# In Print

## Three-dimensional stability of leapfrogging quantum vortex rings

21 September in 11:30

V.P. Ruban

It is shown by numerical simulations within a regularized Biot-Savart law
that dynamical systems of two or three leapfrogging coaxial quantum vortex
rings having a core width $\xi$ and initially placed near a torus of radii
$R_0$ and $r_0$, can be three-dimensionally (quasi-)stable in some regions
of parameters $\Lambda=\ln(R_0/\xi)$ and $W=r_0/R_0$. At fixed $\Lambda$,
stable bands on $W$ are intervals between non-overlapping main parametric
resonances for different (integer) azimuthal wave numbers $m$.
The stable intervals are most wide ($\Delta W\sim$ 0.01--0.05) between
$m$-pairs $(1,2)$ and $(2,3)$ at $\Lambda\approx$ 4--12 thus corresponding
to micro/mesoscopic sizes of vortex rings in the case of superfluid $^4$He.
With four and more rings, at least for $W>0.1$, resonances
overlap for all $\Lambda$ and no stable domains exist.

## Synchronization of Conservative Parallel Discrete Event Simulations on a Small-World Network

7 September in 11:30

__Lev N. Shchur__и Liliia Ziganurova

We examine the question of the influence of sparse long-range communications on the synchronization in parallel discrete event simulations (PDES). We build a model of the evolution of local virtual times (LVT) in a conservative algorithm including several choices of local links. All network realizations belong to the small-world network class. We find that synchronization depends on the average shortest path of the network. The time profile dynamics are similar to the surface profile growth, which helps to analyze synchronization effects using a statistical physics approach. Without long-range links of the nodes, the model belongs to the universality class of the Kardar–Parisi–Zhang equation for surface growth. We find that the critical exponents depend logarithmically on the fraction of long-range links. We present the results of simulations and discuss our observations.

## Quantum Many-Body Physics of Qubits

22 June in 11:30

L. Glazman (Yale University)

The ongoing development of superconducting qubits has brought some basic questions of many-body physics to the research forefront, and in some cases helped solving them. I will address two effects in quantum condensed matter highlighted by the development of a fluxonium qubit. The first one is the so-called cosine-phi problem stemming from the seminal paper of Brian Josephson: the predicted there phase dependence of the dissipative current across a Josephson junction was observed in a fluxonium, after nearly 50 years of unsuccessful attempts by other techniques. The second one is the dynamics of a weakly-pinned charge density wave: we predict that the dynamics may be revealed in measurements of microwave reflection off a superinductor, which is a key element of the fluxonium.

## Lazernoe vozdeistvie na veshchestvo: sovremennoe sostoyanie

15 June in 11:30

Anisimov S.I.,

__Inogamov N.A.__, Petrov Yu.P., Khokhlov V.A.
V doklade aktsentiruetsya vnimanie na sravnenii rezhimov oblucheniya s raznoi dlitel’nost’yu impul’sa.
V odnom sluchae eto ul’trakorotkie lazernye impul’sy (UkLI), v drugom subnanosekundnye. Ul’trakorotkimi nazyvayut impul’sy prodolzhitel’nost’yu poryadka pikosekund i koroche, t.e. i 2 ps, i 10 fs - eto UkLI. Rech’ idet o vozdeistvii na metall cherez prozrachnuyu sredu. Prozrachnaya sreda mozhet byt’ tverdoi, a mozhet byt’ zhidkoi. Ponyatno, chto energetika takogo vozdeistviya ogranichena, poskol’ku neobkhodimo izbegat’ razvitogo opticheskogo proboya prozrachnoi sredy - takoi proboi otsekaet lazernoe izluchenie ot metallicheskoi misheni. Zadacha imeet vazhnye prilozheniya v fizike lazernoi ablyatsii v zhidkost’, ablyatsii, soprovozhdayushcheisya generatsiei nanochastits i formirovaniem kolloidov. Eto burno rastushchee nauchno-tekhnologicheskoe napravlenie, ob’edinyayushchee fiziku lazernogo vozdeistviya i khimiyu protsessov mezhdu produktami ablyatsii i zhidkost’yu, predstavlennuyu rastvorami solei ili organiki.
Vo vtoroi chasti doklada daetsya obzor rezul’tatov, poluchennykh za poslednie dva goda.
Razlichnye razdely raboty vypolneny v sootvetstvii s goszadaniem i po grantam RNF (14-19-01599) i RFFI (16-02-00864, 16-08-01181).

## Dynamics of Poles in 2D Hydrodynamics with Free Surface: New Constants of Motion

8 June in 11:30

A. I. Dyachenko, S. A. Dyachenko,

__P. M. Lushnikov__and V. E. Zakharov
We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. We admit a presence of gravity forces and surface tension. A time-dependent conformal mapping z(w,t) of the
lower complex half-plane of the variable w into the area filled with fluid is performed with the real line of w mapped into the free fluid's surface. We study the dynamics of singularities of both z(w,t) and the complex fluid potential Pi(w,t) in the upper complex half-plane of w. We show the existence of solutions with an arbitrary finite number N of simple complex poles in z_w(w,t) and Pi_w(w,t) which are the derivatives of z(w,t) and Pi(w,t) over w. These poles are often coupled with branch points located at other points of the upper half-plane of w. We find that the residues of
the simple poles of z_w(w,t) are new, previously unknown constants of motion, provided surface tension is zero. All these constants of motion commute with each other in the sense of underlying Hamiltonian dynamics. In absence of both gravity and
surface tension, the residues of simple poles of Pi_w(w,t) are also the constants of motion. For nonzero gravity and zero surface tension, the residues of poles of any order of Pi_w(w,t) are the trivial linear functions of time. Nonzero surface tension allows residues of poles of even order to be compatible with the fluid dynamics. We also found solutions with N higher order poles. In all above cases the number of independent real integrals of motion is 4N for zero gravity and 4N-1 for nonzero gravity. We suggest that the existence of these nontrivial constants of motion provides an argument in support of the conjecture of complete integrability of free surface hydrodynamics in deep water.

## Spetsial’naya geometriya v strunnykh kompaktifikatsiyakh i kiral’nye algebry

1 June in 11:30

Konstantin Aleshkin

V doklade ya planiruyu izlozhit’ nedavnie uspekhi v vychislenii geometrii prostranstv moduleimnogoobrazii Kalabi-Yau, neobkhodimykh dlya opisaniya nizkoenergetichnogo predela teorii strun. Sovmestno s A. Belavinym nami byli polucheny obshchie formuly dlya normalizatsii konstant svyazi nizkoenergetichnoi teorii (spetsial’naya geometriya). A imenno, ispol’zuya svyaz’ s kiral’nymi algebrami, my napisali yavnye formuly v vide ryadov dlya spetsial’noi geometrii dlya klassov mnogoobrazii Kalabi-Yau tipa Ferma.