07, and 100±2.4, respectively. Hence, the data presented here exhibit the potential of A. thiooxidans DSM 26636 for the simultaneous bioleaching of metals contained in spent catalysts from diverse provenance.

Feature Extraction Technique for Prediction the Antigenic Variants of the Influenza Virus

In genetics, the impact of neighboring amino acids on a target site is referred as the nearest-neighbor effect or simply neighbor effect. In this paper, a new method called wavelet particle decomposition representing the one-dimensional neighbor effect using wavelet packet decomposition is proposed. The main idea lies in known dependence of wavelet packet sub-bands on location and order of neighboring samples. The method decomposes the value of a signal sample into small values called particles that represent a part of the neighbor effect information. The results have shown that the information obtained from the particle decomposition can be used to create better model variables or features. As an example, the approach has been applied to improve the correlation of test and reference sequence distance with titer in the hemagglutination inhibition assay.

Taxonomic and Faunistic Data on the Genus Triaspis Haliday, 1835 (Hymenoptera: Braconidae: Brachistinae) from Turkey

Brachistinae Föerster, 1862 is a subfamily of the family Braconidae (order Hymenoptera) with about 410 species distributed all around the world. Brachistinae includes the genera, Eubazus Nees von Esenbeck 1814, Foersteria Szépligeti 1896, Chelostes van Achterberg 1990, Triaspis Haliday 1835 and Schizoprymnus Förster 1862. Members of the subfamily live as parasitoids on the families Curculionidae and Apionidae (Coleoptera), which also include very important agricultural pests.  In generally, members of the genus Triaspis are poorly known biologically. The genus is represented by 37 species in the West Palearctic region and 118 species worldwide. Adult specimens of Triaspis were collected from as wide a range of habitats as possible at different altitudes in different parts of Turkey between 1982 and 2010. Samples collected from short plants using standard insect sweeping nets were transferred into tubes containing 70% ethanol and labelled following their preparations according to museum techniques. Seven Triaspis species have been reported from Turkey in this study. Five of these species are new to the fauna of Turkey.

The Optimum Operating Conditions for the Synthesis of Zeolite from Waste Incineration Fly Ash by Alkali Fusion and Hydrothermal Methods

The fly ash of waste incineration processes is usually hazardous and the disposal or reuse of waste incineration fly ash is difficult. In this study, the waste incineration fly ash was converted to useful zeolites by the alkali fusion and hydrothermal synthesis method. The influence of different operating conditions (the ratio of Si/Al, the ratio of hydrolysis liquid to solid, and hydrothermal time) was investigated to seek the optimum operating conditions for the synthesis of zeolite from waste incineration fly ash. The results showed that concentrations of heavy metals in the leachate of Toxicity Characteristic Leaching Procedure (TCLP) were all lower than the regulatory limits except lead. The optimum operating conditions for the synthesis of zeolite from waste incineration fly ash by the alkali fusion and hydrothermal synthesis method were Si/Al=40, NaOH/ash=1.5, alkali fusion at 400 oC for 40 min, hydrolysis with Liquid to Solid ratio (L/S)= 200 at 105 oC for 24 h, and hydrothermal synthesis at 105 oC for 24 h. The specific surface area of fly ash could be significantly increased from 8.59 m2/g to 651.51 m2/g (synthesized zeolite). The influence of different operating conditions on the synthesis of zeolite from waste incineration fly ash followed the sequence of Si/Al ratio > hydrothermal time > hydrolysis L/S ratio. The synthesized zeolites can be reused as good adsorbents to control the air or wastewater pollutants. The purpose of fly ash detoxification, reduction and waste recycling/reuse is achieved successfully.

Pollutants Removal from Synthetic Wastewater by the Combined Electrochemical Sequencing Batch Reactor

Synthetic domestic wastewater was treated via combining treatment methods, including electrochemical oxidation, adsorption, and sequencing batch reactor (SBR). In the upper part of the reactor, an anode and a cathode (Ti/RuO2-IrO2) were organized in parallel for the electrochemical oxidation procedure. Sodium sulfate (Na2SO4) with a concentration of 2.5 g/L was applied as the electrolyte. The voltage and current were fixed on 7.50 V and 0.40 A, respectively. Then, 15% working value of the reactor was filled by activated sludge, and 85% working value of the reactor was added with synthetic wastewater. Powdered cockleshell, 1.5 g/L, was added in the reactor to do ion-exchange. Response surface methodology was employed for statistical analysis. Reaction time (h) and pH were considered as independent factors. A total of 97.0% biochemical oxygen demand, 99.9% phosphorous and 88.6% cadmium were eliminated at the optimum reaction time (80.0 min) and pH (6.4).

