Stochastic boundary conditions for molecular dynamics simulations

In this paper we develop a stochastic boundary conditions (SBC) for event-driven molecular dynamics simulations of a finite volume embedded within an infinite environment. In this method, we first collect the statistics of injection/ejection events in periodic boundary conditions (PBC). Once sufficient statistics are collected, we remove the PBC and turn on the SBC. In the SBC simulations, we allow particles leaving the system to be truly ejected from the simulation, and randomly inject particles at the boundaries by resampling from the injection/ejection statistics collected from the current or previous simulations. With the SBC, we can measure thermodynamic quantities within the grand canonical ensemble, based on the particle number and energy fluctuations. To demonstrate how useful the SBC algorithm is, we simulated a hard disk gas and measured the pair distribution function, the compressibility and the specific heat, comparing them against literature values.Comment: 24 pages, 16 figure

Experimental Investigations of I-beams

I - beams made of cold - formed thin - walled channels, back to back, can be connected by resistance spot welding or arc-welding. Both stability and ultimate strength of these beams are different for welding method. The stability can be increased provided several battens are attached on the open sections of these beams

(E)-1-(3-Methoxy­phen­yl)ethanone 4-nitro­phenyl­hydrazone

Crystals of the title compound, C15H15N3O3, were obtained from a condensation reaction of 4-nitro­phenyl­hydrazine and 3-methoxy­acetophenone. In the crystal structure, the methoxy­phenyl ring is twisted slightly with respect to the nitro­phenyl­hydrazine plane, making a dihedral angle of 14.81 (8)°. The nitro and meth­oxy groups are each coplanar with the attached benzene rings. The nitro­phenyl and methoxy­phenyl groups are located on opposite sides of the C=N double bond, indicating an E configuration of the mol­ecule. Adjacent mol­ecules are linked together via N—H⋯O hydrogen bonding, forming chains along the [101] direction

3-Penta­none 2,4-dinitro­phenyl­hydrazone

Crystals of the title compound, C11H14N4O4, were obtained from a condensation reaction of 2,4-dinitro­phenyl­hydrazine and 3-penta­none. In the crystal structure, the mol­ecule, except one methyl group, displays a nearly planar structure. The imino group links to the adjacent nitro group via intra­molecular hydrogen bonding. The partially overlapped arrangement and face-to-face separation of 3.410 (9) Å between parallel benzene rings indicate the existence of π–π stacking between adjacent mol­ecules. The crystal structure also contains weak inter­molecular C—H⋯O hydrogen bonding

Methyl 2-[2-(benzyl­oxycarbonyl­amino)­propan-2-yl]-5-hy­droxy-6-meth­oxy­pyrimidine-4-carboxyl­ate

In the title compound, C18H21N3O6, a pyrimidine derivative, the dihedral angle between the benzene and pyrimidine rings is 52.26 (12)°. The carboxyl­ate unit is twisted with respect to the pyrimidine ring, making a dihedral angle of 12.33 (7)°. In the crystal, mol­ecules are linked by a pair of O—H⋯O hydrogen bonds, forming an inversion dimer. The dimers are stacked into columns along the b axis through weak C—H⋯O inter­actions

2-Methyl­benzaldehyde 2-methyl­benzyl­idenehydrazone

The mol­ecule of the title compound, C16H16N2, is centrosymmetric and the dihedral angle between the benzene ring and the dimethyl­hydrazine mean plane is 16.11 (15)°

Benzyl (E)-3-(2-methyl­benzyl­idene)dithio­carbazate

The title compound, C16H16N2S2, was obtained from the condensation reaction of benzyl dithio­carbazate and 2-methyl­benzaldehyde. The asymmetric unit contains two independent mol­ecules. In both mol­ecules, the methyl­phenyl ring and the dithio­carbazate fragment are located on opposite sides of the C=N bond, showing an E conformation. In each mol­ecule, the dithio­carbazate fragment is approximately planar, the r.m.s deviations being 0.018 and 0.025 Å. The mean plane of dithio­carbazate group is oriented at dihedral angles of 7.9 (3) and 68.24 (12)°, respectively, to the methyl­phenyl and phenyl rings in one mol­ecule, while the corresponding angles in the other mol­ecule are 10.9 (3) and 69.76 (16)°. Inter­molecular N—H⋯S hydrogen bonding occurs in the crystal structure to generate inversion dimers for both molecules

Methyl (E)-3-(2-bromo-4,5-dimeth­oxy­benzyl­idene)dithio­carbazate

The title compound, C11H13BrN2O2S2, was obtained from the condensation reaction of methyl dithio­carbazate and 2-bromo-4,5-dimeth­oxy­benzaldehyde. In the mol­ecule, the benzene ring and dithio­carbazate fragment are located on opposite sides of the C=N bond, showing an E conformation. The dithio­carbazate fragment is approximately planar (r.m.s deviation = 0.0281 Å) and the mean plane is oriented at a dihedral angle of 11.38 (15)° with respect to the benzene ring. In the crystal, pairs of N—H⋯S hydrogen bonds link the mol­ecules into centrosymmetric dimers