S. Haslinger, N. Movchan, A. Movchan, I. Jones, R. Craster
We address the problem of scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener-Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems to exhibit dynamic neutrality (perfect transmission) and localisation close to the structured interface.
{"title":"Controlling flexural waves in semi-infinite platonic crystals","authors":"S. Haslinger, N. Movchan, A. Movchan, I. Jones, R. Craster","doi":"10.1093/QJMAM/HBX005","DOIUrl":"https://doi.org/10.1093/QJMAM/HBX005","url":null,"abstract":"We address the problem of scattering and transmission of a plane flexural wave through a semi-infinite array of point scatterers/resonators, which take a variety of physically interesting forms. The mathematical model accounts for several classes of point defects, including mass-spring resonators attached to the top surface of the flexural plate and their limiting case of concentrated point masses. We also analyse the special case of resonators attached to opposite faces of the plate. The problem is reduced to a functional equation of the Wiener-Hopf type, whose kernel varies with the type of scatterer considered. A novel approach, which stems from the direct connection between the kernel function of the semi-infinite system and the quasi-periodic Green's functions for corresponding infinite systems, is used to identify special frequency regimes. We thereby demonstrate dynamically anisotropic wave effects in semi-infinite platonic crystals, with particular attention paid to designing systems to exhibit dynamic neutrality (perfect transmission) and localisation close to the structured interface.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123696813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Galilean transformation properties of different physical quantities are investigated from the point of view of four dimensional Galilean relativistic (non-relativistic) space-time. The objectivity of balance equations of general heat conducting fluids and of the related physical quantities is treated as an application.
{"title":"Generalized Galilean transformations of tensors and cotensors with application to general fluid motion","authors":"P. V'an, V. Ciancio, L. Restuccia","doi":"10.1478/AAPP.97S1A25","DOIUrl":"https://doi.org/10.1478/AAPP.97S1A25","url":null,"abstract":"Galilean transformation properties of different physical quantities are investigated from the point of view of four dimensional Galilean relativistic (non-relativistic) space-time. The objectivity of balance equations of general heat conducting fluids and of the related physical quantities is treated as an application.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"182 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133970289","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-06-29DOI: 10.1142/S0217984917500816
Sang-Hoon Kim, Sy Pham-Van, M. P. Das
A principle of an acoustic Eaton Lens array and its application as a removable tsunami wall is proposed theoretically. The lenses are made of expandable rubber pillars or balloons and create a stop-band by the rotating the incoming tsunami wave and reduce the pressure by canceling each other. The diameter of each lens is larger than the wavelength of the tsunami near the coast, that is, order of a kilometer. The impedance matching on the border of the lenses results in little reflection. Before a tsunami, the balloons are buried underground in shallow water near the coast in folded or rounded form. Upon sounding of the tsunami alarm, water and air are pumped into the pillars, which expand and erect the wall above the sea level within a few hours. After the tsunami, the water and air are released from the pillars, which are then buried underground for reuse. Electricity is used to power the entire process. A numerical simulation with a linear tsunami model was carried out.
{"title":"Acoustic Eaton lens array and its fluid application","authors":"Sang-Hoon Kim, Sy Pham-Van, M. P. Das","doi":"10.1142/S0217984917500816","DOIUrl":"https://doi.org/10.1142/S0217984917500816","url":null,"abstract":"A principle of an acoustic Eaton Lens array and its application as a removable tsunami wall is proposed theoretically. The lenses are made of expandable rubber pillars or balloons and create a stop-band by the rotating the incoming tsunami wave and reduce the pressure by canceling each other. The diameter of each lens is larger than the wavelength of the tsunami near the coast, that is, order of a kilometer. The impedance matching on the border of the lenses results in little reflection. Before a tsunami, the balloons are buried underground in shallow water near the coast in folded or rounded form. Upon sounding of the tsunami alarm, water and air are pumped into the pillars, which expand and erect the wall above the sea level within a few hours. After the tsunami, the water and air are released from the pillars, which are then buried underground for reuse. Electricity is used to power the entire process. A numerical simulation with a linear tsunami model was carried out.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"485 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133731108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
N. Jim'enez, Weichun Huang, V. Romero-Garc'ia, V. Pagneux, J. Groby
Using the concepts of slow sound and of critical coupling, an ultra-thin acoustic metamaterial panel for perfect and omnidirectional absorption is theoretically and experimentally conceived in this work. The system is made of a rigid panel with a periodic distribution of thin closed slits, the upper wall of which is loaded by Helmholtz Resonators (HRs). The presence of resonators produces a slow sound propagation shifting the resonance frequency of the slit to the deep sub-wavelength regime ($lambda/88$). By controlling the geometry of the slit and the HRs, the intrinsic visco-thermal losses can be tuned in order to exactly compensate the energy leakage of the system and fulfill the critical coupling condition to create the perfect absorption of sound in a large range of incidence angles due to the deep subwavelength behavior.
