Kinetic Anomalies in Addition-Aggregation Processes

We investigate irreversible aggregation in which monomer-monomer, monomer-cluster, and cluster-cluster reactions occur with constant but distinct rates K_{MM}, K_{MC}, and K_{CC}, respectively. The dynamics crucially depends on the ratio gamma=K_{CC}/K_{MC} and secondarily on epsilon=K_{MM}/K_{MC}. For epsilon=0 and gamma<2, there is conventional scaling in the long-time limit, with a single mass scale that grows linearly in time. For gamma >= 2, there is unusual behavior in which the concentration of clusters of mass k, c_k decays as a stretched exponential in time within a boundary layer k<k* propto t^{1-2/gamma} (k* propto ln t for gamma=2), while c_k propto t^{-2} in the bulk region k>k*. When epsilon>0, analogous behaviors emerge for gamma<2 and gamma >= 2.Comment: 6 pages, 2 column revtex4 format, for submission to J. Phys.

Scaling Theory for Migration-Driven Aggregate Growth

We give a comprehensive rate equation description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j, that is, K(ai;aj) ~ a^{lambda} K(i,j), the mean aggregate size grows with time as t^{1/(2-lambda)} for lambda<2. The aggregate size distribution exhibits distinct regimes of behavior which are controlled by the scaling properties of the migration rate from the smallest to the largest aggregates. Our theory applies to diverse phenomena, such as the distribution of city populations, late stage coarsening of non-symmetric binary systems, and models for wealth exchange.Comment: 4 pages, 2-column revtex format. Revision to appear in PRL. Various changes in response to referee comments. Figure from version 1 deleted but is available at http://physics.bu.edu/~redne

Superior localisation and imaging of radiolabelled monoclonal antibody E48 F(ab')2 fragment in xenografts of human squamous cell carcinoma of the head and neck and of the vulva as compared to monoclonal antibody E48 IgG.

Monoclonal antibody (MAb) E48 and its F(ab')2 fragment, radiolabelled with 131I, were tested for tumour localisation and imaging in nude mice bearing a squamous cell carcinoma xenograft line derived from a head and neck carcinoma (HNX-HN) or from a vulva carcinoma (VX-A431). MAb IgG or F(ab')2 fragments were injected in parallel and at day 1, 2, 3 and 6 or 7, mice were either scanned with a gamma camera or dissected for determination of isotope biodistribution. In HNX-HN bearing mice, E48 IgG as well as F(ab')2 showed highly specific localisation in tumour tissue. The mean tumour uptake (n = 4) expressed as the percentage of the injected dose per gram of tumour tissue (percentage ID/g) of IgG was 11.9% at day 1 and increased to 14.6% at day 6 whereas percentage ID/g of F(ab')2 was 7.2% at day 1 and decreased during subsequent days. Tumour to blood ratios (T/B) at day 1 were 1.2 for IgG and 13.6 for F(ab')2 and reached a maximum at day 6 with values of 6.4 and 54.2 respectively. In VX-A431 bearing mice, only E48 F(ab')2 showed preferential localisation in tumour tissue. At day 1, Percentage ID/g of IgG was 3.7 and T/B was 0.3, while percentage ID/g of F(ab')2 was 2.4 and T/B was 3.2. Percentage ID/g decreased after day 1 while T/B increased. In these experiments no preferential localisation of either isotype matched 125I-labelled control IgG or F(ab')2 was observed. In F(ab')2 injected HNX-HN bearing mice as well as VX-A431 bearing mice, tumours could be visualised at day 1 and 2 without any appreciable background activity. With MAb IgG this was also possible in HNX-HN bearing mice (but not in VX-A431 bearing mice) but only at day 3 and 6. These findings suggest that the superior tumour to non-tumour ratios render the E48 F(ab')2 fragment more qualified for specific targeting of radioisotopes to tumour xenografts in this experimental setting

Symmetry breaking in the Hubbard model at weak coupling

The phase diagram of the Hubbard model is studied at weak coupling in two and three spatial dimensions. It is shown that the Neel temperature and the order parameter in d=3 are smaller than the Hartree-Fock predictions by a factor of q=0.2599. For d=2 we show that the self-consistent (sc) perturbation series bears no relevance to the behavior of the exact solution of the Hubbard model in the symmetry-broken phase. We also investigate an anisotropic model and show that the coupling between planes is essential for the validity of mean-field-type order parameters

