# No Break Particles ((BETTER))

The dispersal of buoyant particles in the ocean mixed layer is influenced by a variety of physical factors including wind, waves, and turbulence. Microplastics observations are often made at the free surface, which is strongly forced by surface gravity waves. Many studies have used numerical simulations to examine how turbulence and wave effects (e.g., breaking waves, Langmuir circulation) control buoyant particle dispersal at the ocean surface. However these simulations are not wave phase-resolving. Therefore, the effects of an unsteady free surface due to surface gravity waves remain unknown in this context. To address this, we develop an analytical model for the distribution of buoyant particles as a function of wave-phase under wind-wave conditions in deep-water. Using this analytical model and complementary numerical simulations, we quantify the effects of a nonbreaking, monochromatic, progressive wave train on the equilibrium vertical and horizontal distributions of buoyant particles. We find that waves result in non-uniform horizontal distributions of particles with more particles under the wave crests than the troughs. We also find that the waves can stretch or compress the equilibrium vertical distribution. Finally, we consider the effects of waves on the sampling of microplastics with a towed net, and we show that waves have the ability to lower the measured concentrations relative to nets sampling without the influence of waves.

## No Break Particles

Figure 1. Depth profile of normalized concentration of buoyant particles c/c0 as a function of z/Lm according to the wind-mixing model as described by Equation (2).

Figure 3. Wave-averaged concentration of particles over the water column. The ratio A/Lm was varied with constant ϵ = 0.15. The solid lines denote the results from numerical simulations, and the dashed lines denote Equation (6).

Figure 9. Modeled captured particles as a function of net lag parameter α for various A/Lm. The total number of particles captured in a net tow per volume ctow is normalized by ctow0 which represents the predicted amount without waves. The solid lines denote the results from numerical simulations, and the dashed line denote the results using the analytically modeled concentration as described by Equation (13). The vertical gray line denotes the α value when the net drops below the free surface for part of the wave cycle. In these data, ϵ = 0.1 in both cases, and δ/A=0.2 (A) and δ/A=0.5 (B).

The same thing that happens to your hand when you stick it out of your car window as your vehicle travels down the highway. When your car is stationary, only the moving air molecules collide with you, and only at the low speeds/energies at which they travel relative to your stationary hand. When your car is in motion, however, your moving hand will preferentially collide with greater numbers of particles in the direction your hand is in motion. And the faster you go, the greater:

However, at even the speeds achievable at the Large Hadron Collider, the effects of these photons can be neglected. Even for particles that travel through the intergalactic medium for billions of years, even at 99.999999% the speed of light, these common photons are so low in energy that they fail to slow down these particles by even a single meter-per-second, cumulatively, over the history of the Universe.

Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state.[1][2][3] In particular, it can describe systems where the equations of motion or the Lagrangian obey symmetries, but the lowest-energy vacuum solutions do not exhibit that same symmetry. When the system goes to one of those vacuum solutions, the symmetry is broken for perturbations around that vacuum even though the entire Lagrangian retains that symmetry.

By definition, spontaneous symmetry breaking requires the existence of physical laws (e.g. quantum mechanics) which are invariant under a symmetry transformation (such as translation or rotation), so that any pair of outcomes differing only by that transformation have the same probability distribution. For example if measurements of an observable at any two different positions have the same probability distribution, the observable has translational symmetry.

Conversely, in explicit symmetry breaking, if two outcomes are considered, the probability distributions of a pair of outcomes can be different. For example in an electric field, the forces on a charged particle are different in different directions, so the rotational symmetry is explicitly broken by the electric field which does not have this symmetry.

Phases of matter, such as crystals, magnets, and conventional superconductors, as well as simple phase transitions can be described by spontaneous symmetry breaking. Notable exceptions include topological phases of matter like the fractional quantum Hall effect.

Typically, when spontaneous symmetry breaking occurs, the observable properties of the system change in multiple ways. For example the density, compressibility, coefficient of thermal expansion, and specific heat will be expected to change when a liquid becomes a solid.