{"title":"Ultra-thin metamaterial for perfect and omnidirectional sound absorption","authors":"N. Jim'enez, Weichun Huang, V. Romero-Garc'ia, V. Pagneux, J. Groby","doi":"10.1063/1.4962328","DOIUrl":"https://doi.org/10.1063/1.4962328","url":null,"abstract":"Using the concepts of slow sound and of critical coupling, an ultra-thin acoustic metamaterial panel for perfect and omnidirectional absorption is theoretically and experimentally conceived in this work. The system is made of a rigid panel with a periodic distribution of thin closed slits, the upper wall of which is loaded by Helmholtz Resonators (HRs). The presence of resonators produces a slow sound propagation shifting the resonance frequency of the slit to the deep sub-wavelength regime ($lambda/88$). By controlling the geometry of the slit and the HRs, the intrinsic visco-thermal losses can be tuned in order to exactly compensate the energy leakage of the system and fulfill the critical coupling condition to create the perfect absorption of sound in a large range of incidence angles due to the deep subwavelength behavior.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124768959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
X. Bai, Chunyin Qiu, Xinhua Wen, Shasha Peng, M. Ke, Zhengyou Liu
Underwater sound isolation has been a long-standing fundamental issue in industry and military fields. Starting from a simple theoretical model, here an air-sealed metasurface is proposed to overcome this problem. Comparing with the sample without filling air, the effective impedance of the air-sealed one is greatly reduced and strikingly mismatch with water, accompanying another merit of low sound speed. Deeply suppressed sound transmission (~10-5) through such a metasurface is observed experimentally over a wide range of ultrasonic frequencies and incident angles.
{"title":"Highly efficient isolation of waterborne sound by an air-sealed metasurface","authors":"X. Bai, Chunyin Qiu, Xinhua Wen, Shasha Peng, M. Ke, Zhengyou Liu","doi":"10.1063/1.4983035","DOIUrl":"https://doi.org/10.1063/1.4983035","url":null,"abstract":"Underwater sound isolation has been a long-standing fundamental issue in industry and military fields. Starting from a simple theoretical model, here an air-sealed metasurface is proposed to overcome this problem. Comparing with the sample without filling air, the effective impedance of the air-sealed one is greatly reduced and strikingly mismatch with water, accompanying another merit of low sound speed. Deeply suppressed sound transmission (~10-5) through such a metasurface is observed experimentally over a wide range of ultrasonic frequencies and incident angles.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"03 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132795070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-05-02DOI: 10.13140/RG.2.1.3648.0880
J. Fricke
Three thought experiments demonstrate that under certain circumstances electromagnetic fields have to be attenuated or amplified multiplicatively in order not to violate the conservation of energy. Modulation of radiation by means other than superposition is theoretically made possible by plugging additional terms into the source slots of the Maxwell equations. Thus modulated radiation would enable the well focused stimulation of neurons for diagnostic and therapeutic purposes and for HCI applications.
{"title":"On Divergence in Radiation Fields","authors":"J. Fricke","doi":"10.13140/RG.2.1.3648.0880","DOIUrl":"https://doi.org/10.13140/RG.2.1.3648.0880","url":null,"abstract":"Three thought experiments demonstrate that under certain circumstances electromagnetic fields have to be attenuated or amplified multiplicatively in order not to violate the conservation of energy. Modulation of radiation by means other than superposition is theoretically made possible by plugging additional terms into the source slots of the Maxwell equations. Thus modulated radiation would enable the well focused stimulation of neurons for diagnostic and therapeutic purposes and for HCI applications.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121137240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the spectrum, which is slightly inharmonic. Therefore, the widespread scale of 12 equal divisions of the just octave is not the best choice to tune instruments like the piano. Basing on the theory of dissonance, we provide a way to tune the piano in order to improve its consonance. A good solution is obtained by tuning a note and its fifth by minimizing their beats.