Optimization of Biodiesel Production from Sunflower Oil Using Central Composite Design

The current study investigated the effect of catalyst ratio and methanol to oil ratio on biodiesel production by using central composite design. Biodiesel was produced by transesterification using sodium hydroxide as a homogeneous catalyst, a laboratory scale reactor consisting of flat bottom flask mounts with a reflux condenser, and a heating plate was used to produce biodiesel. Key parameters, including time, temperature, and mixing rate was kept constant at 60 minutes, 60 oC and 600 RPM, respectively. From the results obtained, it was observed that the biodiesel yield depends on catalyst ratio and methanol to oil ratio. The highest yield of 50.65% was obtained at catalyst ratio of 0.5 wt.% and methanol to oil mole ratio 10.5. The analysis of variances of biodiesel yield showed the R Squared value of 0.8387. A quadratic mathematical model was developed to predict the biodiesel yield in the specified parameters ranges.

Restrictedly-Regular Map Representation of n-Dimensional Abstract Polytopes

Regularity has often been present in the form of regular polyhedra or tessellations; classical examples are the nine regular polyhedra consisting of the five Platonic solids (regular convex polyhedra) and the four Kleper-Poinsot polyhedra. These polytopes can be seen as regular maps. Maps are cellular embeddings of graphs (with possibly multiple edges, loops or dangling edges) on compact connected (closed) surfaces with or without boundary. The n-dimensional abstract polytopes, particularly the regular ones, have gained popularity over recent years. The main focus of research has been their symmetries and regularity. Planification of polyhedra helps its spatial construction, yet it destroys its symmetries. To our knowledge there is no “planification” for n-dimensional polytopes. However we show that it is possible to make a “surfacification” of the n-dimensional polytope, that is, it is possible to construct a restrictedly-marked map representation of the abstract polytope on some surface that describes its combinatorial structures as well as all of its symmetries. We also show that there are infinitely many ways to do this; yet there is one that is more natural that describes reflections on the sides ((n−1)-faces) of n-simplices with reflections on the sides of n-polygons. We illustrate this construction with the 4-tetrahedron (a regular 4-polytope with automorphism group of size 120) and the 4-cube (a regular 4-polytope with automorphism group of size 384).

Theoretical, Numerical and Experimental Assessment of Elastomeric Bearing Stability

Elastomeric bearings (EB) are used in many applications, such as base isolation of bridges, seismic protection and vibration control of other structures and machinery. Their versatility is due to their particular behavior since they have different stiffness in the vertical and horizontal directions, allowing to sustain vertical loads and at the same time horizontal displacements. Therefore, vertical, horizontal and bending stiffnesses are important parameters to take into account in the design of EB. In order to acquire a proper design methodology of EB all three, theoretical, finite element analysis and experimental, approaches should be taken into account to assess stability due to different loading states, predict their behavior and consequently their effects on the dynamic response of structures, and understand complex behavior and properties of rubber-like materials respectively. In particular, the recent large-displacement theory on the stability of EB formulated by Forcellini and Kelly is validated with both numerical simulations using the finite element method, and experimental results set at the University of Antioquia in Medellin, Colombia. In this regard, this study reproduces the behavior of EB under compression loads and investigates the stability behavior with the three mentioned points of view.

Problems and Prospects of Agricultural Biotechnology in Nigeria’s Developing Economy