Consider a symmetric upward dome with a trough circling the bottom. If a ball is put at the very peak of the dome, the system is symmetric with respect to a rotation around the center axis. But the ball may spontaneously break this symmetry by rolling down the dome into the trough, a point of lowest energy. Afterward, the ball has come to a rest at some fixed point on the perimeter. The dome and the ball retain their individual symmetry, but the system does not.[4]

In particle physics, the force carrier particles are normally specified by field equations with gauge symmetry; their equations predict that certain measurements will be the same at any point in the field. For instance, field equations might predict that the mass of two quarks is constant. Solving the equations to find the mass of each quark might give two solutions. In one solution, quark A is heavier than quark B. In the second solution, quark B is heavier than quark A by the same amount. The symmetry of the equations is not reflected by the individual solutions, but it is reflected by the range of solutions.

Without spontaneous symmetry breaking, the Standard Model of elementary particle interactions requires the existence of a number of particles. However, some particles (the W and Z bosons) would then be predicted to be massless, when, in reality, they are observed to have mass. To overcome this, spontaneous symmetry breaking is augmented by the Higgs mechanism to give these particles mass. It also suggests the presence of a new particle, the Higgs boson, detected in 2012.

Superconductivity of metals is a condensed-matter analog of the Higgs phenomena, in which a condensate of Cooper pairs of electrons spontaneously breaks the U(1) gauge symmetry associated with light and electromagnetism.

Dynamical symmetry breaking (DSB) is a special form of spontaneous symmetry breaking in which the ground state of the system has reduced symmetry properties compared to its theoretical description (i.e., Lagrangian).

Dynamical breaking of a global symmetry is a spontaneous symmetry breaking, which happens not at the (classical) tree level (i.e., at the level of the bare action), but due to quantum corrections (i.e., at the level of the effective action).

There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: topologically ordered phases of matter, such as fractional quantum Hall liquids, and spin-liquids. These states do not break any symmetry, but are distinct phases of matter. Unlike the case of spontaneous symmetry breaking, there is not a general framework for describing such states.[12]

Spontaneously-symmetry-broken phases of matter are characterized by an order parameter that describes the quantity which breaks the symmetry under consideration. For example, in a magnet, the order parameter is the local magnetization.

For spontaneous symmetry breaking to occur, there must be a system in which there are several equally likely outcomes. The system as a whole is therefore symmetric with respect to these outcomes. However, if the system is sampled (i.e. if the system is actually used or interacted with in any way), a specific outcome must occur. Though the system as a whole is symmetric, it is never encountered with this symmetry, but only in one specific asymmetric state. Hence, the symmetry is said to be spontaneously broken in that theory. Nevertheless, the fact that each outcome is equally likely is a reflection of the underlying symmetry, which is thus often dubbed "hidden symmetry", and has crucial formal consequences. (See the article on the Goldstone boson.)

When a theory is symmetric with respect to a symmetry group, but requires that one element of the group be distinct, then spontaneous symmetry breaking has occurred. The theory must not dictate which member is distinct, only that one is. From this point on, the theory can be treated as if this element actually is distinct, with the proviso that any results found in this way must be resymmetrized, by taking the average of each of the elements of the group being the distinct one.

The symmetry group can be discrete, such as the space group of a crystal, or continuous (e.g., a Lie group), such as the rotational symmetry of space. However, if the system contains only a single spatial dimension, then only discrete symmetries may be broken in a vacuum state of the full quantum theory, although a classical solution may break a continuous symmetry.

On October 7, 2008, the Royal Swedish Academy of Sciences awarded the 2008 Nobel Prize in Physics to three scientists for their work in subatomic physics symmetry breaking. Yoichiro Nambu, of the University of Chicago, won half of the prize for the discovery of the mechanism of spontaneous broken symmetry in the context of the strong interactions, specifically chiral symmetry breaking. Physicists Makoto Kobayashi and Toshihide Maskawa, of Kyoto University, shared the other half of the prize for discovering the origin of the explicit breaking of CP symmetry in the weak interactions.[14] This origin is ultimately reliant on the Higgs mechanism, but, so far understood as a "just so" feature of Higgs couplings, not a spontaneously broken symmetry phenomenon. 041b061a72