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 Computer Science , 2011, Abstract: As an applicaton of sonification, a simulation of the early universe was developed to portray a phase transition that occurred shortly after the Big Bang. The Standard Model of particle physics postulates that a hypothetical particle, the Higgs boson, is responsible for the breaking of the symmetry between the electromagnetic force and the weak force. This phase transition may have been responsible for triggering Baryogenesis, the generation of an abundance of matter over anti-matter. This hypothesis is known as Electroweak Baryogenesis. In this simulation, aspects of bubble nucleation in Standard Model Electroweak Baryogenesis were examined and modeled using Mathematica, and sonified using SuperCollider3. The resulting simulation, which has been used for pedagogical purposes by one of the authors, suggests interesting possibilities for the integration of science and aesthetics as well as auditory perception. The sonification component in particular also had the unexpected benefit of being useful in debugging the Mathematica code.
 Arnd Surig Physics , 1997, DOI: 10.1103/PhysRevD.57.5049 Abstract: In the standard procedure for calculating the decay rate of a metastable vacuum the solution of the classical Euclidean equation of motion of the background field is needed. On the other hand radiative corrections have to be taken into account already in the equation of motion. Hence, the latter one has to be the functional derivative of the effective action with respect to the background field. This is of crucial importance in theories in which the symmetry breaking is due to radiative corrections. Usually the effective potential is considered only, neglecting the corrections due to the derivative terms of the effective action. In this article a bounce solution from an equation of motion which takes into account the full effective action in the one-loop approximation is calculated. A computational method that yields a strict separation of the divergent contributions to the effective action from the convergent ones is obtained. This allows a wide freedom in the choice of regularization and renormalization schemes. The model under consideration is the SU(2)-Higgs model. The fluctuations of the complete bosonic sector, i.e. gauge field, Higgs and Goldstone boson contributions, are taken into account. The bounce is then self-consistent to one-loop order. The obtained results for characteristic quantities of the transition as the nucleation rate and the number of nucleated bubbles per volume are compared to other, non-self-consistent approaches.
 Physics , 2000, DOI: 10.1142/S0217751X01006917 Abstract: Bubble nucleation has been studied on lattices using phenomenological Langevin equations. Recently there have been theoretical motivations for using these equations. These studies also conclude that the simple Langevin description requires some modification. We study bubble nucleation on a lattice and determine effects of the modified Langevin equations.
 Erick J. Weinberg Physics , 1994, Abstract: A formalism is developed to calculate the bubble nucleation rate in theories where the symmetry breaking is by radiative corrections. Although to leading and next-to-leading order the result can be expressed in terms of the effective action of the theory, this is not true of the higher order corrections. In particular, the imaginary part of the effective potential does not explicitly enter the calculation and the problems of interpretation which it would entail are avoided. Based on a talk given at the NATO Advanced Research Workshop Electroweak Physics and the Early Universe, Sintra, Portugal, March 25, 1994
 N. Tetradis Physics , 1999, Abstract: We summarize recent work on the consistent calculation of bubble-nucleation rates. Our approach is based on the notion of a real coarse-grained potential. The bubble-nucleation rate is calculated through an expansion around the semiclassical saddle point associated with tunnelling. We resolve outstanding problems related to the convexity of the potential, the double-counting of the effect of fluctuations and the inherent ultraviolet divergences. We determine the region of validity of the expansion around the saddle point. We find that this expansion fails near the spinodal line, and for weak or radiatively-induced first-order phase transitions. We apply our method to the bound on the Higgs-boson mass from vacuum metastability and the electroweak phase transition.
 Physics , 2011, DOI: 10.1103/PhysRevE.83.051609 Abstract: Bubble nucleation in weakly supersaturated solutions of carbon dioxide - such as champagne, sparkling wines and carbonated beers - is well understood. Bubbles grow and detach from nucleation sites: gas pockets trapped within hollow cellulose fibres. This mechanism appears not to be active in stout beers that are supersaturated solutions of nitrogen and carbon dioxide. In their canned forms these beers require additional technology (widgets) to release the bubbles which will form the head of the beer. We extend the mathematical model of bubble nucleation in carbonated liquids to the case of two gasses and show that this nucleation mechanism is active in stout beers, though substantially slower than in carbonated beers and confirm this by observation. A rough calculation suggests that despite the slowness of the process, applying a coating of hollow porous fibres to the inside of a can or bottle could be a potential replacement for widgets.
 Physics , 1996, DOI: 10.1103/PhysRevD.55.4947 Abstract: We present a study of the role of fermions in the decay of metastable states of a scalar field via bubble nucleation. We analyze both one and three-dimensional systems by using a gradient expansion for the calculation of the fermionic determinant. The results of the one-dimensional case are compared to the exact results of previous work.
 Physics , 1999, DOI: 10.1088/1126-6708/1999/11/023 Abstract: We estimate bubble-nucleation rates for cosmological phase transitions. We concentrate on the evaluation of the pre-exponential factor, for which we give approximate analytical expressions. Our approach relies on the use of a real coarse-grained potential. We show how the coarse-graining scale can be determined in the studies of high-temperature phase transitions. We discuss the metastability bound on the Higgs-boson mass and the electroweak phase transition. We find that the saddle-point approximation is reliable in the first case and breaks down in the second case.
 J. Baacke Physics , 1995, DOI: 10.1103/PhysRevD.52.6760 Abstract: The fluctuation determinant which determines the preexponential factor of the transition rate for minimal bubbles is computed for the electroweak theory with $\sin \Theta_W = 0$. As the basic action we use the three-dimensional high-temperature action including, besides temperature dependent masses, the $T \Phi^3$ one-loop contribution which makes the phase transition first order. The results show that this contribution (which has then to be subtracted from the exact result) gives the dominant contribution to the one-loop effective action. The remaining correction is of the order of, but in general larger than the critical bubble action and suppresses the transition rate. The results for the Higgs field fluctuations are compared with those of an approximate heat kernel computation of Kripfganz et al., good agreement is found for small bubbles, strong deviations for large thin-wall bubbles.
 Physics , 2009, DOI: 10.1016/j.nuclphysb.2009.09.019 Abstract: We study the velocity of bubble walls in the electroweak phase transition. For several extensions of the Standard Model, we estimate the friction and calculate the wall velocity, taking into account the hydrodynamics. We find that deflagrations are generally more likely than detonations. Nevertheless, for models with extra bosons, which give a strongly first-order phase transition, the deflagration velocity is in general quite high, $0.1\lesssim v_w\lesssim 0.6$. Therefore, such phase transitions may produce an important signal of gravitational waves. On the other hand, models with extra fermions which are strongly coupled to the Higgs boson may provide a strongly first-order phase transition and small velocities, $10^{-2}\lesssim v_w\lesssim 10^{-1}$, as required by electroweak baryogenesis.
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