{"title":"The wave equation for stiff strings and piano tuning","authors":"Xavier Gràcia, Tomás Sanz-Perela","doi":"10.2436/20.2002.02.11","DOIUrl":"https://doi.org/10.2436/20.2002.02.11","url":null,"abstract":"We study the wave equation for a string with stiffness. We solve the equation and provide a uniqueness theorem with suitable boundary conditions. For a pinned string we compute the spectrum, which is slightly inharmonic. Therefore, the widespread scale of 12 equal divisions of the just octave is not the best choice to tune instruments like the piano. Basing on the theory of dissonance, we provide a way to tune the piano in order to improve its consonance. A good solution is obtained by tuning a note and its fifth by minimizing their beats.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132787360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dielectric is considered in the electric field that has equal to zero the first moment and different from zero the second moment of strength in an equilibrium. The equations of ideal hydrodynamics are obtained in such a field for the case of the neglect of dissipative effects. A new variable - the second moment of electric field strength is included in the Euler equation. A temporal equation for this variable is obtained on the basis of Maxwell equations in the hydrodynamic approximation. Adiabatic one-dimensional waves of small amplitude are studied in this system. Proceeding from the theoretical estimation of the intracrystalline field in an ionic crystal the good consent of the obtained numerical values of transversal velocity of this wave with transversal velocity of sound for isotropic crystals of alkali halides is found.
{"title":"Adiabatic hydrodynamic modes in dielectric environment in a random electric field","authors":"A. Stupka","doi":"10.22364/mhd.50.1.2","DOIUrl":"https://doi.org/10.22364/mhd.50.1.2","url":null,"abstract":"Dielectric is considered in the electric field that has equal to zero the first moment and different from zero the second moment of strength in an equilibrium. The equations of ideal hydrodynamics are obtained in such a field for the case of the neglect of dissipative effects. A new variable - the second moment of electric field strength is included in the Euler equation. A temporal equation for this variable is obtained on the basis of Maxwell equations in the hydrodynamic approximation. Adiabatic one-dimensional waves of small amplitude are studied in this system. Proceeding from the theoretical estimation of the intracrystalline field in an ionic crystal the good consent of the obtained numerical values of transversal velocity of this wave with transversal velocity of sound for isotropic crystals of alkali halides is found.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125193478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper deals with the generic problem of two waveguides coupled by perforations, which can be perforated tube mufflers without or with partitions, possibly with absorbing materials. Other examples are ducts with branched resonators of honeycomb cavities , which can be coupled or not, and splitter silencers. Assuming low frequencies, only one mode is considered in each guide. The propagation in the two waveguides can be very different, thanks e.g. to the presence of constrictions. The model is a discrete, periodic one, based upon 4th-order impedance matrices and their diagonalization. All the calculation is analytical, thanks to the partition of the matrices in 2nd-order matrices, and allows the treatment of a very wide types of problems. Several aspects are investigated: the local or non-local character of the reaction of one guide to the other; the definition of a coupling coefficient; the effect of finite size when a lattice with n cells in inserted into an infinite guide; the relationship between the Insertion Loss and the dispersion. The assumptions are as follows: linear acoustics, no mean flow, rigid wall. However the effect of the series impedance of the perforations, which is generally ignored, is taken into account, and is dis- cussed. When there are no losses, it is shown that, for symmetry reasons, the cutoff frequencies depend on either the series impedance or the shunt admittance , and are the eigenfrequencies of the cells of the lattice, with zero-pressure or zero-velocity at the ends of the cells.
