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Three different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are…
This paper introduces two mechanisms for computing over-approximations of sets of reachable states, with the aim of ensuring termination of state-space exploration. The first mechanism consists in over-approximating the automata…
In their comment, Murphy et al. (arxiv:0708.3677) criticize the fitting procedure we used in two previous papers [Srianand et al. 2004(Paper I) and Chand et al. 2004 (Paper II)] and conclude that the above papers offers no stringent test to…
We investigate the influence of the additional third level on the dynamic evolution of a Two-Level system interacting with a coherent field in the strong coupling regime where Rotating Wave Approximation is not valid. We find that the…
The paper by Bowen, Mancini, Fessatidis, and Murawski (2012 Phys. Scr. {\bf 85}, 065005) demonstrates in a dramatic fashion the serious difficulties that can arise when one rushes to perform numerical studies before understanding the…
We discuss generic limits posed by the trap in atomic systems on the accurate determination of critical parameters for second-order phase transitions, from which we deduce optimal protocols to extract them. We show that under current…
Recent FDA guidance on adaptive clinical trial designs defines bias as "a systematic tendency for the estimate of treatment effect to deviate from its true value", and states that it is desirable to obtain and report estimates of treatment…
Applications' performance is influenced by the mapping of processes to computing nodes, the frequency and volume of exchanges among processing elements, the network capacity, and the routing protocol. A poor mapping of application processes…
Statistical estimation of the prediction uncertainty of physical models is typically hindered by the inadequacy of these models due to various approximations they are built upon. The prediction errors due to model inadequacy can be handled…
We interpret anomalies, deviations, from the standard model as being in fact due to effects not given by perturbation, because the top Yukawa coupling is after all so large that not by perturbation effects become important. Most of the…
We investigate the performance of parallel and adaptive quantum channel discrimination strategies for a finite number of channel uses. It has recently been shown that, in the asymmetric setting with asymptotically vanishing type I error…
A theoretical model is presented which allows to reconcile findings of scanning tunnelling spectroscopy for (Ga,Mn)As [Richardella et al. Science 327, 66 (2010)] with results for tunneling across (Ga,Mn)As thin layers [Ohya et al. Nature…
An inadequate approximation and its consequences as well as an incorrect statement made in cond-mat/0102150v2 are pointed out.
We map molecular dynamics simulations of fluid-fluid interfaces onto mesoscale continuum theories for partially miscible fluids. Unlike most previous work, we examine not only the interface order parameter and density profiles, but also the…
We show that the ``effective Lagrangian'' constructed in [1] is inconsistent with the exact result for the complete Lagrangian presented in [2]. We trace the origin of the inconsistence to the peculiar way in which the path integral methods…
The paper has been withdrawn due to an error in Lemma 1.
We learn mathematics subjectively and must apply it objectively. But sometimes, we apply it subjectively by using wrong intuitions which may be elusive to our eyes. The aim of this note is to disclose the secretes of two kinds of these…
We obtain a criterion for approximability by embeddings of piecewise linear maps of a circle to the plane, analogous to the one proved by Minc for maps of a segment to the plane. Theorem. Let S be a triangulation of a circle with s…
Mechanistic interpretability aims to understand model behaviors in terms of specific, interpretable features, often hypothesized to manifest as low-dimensional subspaces of activations. Specifically, recent studies have explored subspace…
Recent experimental results showing untypical nonlinear absorption and marked deviations from well known universality in the low temperature acoustic and dielectric losses in amorphous solids prove the need for improving the understanding…