Визначення акустичної радіаційної сили, що діє на тверду сферичну частинку в пружній трубі з рідиною

Acoustic radiation force effect upon a rigid spherical particle placed in the thin elastic tube is studied. The problem of determination of the acoustic radiation forces acting on an obstacle in an ideal liquid is formulated with respect to the Lagrange coordinate system. Thus, the radiation pressure is defined as time-averaged value of the acoustic pressure over the obstacle surface. This approach is adequate if, at determining of the acoustic pressure in a fluid, the deviation of the pressure from the harmonic law in time domain is taken into account in the obstacle vicinity. An action of the acoustic radiation force on the rigid spherical particle placed in the thin tube with elastic wall is studied here for the case of the incident plane sound wave propagating along the tube axis. Model is developed to describe the response of the system consisting of the compliant infinite thin circular cylindrical tube filled with the ideal compressible liquid and rigid spherical body which is immovable and located on the tube axis under the plane wave propagating along the tube axis. The problem of the hydrodynamic characteristics determination is reduced to the solution of the infinite system of algebraic equations that can be solved by the reduction method. The formula for the acoustic radiation force calculation is derived to characterize the force acting upon rigid spherical particle in the thin compliant elastic cylindrical tube. Pages of the article in the issue: 38 - 41 Language of the article: UkrainianРозглянуто випадок поширення у вузькій циліндричній трубі плоскої поздовжньої звукової хвилі, в якій складові руху рідини, паралельні осі труби, мають значно більшу кінетичну енергію ніж складові, перпендикулярні осі труби. Дослідження дії акустичної радіаційної сили звукового поля на тверду сферичну частинку в заповненій ідеальною рідиною тонкостінній пружній циліндричній трубі проведено у два етапи: перший – розв’язання лінійної задачі розсіяння первинної хвилі на перешкодах; другий – обчислення гідродинамічних сил, які діють на сферичну частинку, з наступним осередненням їх в часі. Виведено формулу для обчислення акустичної радіаційної сили для такого випадку

Non-relativistic limit of multidimensional gravity: exact solutions and applications

It is found the exact solution of the Poisson equation for the multidimensional space with topology $M_{3+d}=\mathbb{R}^3\times T^d$. This solution describes smooth transition from the newtonian behavior $1/r_3$ for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior $1/r^{1+d}_{3+d}$ in opposite limit. In the case of one extra dimension $d=1$, the gravitational potential is expressed via compact and elegant formula. These exact solutions are applied to some practical problems to get the gravitational potentials for considered configurations. Found potentials are used to calculate the acceleration for point masses and gravitational self-energy.It is proposed models where the test masses are smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3 smeared extra dimensions, it is shown that the size of 3 rest extra dimensions can be enlarged up to submillimeter for the case of 1TeV fundamental Planck scale $M_{Pl(10)}$. In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the newtonian one regardless of size of the extra dimensions. Nevertheless, the hierarchy problem can be solved in these models.Comment: LaTex file, 18 pages, 4 figure

Взаємодія системи сторонніх об’єктів у рідині, обумовлена силами акустичного випромінювання

The problem of interaction of two foreign bodies placed in a liquid in an acoustic field propagating along the line connecting the bodies is under investigation. An approach is elaborated to characterize the interaction between the bodies caused by the acoustic radiation forces that are the time-constant components of hydrodynamic forces acting upon the bodies located in the outer liquidmedium. For example of the method application, propagation of the plane acoustic wave along the center line of two liquid spherical drops placed into a space filled with another liquid is under investigation. Study of the acoustic radiation forces is performed in the frame of two-step procedure. The first step comprises solution of the linear problem of incident wave diffraction on the bodies.The problem is solved by the variable separation method. To satisfy the boundary conditions on spherical surfaces, the expansion of the incident and reflected wave potentials over the spherical wave functions are used. The second step is calculation of the hydrodynamic forces acting upon each body followed by time averaging of forces determined. The analytical formula for the acoustic radiation force calculation is derived for the case under consideration.It is established that value of the acoustic radiation force affecting each liquid drop depends significantly on the incident wave frequency, densities, speed of sound in the outer and internal liquid as well as on the radius and distance between drops. Pages of the article in the issue: 104 - 107 Language of the article: UkrainianРозглянуто задачу про взаємодію двох сторонніх об’єктів, розташованих у рідині в полі акустичної хвилі, яка поширюється вздовж лінії розташування цих тіл. Узагальнено метод розв’язання задачі, який полягає у дослідженні лінійної задачі розсіювання первинної хвилі на сторонніх об’єктах, обчисленні гідродинамічних сил, які діють на кожний об’єкт, з наступним осередненням їх в часі. В рамках цього підходу виведено формулу для обчислення акустичної радіаційної сили (АРС) для випадку, коли сторонні тіла є краплями рідини, що розташовані в зовнішній рідині. Досліджено вплив на акустичну радіаційну силу частоти падаючої хвилі, відстані між краплями, їх радіусів і фізичних параметрів рідин

