Orientation of a chiral smectic C elastomer by mechanical fields

It is well known that, with respect to the director, nematic elastomers can be macroscopically aligned by uniaxial mechanical fields. Extending this method to a chiral smectic C elastomer, depending on the experimental set-up either smectic layer orientation or director orientation parallel to the stress axis occurs. In order to align the director and the smectic layers a biaxial mechanical field (e.g. shear field) consistent with the phase symmetry has to be used to achieve a macroscopically uniform orientation of the untwisted smectic C^* structure.     

Automatic β-expansions of formal Laurent series over finite fields

We consider β-expansions of formal Laurent series over finite fields. If the base β is a Pisot or Salem series, we prove that the β-expansion of a Laurent series α is automatic if and only if α is algebraic.     

Comparison of Force Fields on the Basis of Various Model Approaches—How To Design the Best Model for the [CnMIM][NTf2] Family of Ionic Liquids

In this contribution, we present two new united‐atom force fields (UA‐FFs) for 1‐alkyl‐3‐methylimidazolium bis(trifluoromethylsulfonyl)imide [C_nMIM][NTf₂] (n=1, 2, 4, 6, 8) ionic liquids (ILs). One is parametrized manually, and the other is developed with the gradient‐based optimization workflow (GROW). By doing so, we wanted to perform a hard test to determine how researchers could benefit from semiautomated optimization procedures. As with our already published all‐atom force field (AA‐FF) for [C_nMIM][NTf₂] (T. Köddermann, D. Paschek, R. Ludwig, ChemPhysChem­ 2007, 8, 2464 ), the new force fields were derived to fit experimental densities, self‐diffusion coefficients, and NMR rotational correlation times for the IL cation and for water molecules dissolved in [C₂MIM][NTf₂]. In the manual force field, the alkyl chains of the cation and the CF₃ groups of the anion were treated as united atoms. In the GROW force field, only the alkyl chains of the cation were united. All other parts of the structures of the ions remained unchanged to prevent any loss of physical information. Structural, dynamic, and thermodynamic properties such as viscosity, cation rotational correlation times, and heats of vaporization calculated with the new force fields were compared with values simulated with the previous AA‐FF and the experimental data. All simulated properties were in excellent agreement with the experimental values. Altogether, the UA‐FFs are slightly superior for speed‐up reasons. The UA‐FF speeds up the simulation by about 100 % and reduces the demanded disk space by about 78 %. More importantly, real time and efforts to generate force fields could be significantly reduced by utilizing GROW. The real time for the GROW parametrization in this work was 2 months. Manual parametrization, in contrast, may take up to 12 months, and this is, therefore, a significant increase in speed, though it is difficult to estimate the duration of manual parametrization.     

Mobility of small molecules in membrane materials based on copolyimide P84

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驱动两能级原子和真空场相互作用系统中纠缠突然死亡的操控

利用并发度和线性熵作为纠缠度量研究了两个驱动两能级原子和真空场相互作用系统中的纠缠动力学特性,分析了经典驱动场频率、原子和经典场的耦合系数以及参数α对并发度和线性熵的影响。结果发现通过调控经典驱动场能够提高两原子之间和两原子与场之间的纠缠,实现两原子之间纠缠突然死亡现象的操控,理论上提供了一种调控纠缠的方式。     

Tensor gauge field localization on a string-like defect

This work is devoted to the study of tensor gauge fields on a string-like defect in six dimensions. This model is very successful in localizing fields of various spins only by gravitational interaction. Due to problems of field localization in membrane models we are motivated to investigate if a string-like defect localizes the Kalb–Ramond field. In contrast to what happens in Randall–Sundrum and thick brane scenarios we find a localized zero mode without the addition of other fields in the bulk. Considering the local string defect we obtain analytical solutions for the massive modes. Also, we take the equations of motion in a supersymmetric quantum mechanics scenario in order to analyze the massive modes. The influence of the mass as well as the angular quantum number in the solutions is described. An additional analysis on the massive modes is performed by the Kaluza–Klein decomposition, which provides new details about the KK masses.     

A Bertini type theorem for pencils over finite fields

We study the question of finding smooth hyperplane sections to a pencil of hypersurfaces over finite fields.     

Permutation trinomials over Fq3

We consider four classes of polynomials over the fields ${\mathbb{F}}_{q^3}$, $q=p^h$, $p>3$, $f_1(x)=x^{q^2+q-1}+A{x}^{q^2-q+1}+Bx$, $f_2(x)=x^{q^2+q-1}+A{x}^{q^3-q^2+q}+Bx$, $f_3(x)=x^{q^2+q-1}+A{x}^{q^2}-Bx$, $f_4(x)=x^{q^2+q-1}+A{x}^q-Bx$, where $A,B\in {\mathbb{F}}_q$. We find sufficient conditions on the pairs $(A,B)$ for which these polynomials permute ${\mathbb{F}}_{q^3}$ and we give lower bounds on the number of such pairs.