Science offers opportunities for revolutionizing human activities, enriched by input from scientific research and technology. Biotechnology is a major force for development in developing countries such as Nigeria. It is found to contribute to solving human problems like water and food insecurity that impede national development and threaten peace wherever it is applied. This review identified the problems of agricultural biotechnology in Nigeria. On the part of rural farmers, there is a lack of adequate knowledge or awareness of biotechnology despite the fact that they constitute the bulk of Nigerian farmers. On part of the government, the problems include: lack of adequate implementation of government policy on bio-safety and genetically modified products, inadequate funding of education as well as research and development of products related to biotechnology. Other problems include: inadequate infrastructures (including laboratory), poor funding and lack of national strategies needed for development and running of agricultural biotechnology. In spite of all the challenges associated with agricultural biotechnology, its prospects still remain great if Nigeria is to meet with the food needs of the country’s ever increasing population. The introduction of genetically engineered products will lead to the high productivity needed for commercialization and food security. Insect, virus and other related diseases resistant crops and livestock are another viable area of contribution of biotechnology to agricultural production. In conclusion, agricultural biotechnology will not only ensure food security, but, in addition, will ensure that the local farmers utilize appropriate technology needed for large production, leading to the prosperity of the farmers and national economic growth, provided government plays its role of adequate funding and good policy implementation.

Formation of Protective Aluminum-Oxide Layer on the Surface of Fe-Cr-Al Sintered-Metal-Fibers via Multi-Stage Thermal Oxidation

The objective of this paper is to investigate the formation and adhesion of a protective aluminum-oxide (Al2O3, alumina) layer on the surface of Iron-Chromium-Aluminum Alloy (Fe-Cr-Al) sintered-metal-fibers. The oxide-scale layer was developed via multi-stage thermal oxidation at 930 oC for 1 hour, followed by 1 hour at 960 oC, and finally at 990 oC for 2 hours. Scanning Electron Microscope (SEM) images show that the multi-stage thermal oxidation resulted in the formation of predominantly Al2O3 platelets-like and whiskers. SEM images also reveal non-uniform oxide-scale growth on the surface of the fibers. Furthermore, peeling/spalling of the alumina protective layer occurred after minimum handling, which indicates weak adhesion forces between the protective layer and the base metal alloy.  Energy Dispersive Spectroscopy (EDS) analysis of the heat-treated Fe-Cr-Al sintered-metal-fibers confirmed the high aluminum content on the surface of the protective layer, and the low aluminum content on the exposed base metal alloy surface. In conclusion, the failure of the oxide-scale protective layer exposes the base metal alloy to further oxidation, and the fragile non-uniform oxide-scale is not suitable as a support for catalysts.

Multiscale Modelization of Multilayered Bi-Dimensional Soils

Soil moisture content is a key variable in many environmental sciences. Even though it represents a small proportion of the liquid freshwater on Earth, it modulates interactions between the land surface and the atmosphere, thereby influencing climate and weather. Accurate modeling of the above processes depends on the ability to provide a proper spatial characterization of soil moisture. The measurement of soil moisture content allows assessment of soil water resources in the field of hydrology and agronomy. The second parameter in interaction with the radar signal is the geometric structure of the soil. Most traditional electromagnetic models consider natural surfaces as single scale zero mean stationary Gaussian random processes. Roughness behavior is characterized by statistical parameters like the Root Mean Square (RMS) height and the correlation length. Then, the main problem is that the agreement between experimental measurements and theoretical values is usually poor due to the large variability of the correlation function, and as a consequence, backscattering models have often failed to predict correctly backscattering. In this study, surfaces are considered as band-limited fractal random processes corresponding to a superposition of a finite number of one-dimensional Gaussian process each one having a spatial scale. Multiscale roughness is characterized by two parameters, the first one is proportional to the RMS height, and the other one is related to the fractal dimension. Soil moisture is related to the complex dielectric constant. This multiscale description has been adapted to two-dimensional profiles using the bi-dimensional wavelet transform and the Mallat algorithm to describe more correctly natural surfaces. We characterize the soil surfaces and sub-surfaces by a three layers geo-electrical model. The upper layer is described by its dielectric constant, thickness, a multiscale bi-dimensional surface roughness model by using the wavelet transform and the Mallat algorithm, and volume scattering parameters. The lower layer is divided into three fictive layers separated by an assumed plane interface. These three layers were modeled by an effective medium characterized by an apparent effective dielectric constant taking into account the presence of air pockets in the soil. We have adopted the 2D multiscale three layers small perturbations model including, firstly air pockets in the soil sub-structure, and then a vegetable canopy in the soil surface structure, that is to simulate the radar backscattering. A sensitivity analysis of backscattering coefficient dependence on multiscale roughness and new soil moisture has been performed. Later, we proposed to change the dielectric constant of the multilayer medium because it takes into account the different moisture values of each layer in the soil. A sensitivity analysis of the backscattering coefficient, including the air pockets in the volume structure with respect to the multiscale roughness parameters and the apparent dielectric constant, was carried out. Finally, we proposed to study the behavior of the backscattering coefficient of the radar on a soil having a vegetable layer in its surface structure.

