Nuclear Structure Evolution Reflected from Local Relations

The structure evolution of nuclei which are in connection with symmetry breaking is one of the important problems not only for nuclear structures, but also for astrophysics and the spectroscopy of exotic nuclei. Many physical quantities can provide useful information of a shell structure, such as nuclear masses and nuclear charge radii. This paper introduces three kinds of local relations, i.e., the NpNn scheme respectively for the quadrupole deformation parameter and the excitation energy of the first 2+, 4+, 6+ states, the (αN′n+N′p) relation for nuclear charge radii and α decay energies, and the so-called “nonpairing” relation for binding energies and nuclear charge radii. All these relations reflect the evolution of nuclear structures, involving shells, subshells, shape coexistence, phase transition and the Wigner effect. Some results from different models can be verified with each other.

Optimized Design of Various Ag Decorated Sn-xAg-Cu0.7 Solder Bump on Cycling Fatigue Reliability for Wafer-Level Chip Scale Packaging

Effects of Ag content (0 ~ 3 wt.%) in Sn-xAgCu0.7 solders on microstructure characteristics and low cycling fatigue at different temperature conditions are overall investigated. To increase Ag content, the solidus point 228.8 ? of Sn-Cu0.7 gradually decreases to 218.5 ? and temperature range of solid-liquid coexistence phase is also decrease. The Sn-Cu0.7 matrix consisted of small particles of Cu6Sn5 within ß-Sn equiaxial grains and did not significantly influence solder hardness. Moreover, much intermetallic compound of plate-like Ag3Sn and rod-like Cu6Sn5 existed in Sn-xAgCu0.7 solders enables to enhance the hardness due to dense network of Ag3Sn precipitation and near eutectic point. As a result of plastic displacement decreases with higher Ag additions, better fatigue lifetime could be achieved at Ag content to 1.5 wt.%. Besides, crack stemmed from thicker IMC layer in Sn-3.0Ag-Cu0.7 solder interface will decrease fatigue performance especially for 80 ? and 120 ?.

Inhomogeneous chiral condensates in low-energy color-superconductivity models of QCD

This thesis explores the phase diagrams of the Nambu--Jona-Lasinio (NJL) and quark-meson (QM) model in the mean-field approximation and beyond. The focus lies in the investigation of the interplay between inhomogeneous chiral condensates and two-flavor color superconductivity. In the first part of this thesis, we study the NJL model with 2SC diquarks in the mean-field approximation and determine the dispersion relations for quasiparticle excitations for generic spatial modulations of the chiral condensate in the presence of a homogeneous 2SC-diquark condensate, provided that the dispersion relations in the absence of color superconductivity are known. We then compare two different Ansätze for the chiral order parameter, the chiral density wave (CDW) and the real-kink crystal (RKC). For both Ansätze we find for specific diquark couplings a so-called coexistence phase where both the inhomogeneous chiral condensate and the diquark condensate coexist. Increasing the diquark coupling disfavors the coexistence phase in favor of a pure diquark phase. On the other hand, decreasing the diquark coupling favors the inhomogeneous phase over the coexistence phase. In the second part of this thesis the functional renormalization group is employed to study the phase diagram of the quark-meson-diquark model. We observe that the region of the phase diagram found in previous studies, where the entropy density takes on unphysical negative values, vanishes when including diquark degrees of freedom. Furthermore, we perform a stability analysis of the homogeneous phase and compare the results with those of previous studies. We find that an increasing diquark coupling leads to a smaller region of instability as the 2SC phase extends to a smaller chemical potential. We also find a region where simultaneously an instability occurs and a non-vanishing diquark condensate forms, which is an indication of the existence of a coexistence phase in accordance with the results of the first part of this work.

Self-dual $S_3$-invariant quantum chains

We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and S_3S3, time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1)U(1) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct “Fermi velocities”. The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.

Emergence of complex structures from nonlinear interactions and noise in coevolving networks

We study the joint effect of the non-linearity of interactions and noise on coevolutionary dynamics. We choose the coevolving voter model as a prototype framework for this problem. By numerical simulations and analytical approximations we find three main phases that differ in the absolute magnetisation and the size of the largest component: a consensus phase, a coexistence phase, and a dynamical fragmentation phase. More detailed analysis reveals inner differences in these phases, allowing us to divide two of them further. In the consensus phase we can distinguish between a weak or alternating consensus and a strong consensus, in which the system remains in the same state for the whole realisation of the stochastic dynamics. In the coexistence phase we distinguish a fully-mixing phase and a structured coexistence phase, where the number of active links drops significantly due to the formation of two homogeneous communities. Our numerical observations are supported by an analytical description using a pair approximation approach and an ad-hoc calculation for the transition between the coexistence and dynamical fragmentation phases. Our work shows how simple interaction rules including the joint effect of non-linearity, noise, and coevolution lead to complex structures relevant in the description of social systems.