Raman scattering through a metal-insulator transition

The exact solution for nonresonant A1g and B1g Raman scattering is presented for the simplest model that has a correlated metal-insulator transition--the Falicov-Kimball model, by employing dynamical mean field theory. In the general case, the A1g response includes nonresonant, resonant, and mixed contributions, the B1g response includes nonresonant and resonant contributions (we prove the Shastry-Shraiman relation for the nonresonant B1g response) while the B2g response is purely resonant. Three main features are seen in the nonresonant B1g channel: (i) the rapid appearance of low-energy spectral weight at the expense of higher-energy weight; (b) the frequency range for this low-energy spectral weight is much larger than the onset temperature, where the response first appears; and (iii) the occurrence of an isosbestic point, which is a characteristic frequency where the Raman response is independent of temperature for low temperatures. Vertex corrections renormalize away all of these anomalous features in the nonresonant A1g channel. The calculated results compare favorably to the Raman response of a number of correlated systems on the insulating side of the quantum-critical point (ranging from Kondo insulators, to mixed-valence materials, to underdoped high-temperature superconductors). We also show why the nonresonant B1g Raman response is ``universal'' on the insulating side of the metal-insulator transition.Comment: 12 pages, 11 figures, ReVTe

Phase separation and the segregation principle in the infinite-U spinless Falicov-Kimball model

The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions contain both second-order phase transitions and first-order phase transitions (that involve phase-separation or segregation) which are likely to illustrate the basic physics behind the static charge-stripe ordering in cuprate systems. In addition, we find the spinodal-decomposition temperature satisfies an approximate scaling law.Comment: 19 pages and 10 figure

Phase Diagram of One-Dimensional Extended Hubbard Model at Half Filling

We reexamine the ground-state phase diagram of the one-dimensional half-filled Hubbard model with on-site and nearest-neighbor repulsive interactions. We calculate second-order corrections to coupling constants in the g-ology to show that the bond-charge-density-wave (BCDW) phase exists for weak couplings in between the charge density wave (CDW) and spin density wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons destabilizes the BCDW state and gives rise to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line.Comment: 4 pages, 3 figure

A Survey of Numerical Solutions to the Coagulation Equation

We present the results of a systematic survey of numerical solutions to the coagulation equation for a rate coefficient of the form A_ij \propto (i^mu j^nu + i^nu j^mu) and monodisperse initial conditions. The results confirm that there are three classes of rate coefficients with qualitatively different solutions. For nu \leq 1 and lambda = mu + nu \leq 1, the numerical solution evolves in an orderly fashion and tends toward a self-similar solution at large time t. The properties of the numerical solution in the scaling limit agree with the analytic predictions of van Dongen and Ernst. In particular, for the subset with mu > 0 and lambda < 1, we disagree with Krivitsky and find that the scaling function approaches the analytically predicted power-law behavior at small mass, but in a damped oscillatory fashion that was not known previously. For nu \leq 1 and lambda > 1, the numerical solution tends toward a self-similar solution as t approaches a finite time t_0. The mass spectrum n_k develops at t_0 a power-law tail n_k \propto k^{-tau} at large mass that violates mass conservation, and runaway growth/gelation is expected to start at t_crit = t_0 in the limit the initial number of particles n_0 -> \infty. The exponent tau is in general less than the analytic prediction (lambda + 3)/2, and t_0 = K/[(lambda - 1) n_0 A_11] with K = 1--2 if lambda > 1.1. For nu > 1, the behaviors of the numerical solution are similar to those found in a previous paper by us. They strongly suggest that there are no self-consistent solutions at any time and that runaway growth is instantaneous in the limit n_0 -> \infty. They also indicate that the time t_crit for the onset of runaway growth decreases slowly toward zero with increasing n_0.Comment: 41 pages, including 14 figures; accepted for publication in J. Phys.

Phase diagram of the quarter-filled extended Hubbard model on a two-leg ladder

We investigate the ground-state phase diagram of the quarter-filled Hubbard ladder with nearest-neighbor Coulomb repulsion V using the Density Matrix Renormalization Group technique. The ground-state is homogeneous at small V, a ``checkerboard'' charge--ordered insulator at large V and not too small on-site Coulomb repulsion U, and is phase-separated for moderate or large V and small U. The zero-temperature transition between the homogeneous and the charge-ordered phase is found to be second order. In both the homogeneous and the charge-ordered phases the existence of a spin gap mainly depends on the ratio of interchain to intrachain hopping. In the second part of the paper, we construct an effective Hamiltonian for the spin degrees of freedom in the strong-coupling charge-ordered regime which maps the system onto a frustrated spin chain. The opening of a spin gap is thus connected with spontaneous dimerization.Comment: 12 pages, 13 figures, submitted to PRB, presentation revised, new results added (metallic phase at small U and V