Result Validation Analysis of Steel Testing Machines

Structural failures occur due to a number of reasons. These may include under design, poor workmanship, substandard materials, misleading laboratory tests and lots more. Reinforcing steel bar is an important construction material, hence its properties must be accurately known before being utilized in construction. Understanding this property involves carrying out mechanical tests prior to design and during construction to ascertain correlation using steel testing machine which is usually not readily available due to the location of project. This study was conducted to determine the reliability of reinforcing steel testing machines. Reconnaissance survey was conducted to identify laboratories where yield and ultimate tensile strengths tests can be carried out. Six laboratories were identified within Ibadan and environs. However, only four were functional at the time of the study. Three steel samples were tested for yield and tensile strengths, using a steel testing machine, at each of the four laboratories (LM, LO, LP and LS). The yield and tensile strength results obtained from the laboratories were compared with the manufacturer’s specification using a reliability analysis programme. Structured questionnaire was administered to the operators in each laboratory to consider their impact on the test results. The average value of manufacturers’ tensile strength and yield strength are 673.7 N/mm2 and 559.7 N/mm2 respectively. The tensile strength obtained from the four laboratories LM, LO, LP and LS are given as 579.4, 652.7, 646.0 and 649.9 N/mm2 respectively while their yield strengths respectively are 453.3, 597.0, 550.7 and 564.7 N/mm2. Minimum tensile to yield strength ratio is 1.08 for BS 4449: 2005 and 1.15 for ASTM A615. Tensile to yield strength ratio from the four laboratories are 1.28, 1.09, 1.17 and 1.15 for LM, LO, LP and LS respectively. The tensile to yield strength ratio shows that the result obtained from all the laboratories meet the code requirements used for the test. The result of the reliability test shows varying level of reliability between the manufacturers’ specification and the result obtained from the laboratories. Three of the laboratories; LO, LS and LP have high value of reliability with the manufacturer i.e. 0.798, 0.866 and 0.712 respectively. The fourth laboratory, LM has a reliability value of 0.100. Steel test should be carried out in a laboratory using the same code in which the structural design was carried out. More emphasis should be laid on the importance of code provisions.

Bidirectional Pendulum Vibration Absorbers with Homogeneous Variable Tangential Friction: Modelling and Design

Passive resonant vibration absorbers are among the most widely used dynamic control systems in civil engineering. They typically consist in a single-degree-of-freedom mechanical appendage of the main structure, tuned to one structural target mode through frequency and damping optimization. One classical scheme is the pendulum absorber, whose mass is constrained to move along a curved trajectory and is damped by viscous dashpots. Even though the principle is well known, the search for improved arrangements is still under way. In recent years this investigation inspired a type of bidirectional pendulum absorber (BPA), consisting of a mass constrained to move along an optimal three-dimensional (3D) concave surface. For such a BPA, the surface principal curvatures are designed to ensure a bidirectional tuning of the absorber to both principal modes of the main structure, while damping is produced either by horizontal viscous dashpots or by vertical friction dashpots, connecting the BPA to the main structure. In this paper, a variant of BPA is proposed, where damping originates from the variable tangential friction force which develops between the pendulum mass and the 3D surface as a result of a spatially-varying friction coefficient pattern. Namely, a friction coefficient is proposed that varies along the pendulum surface in proportion to the modulus of the 3D surface gradient. With such an assumption, the dissipative model of the absorber can be proven to be nonlinear homogeneous in the small displacement domain. The resulting homogeneous BPA (HBPA) has a fundamental advantage over conventional friction-type absorbers, because its equivalent damping ratio results independent on the amplitude of oscillations, and therefore its optimal performance does not depend on the excitation level. On the other hand, the HBPA is more compact than viscously damped BPAs because it does not need the installation of dampers. This paper presents the analytical model of the HBPA and an optimal methodology for its design. Numerical simulations of single- and multi-story building structures under wind and earthquake loads are presented to compare the HBPA with classical viscously damped BPAs. It is shown that the HBPA is a promising alternative to existing BPA types and that homogeneous tangential friction is an effective means to realize systems provided with amplitude-independent damping.