**International Institute of Zakharenko Waves
(IIZWs)**

The International Institute of Zakharenko waves
(IIZWs) is created for support of different Zakharenko waves, as well as for
monitoring the non-dispersive Zakharenko type waves in complex systems such as
layered and quantum systems. Indeed, any complex system, where dispersive waves
(for example, dispersive Rayleigh and Bleustein-Gulyaev type waves as well as
Love and Lamb type waves) can propagate, is of a great interest for the
Institute. The Institute will study different dispersive and non-dispersive
waves both theoretically and experimentally, including different applications
of the waves for signal processing (filters, sensors, etc.) and the so-called
structural health monitoring. Therefore, any interest from individuals and
Institutions/Organizations is welcomed.

Several “hot” MS/PhD-projects (theoretical and,
possibly, experimental) are available starting in 2007/2008:

**1. ****Analytical studying the group velocity of Lamb type
waves in isotropic and anisotropic non-piezoelectric mono-plates.**

**2. ****Analytical studying the group velocity of the second
type of slow surface Zakharenko type waves.**

**3. ****Analytical studying the
group velocity of Love waves propagating in layered systems consisting of two
layers on a substrate (non-piezoelectric case).**

**4. ****Analytical studying the
group velocity of Love waves propagating in layered systems consisting of a
piezo-layer on a substrate.**

**5. ****Analytical studying the
group velocity of Love waves propagating in layered systems consisting of a
layer on a piezo-substrate.**

**6. ****Photonic crystals: analytical studying the group velocity.**

**7. ****Phononic crystals: analytical studying the group velocity.**

**8.
****Further monitoring of existence of the non-dispersive
Zakharenko waves in complex layered systems.**

**9. ****Further monitoring of
existence of the non-dispersive Zakharenko waves in quantum systems. **

**10. ****Analytical studying the
group velocity of dispersive Bleustein-Gulyaev waves propagating in layered
systems consisting of a piezo-layer on a substrate.**

**11. ****Analytical studying the
group velocity of dispersive Bleustein-Gulyaev waves propagating in layered
systems consisting of a layer on a piezo-substrate.**

**12. ****Analytical studying the
group velocity of dispersive Rayleigh type waves propagating in layered systems
consisting of isotropic layer on isotropic substrate (this is a very
complicated case, but an attempt can readily be done).**

**13. ****Analytical studying the group velocity of Lamb type
waves in isotropic non-piezoelectric bi-layered plates (this is a very complicated case, but an attempt can readily be done).**

**Possible additional
projects:**

**1. ****On anisotropy of
non-cubic crystals**** for new supersonic
in-plane surface waves. **Here, It was recently found that new supersonic surface waves with in-plane
polarization, see the paper [1]. However, such materials must be found or
synthesized. There is even a bet such as what will be found first, materials
possessing the room temperature superconductivity (RTSC) or the ones possessing
the new supersonic surface in-plane wave. Note that looking for the RTSC caused
a wide research concerning fabrication of very complex materials and
characterization of their structure and physical properties during the last two
decades. However, RTCS materials are still not found! For finding the RTSC,
trillions US-dollars were spent and over hundred thousands papers were already
published, but we have now the same result that was at the starting point two
decades ago.

**2. ****Analytical investigation
of the group/phase velocity for dispersive waves propagating in an isotropic
cylinder covered with isotropic thin film****. **Here, knowledge of cylindrical functions
such as Bessel, Neumann and Hankel functions is welcomed.

**3. S****low surface Zakharenko
waves (SSZTW7) in piezoelectric layered structures****.** The SSZtW7-waves (soliton-like phonons for some wavenumbers)
can be calculated and shown for several suitable layered systems.

