Low energy spectrum of the XXZ model coupled to a magnetic field

It is shown that, for a class of Hamiltonians of XXZ chains in an external magnetic field that are small perturbations of an Ising Hamiltonian, the spectral gap above the ground-state energy remains strictly positive when the perturbation is turned on, uniformly in the length of the chain. The result is proven for both the ferromagnetic and the antiferromagnetic Ising Hamiltonian; in the latter case the external magnetic field is required to be small, and for an even number of sites the two-fold degenerate ground-state energy of the unperturbed Hamiltonian may split into two energy levels whose difference is small. This result is proven by using a new, quite subtle refinement of a method developed in earlier work and used to iteratively block-diagonalize Hamiltonians of ever larger subsystems with the help of local unitary conjugations. One novel ingredient of the method presented in this paper consists of the use of Lieb-Robinson bounds.Comment: 6 figure

modelling of acoustic ageing of rubberized pavements

Abstract Tyre-road noise is the most important source of traffic noise in the mid-to-high speed range. The use of low noise road surfaces represents an ideal solution to mitigate traffic noise, because it directly affects the source, generating a widespread benefit for all the dwellings near the road and decreasing the number of people annoyed. More knowledge about long-term acoustic performance is required to promote the use of low noise road surfaces as mitigation action. In fact, as for a traditional road surface, the acoustic properties of low noise surfaces worsen over time: only by knowing the initial noise reduction and its time evolution, public administrations can design their application and related maintenance plans. In this work, an innovative approach was used to investigate and model acoustic ageing of some rubberized road surfaces surveyed for several years. This type of quiet pavements represents an efficient road surface technology in terms of traffic noise reduction. A new regression model was applied to estimate the acoustic ageing of the investigated pavements, considering the complex interacting system composed of three main elements: pavement type, traffic loads and climatic conditions

Influence of texture on tyre road noise spectra in rubberized pavements

Abstract Road traffic noise is the most common source of environmental pollution in urban areas and therefore, the study of noise mitigation actions is fundamental for urban planning. The main source of road traffic noise is tyre/road interaction; thus, the use of low noise road surfaces represents an optimal solution for its mitigation. Several studies tried to find a correlation between road texture and broadband noise data, trying to provide guidelines for the development of acoustically optimised road surfaces. The present work studies the correlation between road texture and tyre/road noise from an experimental point of view, by analysing texture and noise spectra on ten different road surfaces. Tyre deformation has also been addressed by analysing two already existing tyre envelopment algorithms. The first algorithm, proposed by Von Meier and based on the limitation of the second order derivative of the profile signal, shows poor correlation with high frequency noise, while the second algorithm, based on a novel method proposed by Sandberg and Goubert and called indenter method, enhances correlation with low frequency noise and preserves information at higher frequencies. Correlation patterns show that rolling noise can be separated in three main contributions: low, middle and high frequency noise. Finally, experimental tyre/road noise and enveloped texture data obtained with the indenter algorithm have been used to elaborate a linear model that relates low and high frequency noise to texture one-third octave bands. This model deepens knowledge on tyre/road interaction

evaluation of tyre road noise and texture interaction on rubberised and conventional pavements using cpx and profiling measurements

Road traffic noise is the most common source of environmental pollution in urban areas, and therefore, the study of noise mitigation actions is fundamental for urban planning. The use of low noise ..

modelling the acoustic performance of newly laid low noise pavements

Abstract Road traffic in urban contexts produces noise mainly by the interaction of tyres with pavement surface and, therefore, the use of low-noise surfaces represents the best solution since they aim to mitigate the source. Moreover, in urban contexts it is often the only viable solution, together with a careful traffic planning. The main challenge in their adoption as noise mitigation actions is to be able to forecast the acoustical performances that the new road surface will be able to offer. In the UE, the new Green Public Procurement requires experimental verification of noise performance compliance: the designer must declare the acoustical performance of the proposed low-noise pavement and, a few months after the laying, the actual performance of the road surface must be tested using the Close Proximity Method (CPX). Due to the importance of being able to forecast CPX levels, the present work reports a novel way to model CPX broadband levels of newly laid low-noise road surfaces using only data available to the designer before the laying or easily obtained through coring tests, such as grading curve, fractal dimension, asphalt binder content, air voids, voids in mineral aggregates. Two models were elaborated, using two different frequency separations for tyre/road noise. The first model separates low and high frequency contributions, while the second one also considers noise around 1 kHz separately, using a three-band model. Both models are capable of forecasting the acoustic performance of newly laid low-noise road surfaces, using different road mixture parameters at different frequency ranges. The three band model shows a lower RMSE