Про взаємодію сферичних крапель рідини в радіаційному полі акустичної хвилі

Propagation of the plane acoustic wave along the center line of two liquid spherical drops placed into a space filled with another liquid is under investigation. An approach is elaborated to characterize the interaction between the liquid drops caused by the acoustic radiation forces that are the time-constant components of hydrodynamic forces acting upon the drops located in the outer liquid. Investigation of the acoustic radiation forces influencing the drops in the acoustic field is performed in the frame of two-step procedure. The first step comprises solution of the linear problem of incident wave diffraction on the drops while the second one is calculation of the hydrodynamic forces acting upon each spherical drop followed by time averaging of forces determined. The analytical formula for the acoustic radiation force calculation is derived for the case under consideration. Pages of the article in the issue: 61 - 64 Language of the article: UkrainianРозглянуто випадок поширення плоскої акустичної хвилі вздовж лінії центрів двох сферичних крапель рідини, які знаходяться в іншій рідині, що заповнює весь простір. Розроблено підхід, який дозволяє встановити характер взаємодії крапель, обумовлений дією на краплі акустичних радіаційних сил – сталих в часі складових гідродинамічних сил, що діють в рідині на краплі. Дослідження дії на краплі акустичних радіаційних сил звукового поля проведено у два етапи: перший – розв’язання лінійної задачі розсіювання первинної хвилі на рідких краплях; другий – обчислення гідродинамічних сил, які діють на кожну сферичну краплю, з наступним осередненням їх в часі. Виведено формулу для обчислення акустичної радіаційної сили для досліджуваного випадку

Dynamical dark energy from extra dimensions

We consider multidimensional cosmological model with a higher-dimensional product manifold M = R x R^{d_0} x H^{d_1}/\Gamma where R^{d_0} is d_0-dimensional Ricci-flat external (our) space and H^{d_1}/\Gamma is d_1-dimensional compact hyperbolic internal space. M2-brane solution for this model has the stage of accelerating expansion of the external space. We apply this model to explain the late time acceleration of our Universe. Recent observational data (the Hubble parameter at the present time and the redshift when the deceleration parameter changes its sign) fix fully all free parameters of the model. As a result, we find that considered model has too big size of the internal space at the present time and variation of the effective four-dimensional fine structure constant strongly exceeds the observational limits.Comment: 5 pages, 3 figures, LaTex, a few remarks and reference adde

Latent solitons, black strings, black branes, and equations of state in Kaluza-Klein models

In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. We single out the physically interesting solution corresponding to a point-like mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the point-like mass soliton has dust-like equations of state in all spaces. We also obtain the PPN parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameter of the model: $\tau = -(2.1\pm 2.3)\times 10^{-5}$. The point-like mass solution contradicts this restriction. The condition $\tau=0$ satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. Black strings and black branes belong to this class. Moreover, the condition of stability of the internal spaces singles out black strings/branes from the latent solitons and leads uniquely to the black string/brane equations of state $p_i=-\epsilon/2$, in the internal spaces and to the number of the external dimensions $d_0=3$. The investigation of multidimensional static spherically symmetric perfect fluid with dust-like equation of state in the external space confirms the above results.Comment: 8 pages, Revtex4, no figures, minor changes adde

Kaluza-Klein models: can we construct a viable example?

In Kaluza-Klein models, we investigate soliton solutions of Einstein equation. We obtain the formulas for perihelion shift, deflection of light, time delay of radar echoes and PPN parameters. We find that the solitonic parameter k should be very big: |k|\geq 2.3\times10^4. We define a soliton solution which corresponds to a point-like mass source. In this case the soliton parameter k=2, which is clearly contrary to this restriction. Similar problem with the observations takes place for static spherically symmetric perfect fluid with the dust-like equation of state in all dimensions. The common for both of these models is the same equations of state in our three dimensions and in the extra dimensions. All dimensions are treated at equal footing. To be in agreement with observations, it is necessary to break the symmetry between the external/our and internal spaces. It takes place for black strings which are particular examples of solitons with k\to \infty. For such k, black strings are in concordance with the observations. Moreover, we show that they are the only solitons which are at the same level of agreement with the observations as in general relativity. Black strings can be treated as perfect fluid with dust-like equation of state p_0=0 in the external/our space and very specific equation of state p_1=-(1/2)\epsilon in the internal space. The latter equation is due to negative tension in the extra dimension. We also demonstrate that dimension 3 for the external space is a special one. Only in this case we get the latter equation of state. We show that the black string equations of state satisfy the necessary condition of the internal space stabilization. Therefore, black strings are good candidates for a viable model of astrophysical objects (e.g., Sun) if we can provide a satisfactory explanation of negative tension for particles constituting these objects.Comment: 11 pages, Revtex4, no figures, appendix and references adde