**4. Lamb
type waves investigations for smart systems.**

**5.
Studying the ultrasonic surface Zakharenko waves (USZWs) in piezoelectric
layered systems.**

**6. The
phenomenon called “(non-dispersive?) Rydberg quasi-particles”:** the applicant task will be
phenomenon history, Rydberg biography, as well as looking for new ways to better
understand/explain the phenomenon. It is noted that because definition of a
quasi-particle (atom or electron) requires the dispersion relation with the
constant relationship between the phase Vph and group Vg velocities such as
Vg=2Vph (that gives the constant value of the Planck’s constant for any
quasi-particle), but non-dispersive waves require Vg=Vph<>0. Note that
the corresponding non-dispersive Zakharenko wave exists in each quantum energy
branch. It is also noted that the special case of Vg=Vph=0 is readily
identified as the so-called Bose-Einstein condensation and the points of
Vg=Vph=0 represent inflection points for both Vph and Vg of dispersive waves. Very
small atoms (for instant, hydrogen atoms) can have the electrons moving very
quickly, close to the nucleus that can be normally true. And when an electron
in an atom is excited with a laser, it can "jump" to very large
orbits. Such electrons are called Rydberg electrons, and they are the subject
of active research, both experimentally and theoretically.

**7. Investigations
of Love as well as dispersive Rayleigh and Bleustein-Gulyaev type waves** in multi-layered structures, for
instants, two layers on a substrate, accounting piezoelectric, piezomagnetic
effects; giant piezo- and dielectric effects, etc.

**Recent Publications**:

1) A.A. Zakharenko. On cubic crystal anisotropy for waves with Rayleigh-wave
polarization. *Non-destructive
Testing and Evaluation* **21** (2) 61
– 77 (2006).

2) A.A. Zakharenko. Love type waves in layered systems consisting of two
piezoelectric cubic crystals. *Journal
of Sound and Vibration*, **285** (4–5)
877 – 886 (2005).

3) A.A. Zakharenko. Analytical studying the group velocity of three-partial
Love (type) waves in both isotropic and anisotropic media. *Non-destructive Testing and Evaluation* **20** (4) 237 – 254 (2005).

4) A.A. Zakharenko. Different dispersive waves of bulk elementary excitations
in bulk superfluid helium–II at low temperatures. *In* *the CD-ROM Proceedings of
the Forum Acusticum*,

5) A.A. Zakharenko. Dispersive Rayleigh type waves in layered systems
consisting of piezoelectric crystals bismuth silicate and bismuth germanate.
*Acta Acustica united with Acustica*, **91** (4) 708 – 715 (2005).

**Requirements for
applicants:** good
knowledge of a computer language (Fortran, Pascal/Delphi, C++; Matlab/Maple is
very useful and preferable). Also, it must be good knowledge of mathematics:
matrices, tensors, constitutive equations, equations of motions, eigenvalues
and eigenvectors, the Leibniz’s formulae for complicated derivatives {d(uv)/dx,
d(u/v)/dx, d(u(v(g(x))))/dx, etc.}, etc. Note that both the phase and group
velocities are complicated functions. It is obvious that each hot project will
allow for a prospective candidate to feel theoretical problems and to use theory
for filter and sensor applications (delay lines, chemical and biosensors), as
well as there are possibilities to propose new acoustic-wave devices (that is
also true for optical devices on different dispersive waves). For instance, for
dispersive delay lines, the delay time has an inflexion point that is used. Also,
it is already well-known that sensor sensitivity is proportional to the first
derivative of the phase velocity *Vph*,
d*Vph*/d(*kh*) with *k* and *h* being the wavenumber and thickness,
respectively. Theoretically obtained results can be published in international
science Journals. Standard mathematical problem of finding extreme and
inflexion points of the phase/group velocity for dispersive waves propagating
in layered systems can give information about possible existence of the
non-dispersive Zakharenko waves in dispersive-wave modes. Note that such the
theoretical investigations were recently carried out for Love waves in Ref. [3]
and are very useful to completely understand layered structures. The
non-dispersive Zakharenko waves existing in layered [5] and quantum [4] systems
mathematically represent extreme points of the phase velocity Vph and split a
dispersive mode into several sub-modes. The hot projects represent research
which should have already been done in the last century, but they are still not
carried out due to significant complexity. The aim of the hot projects is to
create solid fundament for further research.

Send Your CV for MS or CV with a Diploma Copy
for PhD by E-mail, illuminating a project title written above. Female
applicants with good basis in mathematics are also welcomed. Different funding
possibilities, for instance, from the DAAD/Others for West European citizens or
private sponsorships can be also treated.

Contact preferably by E-mail (aazaaz@inbox.ru) to Mr. Aleksey A. Zakharenko,
Diploma Engineer-Physicist, IIZWs. Also, applicants from