Implementation of a laser profilometer for road texture measurements and its correlation with rolling noise

Traffic noise is one of the main sources of acoustic pollution, with an ubiquitous presence in anthropised environments.Therefore, it is a constant component of residual noise during every noise measurement. The generation and propagation of traffic noise is governed by three main different mechanisms: vehicles' power unit (i.e. the engine, gearbox and cooling system), vehicles' profile aerodynamics and tyre-road interaction. While engine noise is the main source up to 35 km/h, for higher speeds propulsion noise is negligible over noise due to tyre/road interaction. For heavy vehicles, like lorries, the contribution of propulsion noise cannot be neglected even at higher speeds. Tyre/road interaction depends greatly on the characteristics of road surfaces: a subtle difference in road surfaces may yield a large variation in noise levels. This idea has lead to a series of studies that focused on providing theoretical and phenomenological analysis of the influence of road profile on noise emission. The characterisation of a road surface requires the measurement of its profile: the device used to carry out these measurements is known as profilometer; modern road profilometry is based on laser triangulation sensors, which allow a simple and direct measurement of road texture. The purpose of this work, carried out at the CNR spin-off company iPool srl, was to develop a laser profilometer focused on measuring the macrotexture and megatexture of road pavements, which cover wavelengths of the same order of magnitude as the size of tyre tread elements and of the tyre/road interface and to verify some of the existing models to predict tyre rolling noise based on road texture knowledge. This work confirms the importance of macrotexture (MaTx) and part of megatexture (MeTx) in the generation of rolling noise. The profilometer, mounted on a vehicle, is composed of a laser displacement sensor, an accelerometer, known in jargon as inertial unit and a rotary encoder attached to a wheel, which provides the horizontal travelled distance. This profilometer presents many strong points, viz. a simple usage and relative low cost compared to other laser profilometers; moreover it presents a new procedure to obtain the road profile by combining the information provided by the laser output, a time-domain displacement signal and a record of the distance travelled by the vehicle, measured by the angular encoder. Chapter 1 provides a description of the main terminology and devices used in profiling, while chapter 2 deals the essential theoretical background of the dominant phenomena involved in the generation of rolling noise and describes the main models that correlate rolling noise and road texture. Chapter 3 accurately explains every component the profilometer; it is roughly divided in two main parts, the first one outlines the hardware components specifications and limits, while the second part overviews the signal processing. An algorithm in Matlab environment for data processing was also developed, dealing with the re-mapping of the time-domain vertical displacement signal with a constant sampling frequency to a space-domain profile, sampled every 0.5 mm, and subsequent evaluation of road texture parameters has been conducted on different sites. A simple mathematical model of road texture enveloped by the tyre has also been used during data analysis, simulating the actual road surface that is in contact with the tyre. The following chapter addresses the possible sources of uncertainty of profiling operations. A theoretical model of the response of the laser sensor at different wavelengths has also been developed, taking into account the finite spot size of the laser and the finite exposure time of the pixel array. These two factors contribute to the identification of the working range of the sensor. Chapter 5 presents a calibration of the device and consequent assessment of reproducibility and repeatability of measurements. Calibration has dealt with every component singularly through specific measurements, such as measurements of the lateral profile of a rotating disc with cogs of different sizes, calibration of the accelerometer with a B&K calibrator and an oscillating bar, and the measurement of the profile of a surface with known characteristics. Repeatability of measurements has been thoroughly verified, via repetitions of measurements of the same road profile; reproducibility has been checked by measuring the same road profile with another profilometer already available on the market, and owned by the Department of Civil Engineering of Università di Pisa. Finally, an evaluation of the correlation between rolling noise and road texture is presented in chapter 6. Measurements of road texture provided by the profilometer are correlated with rolling noise emission on six different kinds of pavements: again, the chapter can be divided in two main sections. The former deals with the calculation of the correlation coefficient between parameters related to road texture, such as third-octave bands texture spectrum and rolling noise measured by CPX method, while the latter deals with the comparison of two existing models and the elaboration of a simple model to obtain the mean CPX broadband level of a road surface based the knowledge of its texture spectrum. The model uses two bands of the octave band texture spectrum, to predict rolling noise: the octave band centred at 5 mm, related to air pumping, is negatively correlated to sound generation, while the band at 80 mm shows a positive correlation, related to tyre vibrations. One of the main innovations of this model, despite the limited number of samples, is the usage of enveloped texture, which distinguishes road surfaces with sharp edges and deep grooves. The correlations found confirm the theoretical knowledge of tyre/road noise, but also underline that a complete description of rolling noise must take into account not only road texture, but also the tyre itself. In fact, a resonance in the CPX noise spectrum at 80 km/h was also successfully identified. The further perfectioning of the profilometer will permit deeper studies of the correlation between properties of road texture and rolling noise, and to develop a comprehensive model of tyre/road interaction noise: possible improvements are the simultaneous usage of two or more displacement sensors that profile adjacent lines, in order to reduce uncertainty in the evaluation of texture spectrum and the substitution of the current sensor with one that has a smaller spot size

