Phase diagram of the 2D 4^4He in the density-temperature plane

Thin $^4$He films adsorbed to weakly attractive substrates form nearly 2D layers. We describe the vortices in 2D superfluid $^4$He like quasiparticles. With the aid of a variational many-body calculation we estimate their inertial mass and describe their interactions with the $^4$He particles and other vortices. Third sound measurements revealed anomalous behavior below the BKT-phase transition temperature. We ascribe this to the sound mode traveling in the fluid of vortex-antivortex pairs. These pairs forms a crystal (or liquid crystal) when the film thickness increases, the third sound mode splits into two separate modes as seen in experiments. Our many-body calculation predicts the critical density, at which the phase transition into the vortex-antivortex state at zero temperature occurs. We also describe the phase diagram of thin $^4$He films.Comment: Contribution paper to LT21 (to be published in Physica B

Structure of metastable 2D liquid helium

We present diffusion Monte Carlo (DMC) results on a new metastable, superfluid phase above the crystal ground state in two-dimensional 4He at densities > 0.065 1/A^2. The state is anisotropic with hexatic orbital order. This implies that the liquid--solid phase transition has two stages: A second order phase transition from the isotropic superfluid to the hexatic superfluid, followed by a first order transition that localizes atoms into the triangular crystal order. This metastable hexatic phase has finite condensate fraction and it provides a natural explanation for the superflow in the supersolid grain boundaries

Dipolar clusters and ferroelectricity in high Tc superconductors

In this paper, we show that doping of hole charge carriers induces formation of resonance plaquettes (RPs) having electric dipolar moments and fluctuating stripes in cuprates. A single RP is created by many-body interactions between the dopant ion or a charge fluctuation outside and holes inside the CuO plane. In such a process, Coulomb interacting holes in the CuO plane are self-organized into four-particles resonance valence bond plaquettes bound with dopants or polarons located in the spacer layer between CuO planes. Such RPs have ordered and disordered phases. They are ordered into charge density waves (CDW) or stripes only at certain conditions. The lowest energy of the ordered phase corresponds to a local antiferroelectric ordering. The RPs mobility is very low at low temperatures and they are bound into dipole–dipole pairs. Electromagnetic radiation interacts strongly with RPs electric dipoles and when the sample is subjected to it, the mobility changes significantly. This leads to a fractal growth of dipolar RP clusters. The existence of electric dipoles and CDW reveal a series of new phenomena such as ferroelectricity, strong light and microwave absorption and the field induced superconductivity

Palindromic Length of Words with Many Periodic Palindromes

The palindromic length $\text{PL}(v)$ of a finite word $v$ is the minimal number of palindromes whose concatenation is equal to $v$. In 2013, Frid, Puzynina, and Zamboni conjectured that: If $w$ is an infinite word and $k$ is an integer such that $\text{PL}(u)\leq k$ for every factor $u$ of $w$ then $w$ is ultimately periodic. Suppose that $w$ is an infinite word and $k$ is an integer such $\text{PL}(u)\leq k$ for every factor $u$ of $w$. Let $\Omega(w,k)$ be the set of all factors $u$ of $w$ that have more than $\sqrt[k]{k^{-1}\vert u\vert}$ palindromic prefixes. We show that $\Omega(w,k)$ is an infinite set and we show that for each positive integer $j$ there are palindromes $a,b$ and a word $u\in \Omega(w,k)$ such that $(ab)^j$ is a factor of $u$ and $b$ is nonempty. Note that $(ab)^j$ is a periodic word and $(ab)^ia$ is a palindrome for each $i\leq j$. These results justify the following question: What is the palindromic length of a concatenation of a suffix of $b$ and a periodic word $(ab)^j$ with "many" periodic palindromes? It is known that $\lvert\text{PL}(uv)-\text{PL}(u)\rvert\leq \text{PL}(v)$, where $u$ and $v$ are nonempty words. The main result of our article shows that if $a,b$ are palindromes, $b$ is nonempty, $u$ is a nonempty suffix of $b$, $\vert ab\vert$ is the minimal period of $aba$, and $j$ is a positive integer with $j\geq3\text{PL}(u)$ then $\text{PL}(u(ab)^j)-\text{PL}(u)\geq 0$

Utveckling av temperaturreguleringskapacitet hos renkalvar

Utveckling av temperaturregleringskapacitet hos nyfodda renkalvar undersöktes vid Paliskuntain Yhdistys (Foreningen for Renbeteslagen) försoksstation i Kaamanen under maj-juli 1981-82

The role of exchangeability in causal inference

The notion of exchangeability has been recognized in the causal inference literature in various guises, but only rarely in the original Bayesian meaning as a symmetry property between individual units in statistical inference. Since the latter is a standard ingredient in Bayesian inference, we argue that in Bayesian causal inference it is natural to link the causal model, including the notion of confounding and definition of causal contrasts of interest, to the concept of exchangeability. Here we relate the Bayesian notion of exchangeability to alternative conditions for unconfounded inferences, commonly stated using potential outcome variables, and define causal contrasts in the presence of exchangeability in terms of limits of posterior predictive expectations for further exchangeable units. We demonstrate that this reasoning also carries over to longitudinal settings where parametric inferences are susceptible to the so-called null paradox. We interpret the paradox in terms of an exchangeability assumption made on too coarse a scale