{"title":"Propagation of acoustic waves in two waveguides coupled by perforations. II. Application to periodic lattices of finite length","authors":"M. Pachebat, J. Kergomard","doi":"10.3813/AAA.918978","DOIUrl":"https://doi.org/10.3813/AAA.918978","url":null,"abstract":"The paper deals with the generic problem of two waveguides coupled by perforations, which can be perforated tube mufflers without or with partitions, possibly with absorbing materials. Other examples are ducts with branched resonators of honeycomb cavities , which can be coupled or not, and splitter silencers. Assuming low frequencies, only one mode is considered in each guide. The propagation in the two waveguides can be very different, thanks e.g. to the presence of constrictions. The model is a discrete, periodic one, based upon 4th-order impedance matrices and their diagonalization. All the calculation is analytical, thanks to the partition of the matrices in 2nd-order matrices, and allows the treatment of a very wide types of problems. Several aspects are investigated: the local or non-local character of the reaction of one guide to the other; the definition of a coupling coefficient; the effect of finite size when a lattice with n cells in inserted into an infinite guide; the relationship between the Insertion Loss and the dispersion. The assumptions are as follows: linear acoustics, no mean flow, rigid wall. However the effect of the series impedance of the perforations, which is generally ignored, is taken into account, and is dis- cussed. When there are no losses, it is shown that, for symmetry reasons, the cutoff frequencies depend on either the series impedance or the shunt admittance , and are the eigenfrequencies of the cells of the lattice, with zero-pressure or zero-velocity at the ends of the cells.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121020702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Analytical expressions for the axial and transverse acoustic radiation forces as well as the radiation torque per length are derived for a rigid elliptical cylinder placed arbitrarily in the field of in plane progressive, quasi-standing or standing waves. The rigid elliptical cylinder case is important to be considered as a first-order approximation of the behavior of a fluid particle suspended in air, because of the significant acoustic impedance mismatch at the particle's boundary. Based on the partial-wave series expansion method in cylindrical coordinates, non-dimensional acoustic radiation force and torque functions are derived and defined in terms of the scattering coefficients of the elliptic cylinder. A coupled system of linear equations is obtained after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. Computational results for the non-dimensional force components and torque, showing the transition from the progressive to the (equi-amplitude) standing wave behavior, are performed with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes of the ellipse, the dimensionless size parameter, as well as the angle of incidence ranging from end-on to broadside incidence. The results show that the elliptical geometry has a direct influence on the radiation force and torque, so that the standard theory for circular cylinders (at normal incidence) leads to significant miscalculations when the cylinder cross-section becomes non-circular. Moreover, the elliptical cylinder experiences, in addition to the acoustic radiation force, a radiation torque that vanishes for the circular cylinder case. The application of the formalism presented here may be extended to other 2D surfaces of arbitrary shape.
{"title":"Radiation forces and torque on a rigid elliptical cylinder in acoustical plane progressive and (quasi)standing waves with arbitrary incidence","authors":"F. Mitri","doi":"10.1063/1.4959071","DOIUrl":"https://doi.org/10.1063/1.4959071","url":null,"abstract":"Analytical expressions for the axial and transverse acoustic radiation forces as well as the radiation torque per length are derived for a rigid elliptical cylinder placed arbitrarily in the field of in plane progressive, quasi-standing or standing waves. The rigid elliptical cylinder case is important to be considered as a first-order approximation of the behavior of a fluid particle suspended in air, because of the significant acoustic impedance mismatch at the particle's boundary. Based on the partial-wave series expansion method in cylindrical coordinates, non-dimensional acoustic radiation force and torque functions are derived and defined in terms of the scattering coefficients of the elliptic cylinder. A coupled system of linear equations is obtained after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. Computational results for the non-dimensional force components and torque, showing the transition from the progressive to the (equi-amplitude) standing wave behavior, are performed with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes of the ellipse, the dimensionless size parameter, as well as the angle of incidence ranging from end-on to broadside incidence. The results show that the elliptical geometry has a direct influence on the radiation force and torque, so that the standard theory for circular cylinders (at normal incidence) leads to significant miscalculations when the cylinder cross-section becomes non-circular. Moreover, the elliptical cylinder experiences, in addition to the acoustic radiation force, a radiation torque that vanishes for the circular cylinder case. The application of the formalism presented here may be extended to other 2D surfaces of arbitrary shape.","PeriodicalId":331413,"journal":{"name":"arXiv: Classical Physics","volume":"223 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114691484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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