A numerical implementation of self-consistent mean-field theory for the structural phase behavior of block copolymers is proposed. Our scheme does not require a priori assumptions of the underlying mesoscopic symmetries. The method potentially enables us to characterize, with high accuracy, the structural phase diagram of block copolymers with significant architectural complexity. We illustrate the method by applying it to a triblock copolymer system.

: We present an improved algorithm of the self-consistent mean-field implementation that has been recently proposed for the calculation of block copolymer self-assembly. Without requiring prior knowledge of the symmetry of the mesophase segregation, the algorithm is numerically stable and significantly faster than previously proposed methods. These advantages provide a valuable tool for combinatorial screening of novel stable and metastable structural phases of block copolymers. We apply the method and demonstrate complex mesophases in linear, asymmetric triblock copolymer melts.

Statistical mechanics of the discrete nonlinear Schrödinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = ∞, we identify a phase transition, through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breather-like localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.The pioneering studies of Fermi, Pasta and Ulam [1] (FPU) showed that energy exchange between coupled systems may be suppressed in the presence of nonlinearity; instead a type of behavior that severely contrasts equipartition among the linear modes is observed. The question of whether equipartition of excitation energy always appears is a contemporary issue in various fields of physics. Many manifestations of nonequilibrium and non-equipartition phenomena equivalent to the dynamical behavior of systems with few degrees of freedom contrasting statistical mechanics expectations have been observed. Some of these phenomena, and therefore the absence of immediate equipartition expressed in terms of self-trapping of energy, play an important role for optical storage patterns in nonlinear fibers, condensed matter physics, and biophysics [2].A particularity of discrete nonlinear systems is their ability to sustain strong localization of energy [3]. This is accomplished via intrinsic localized modes (breathers) which are modes that remain stable for extremely long times. So far it is a largely unaddressed problem how to handle and describe these excitations in a statistical mechanics framework although it has been argued that breathers may act as virtual bottlenecks [4] delaying the thermalization process.In this work, we develop a statistical understanding of the dynamics, including the breathers, in a discrete nonlinear Schrödinger (DNLS) equation. The DNLS equation plays a significant role in several branches nonlinear physics as a simple physical model because it may approximate many of the above mentioned nonlinear systems. We study analytically and numerically the thermalization of the lattice for T ≥ 0. We identify the regime in phase space wherein regular statistical mechanics considerations apply, and hence, thermalization is observed numerically and explored analytically using regular, grand-canonical, Gibbsian equilibrium measures.However, the nonlinear dynamics of the problem renders permissible the realization of regimes of phase space which would formally correspond to "negative temperatures" [5] in the sense of statistical mechanics. The novel feature of these states is that the energy tends to be localized in certain lattice sites forming breather-like excitations. Returning to statistical mechanics, such realizations, which would formally correspond to negative temperatures, are not possible (since the Hamil...

It has long been known that double-stranded DNA is subject to temporary, localized openings of its two strands. Particular regions along a DNA polymer are destabilized structurally by available thermal energy in the system. The localized sequence of DNA determines the physical properties of a stretch of DNA, and that in turn determines the opening profile of that DNA fragment. We show that the Peyrard-Bishop nonlinear dynamical model of DNA, which has been used to simulate denaturation of short DNA fragments, gives an accurate representation of the instability profile of a defined sequence of DNA, as verified using S1 nuclease cleavage assays. By comparing results for a non-promoter DNA fragment, the adenovirus major late promoter, the adeno-associated viral P5 promoter and a known P5 mutant promoter that is inactive for transcription, we show that the predicted openings correlate almost exactly with the promoter transcriptional start sites and major regulatory sites. Physicists have speculated that localized melting of DNA might play a role in gene transcription and other processes. Our data link sequence-dependent opening behavior in DNA to transcriptional activity for the first time.

We derive underdamped evolution equations for the order-parameter (OP ) strains of a ferroelastic material undergoing a structural transition, using Lagrangian variations with Rayleigh dissipation, and a free energy as a polynomial expansion in the N = n + Nop symmetry-adapted strains. The Nop strain equations are structurally similar in form to the Lagrange-Rayleigh 1D strain dynamics of Bales and Gooding (BG), with 'strain accelerations' proportional to a Laplacian acting on a sum of the free energy strain derivative and frictional strain force. The tensorial St. Venant's elastic compatibility constraints that forbid defects, are used to determine the n non-order-parameter strains in terms of the OP strains, generating anisotropic and long-range OP contributions to the free energy, friction and noise. The same OP equations are obtained by either varying the displacement vector components, or by varying the N strains subject to the Nc compatibility constraints. A Fokker-Planck equation, based on the BG dynamics with noise terms, is set up. The BG dynamics corresponds to a set of nonidentical nonlinear (strain) oscillators labeled by wavevector k, with competing short-and long-range couplings. The oscillators have different 'strain-mass' densities ρ(k) ∼ 1/k 2 and dampings ∼ 1/ρ(k) ∼ k 2 , so the lighter large-k oscillators equilibrate first, corresponding to earlier formation of smaller-scale oriented textures. This produces a sequential-scale scenario for post-quench nucleation, elastic patterning, and hierarchical growth. Neglecting inertial effects yields a late-time dynamics for identifying extremal free energy states, that is of the time-dependent Ginzburg-Landau form, with nonlocal, anisotropic Onsager coefficients, that become constants for special parameter values. We consider in detail the two-dimensional (2D) unit-cell transitions from a triangular to a centered rectangular lattice (Nop = 2, n = 1, Nc = 1); and from a square to a rectangular lattice (Nop = 1, n = 2, Nc = 1) for which the OP compatibility kernel is retarded in time, or frequencydependent in Fourier space (in fact, acoustically resonant in ω/k). We present structural dynamics for all other 2D symmetry-allowed ferroelastic transitions: the procedure is also applicable to the 3D case. Simulations of the BG evolution equations confirm the inherent richness of the static and dynamic texturings, including strain oscillations, domain-wall propagation at near sound speeds, grain-boundary motion, and nonlocal 'elastic photocopying' of imposed local stress patterns.