Analysis of Tyre Rolling Noise on Low Noise Pavements

In this work, the relationship between Tyre-Road Noise (TRN) and road surface properties, such as road texture, Mean Profile Depth (MPD) and enveloped texture was studied from an experimental point of view. TRN was measured using the CPX method. The first step consisted in providing a model of the sound pressure field inside the tyre cavity using analytical calculations and a Finite Element Method (FEM) simulation, both in agreement with experimental measurements. These measurements were performed with a Tyre Cavity Noise (TCN) sensor, which was then used on-field to study the relationship between TCN and superficial properties of low noise pavements. Results show that noise inside the tyre cavity is greatly affected by road surface characteristics at frequencies below 1 kHz. The second step consisted in the study of the correlation between TRN outside emission and road texture. Results show that two indicators of TRN can be derived: a low frequency indicator and a high frequency indicator. The correlation between outside noise and cavity noise reveals that the two fields are similar at low frequency, but a model cannot be obtained with a straightforward approach, due to the intrinsic differences between the physical quantities. At last, models for forecasting the initial CPX levels from the Job Mix Formula and the acoustic ageing of low noise surfaces using traffic load, weather and pavement conditions were developed

Recent Developments in Sonic Crystals as Barriers for Road Traffic Noise Mitigation

Noise barriers are the most widespread solution to mitigate noise produced by the continuous growth of vehicular traffic, thus reducing the large number of people exposed to it and avoiding unpleasant effects on health. However, conventional noise barriers present the well-known issues related to the diffraction at the edges which reduces the net insertion loss, to the reflection of sound energy in the opposite direction, and to the complaints of citizens due to the reduction of field of view, natural light, and air flow. In order to avoid these shortcomings and maximize noise abatement, recent research has moved toward the development of sonic crystals as noise barriers. A previous review found in the literature was focused on the theoretical aspects of the propagation of sound through crystals. The present work on the other hand reviews the latest studies concerning the practical application of sonic crystal as noise barriers, especially for road traffic noise mitigation. The paper explores and compares the latest developments reported in the scientific literature, focused on integrating Bragg’s law properties with other mitigation effects such as hollow scatterers, wooden or recycled materials, or porous coating. These solutions could increase the insertion loss and frequency band gap, while inserting the noise mitigation action in a green and circular economy. The pros and cons of sonic crystal barriers will also be discussed, with the aim of finding the best solution that is actually viable, as well as stimulating future research on the aspects requiring improvement

Sensorless Predictive Algorithm for Permanent Magnet Brushless DC Drives

A high resolution speed and position identification algorithm, suitable for brushless DC drives, is presented in this paper. In particular, the algorithm is proposed for BLDC (brushless DC) machines that are characterized by an un-ideal trapezoidal emfs shape. The algorithm, which is developed basing upon the MRAS technique (model reference adaptive system) and the Popov’s Hyperstability criterion, guarantees the convergence of the estimated rotor speed and position signals to their corresponding actual values. The identification procedure can be performed starting from the knowledge of low resolution rotor position signals, phase currents and the BLDC emfs shape. The identification algorithm is properly tested on a BLDC drive controlled by a predictive algorithm, by performing a simulation study in the Matlab-Simulink environment. The corresponding results have highlighted the effectiveness of the proposed sensorless predictive control system, at both low and high speed operation