Unphysical moves

A real strength of MC simulation is that one is not constrained to transition from one configuration to another through a sequence of physically realistic steps such as those prescribed by Newton s Law. Instead, very unphysical moves can be designed, so long as they pre-... 

The main difference between Monte Carlo (MC) and Molecular Dynamics (MD) simulations is that we do not need to follow the physical trajectory of the system with MC, which, in turn, enables us to use unphysical moves to cover the relevant area of phase space more quickly. Such moves include chain breaking and reattachment,configurational bias, and reptation moves. ... 

Starting from stoichiometric conditions (< = 1) and then proceeding in the lean direction (< < 1), we anticipate that the peak fiame temperature will be reduced gradually. In addition, as the maximum temperature is lowered and the corresponding adiabatic fiame speed of an unstrained a = 0) fiame is reduced, we anticipate that the fiame will move closer to the plane of symmetry. Ultimately, as the fuel to air ratio is lowered below a critical value, radical production in the fiame will be severely restricted and the fiame will extinguish (lean extinction). The arclength continuation procedure will then generate unphysical solutions for additional continuation steps until a maximum value of the... 

Figure 6. The shape of a spherical particle as its appears in (a) its rest frame, (b) in a frame moving with subluminal (but relativistic) velocity, (c) a frame moving at the light velocity (an unphysical case ), and (d) a superluminal frame. This last figure clearly shows that, according to ER, tachyons are X-shaped objects (waves). A spatial dimension has been dropped for simplicity of representation. (From Barut et al. [50].)...

If the lifetime x substantially increases (y —> 0), then the loss line tends to 8(x —ro/fl). This unphysical property of the parabolic potential well arises, since the oscillation frequency remains the same for all particles moving in the well. 

It may not be useful to argue about whether Hartree-Fock or Kohn-Sham orbitals would be better. But it is important to note that the KS orbitals are in no way unphysical, nor are they unsuitable for use in MO theoretical considerations. The properties of the KS orbitals we have noted above are a direct consequence of the form of the local potential vs(r) in which the KS electrons move ... 

Using the minimum image distance criteria ensures that the distance between two particles varies continuously as particles move out of the central computational box and reappears at the opposite side. Furthermore, the periodic boundary conditions has the effect of restraining unphysical density fluctuations. However, it also means that particles in the central computational box will never be more than half the box length L apart and phenomena with a characteristic length-scale longer than this will be suppressed [142,143]. 

First, to describe the motion of the substrate on a physical time scale, an equation of motion needs to be solved that inevitably involves the substrate ma.ss. However, there are no physical criteria on which the choice of a specific value for this mass could be based. Second, even though the substrate is a macroscopic object in the SFA experiment, its mass cannot be too mucli larger than the mass of a film molecule in the NEMD simulations because otherwise the wall would remain at rest on the time scale on which film molecules move. In fact, the ratio of the mass of a single film molecule to that of the entire wall is sometimes as small a.s i/8 [191, 192] so that one can expect relaxation phenomena in the film to depend sensibly (and therefore unphysically from an experimental perspective) on this arbitrarily selected wall mass [170]. Third, the speed at which the walls are slid in the SFA experiment is typically of the order of 10" — 10" Aps [136] so that under realistic conditions the walls remain practically stationary on a typical length and time scale of molecular relaxation processes. 

Fortunately, if we use DPT, the Brown-Ravenhall disease does not show up at all, because we start from an n-electron state in the nrl, and there is no chance for unphysical positronic or ultrarelativistic components to mix in. This is easily seen in the quasidegenerate formalism, where we insist on relating the upper and lower components via the correct X-operator for electrons, which clearly takes care that we only move in the world of... 

There are two fixed points (i) r = 0 and (ii) r = —d. The bare coupling constant Tq which originates from where A, the variance of the distribution, is strictly positive, requires a positive r. Therefore, the nontrivial fixed point for d < 1 in negative r is unphysical. It however moves to the physical domain for d > 1. 

Because of the unphysical feature of the Klein-Gordon density and the fact that spin does not emerge naturally (but would have to be included a posteriori as in the nonrelativistic framework) we are not able to deduce a fundamental relativistic quantum mechanical equation of motion for a freely moving electron. However, we may wonder which results of this section may be of importance for the derivation of such an equation of motion for the electron. Certainly, we would like to recover the plane wave solutions of Eq. (5.8) for the freely moving particle, but in order to introduce only a single integration constant (or the choice of a single initial value) for a positive definite density distribution we need to focus on first-order differential equations in time. These must also he first-order differential equations in space for the sake of Lorentz co-variance. 

One disadvantage of the slithering snake model is that the time step cannot be controlled in one step the chain moves exactly one tube segment. This in particular leads to the unphysical oscillations in i,mid(t) at early time in Figure 17. In order to resolve the motion on smaller timescales (and more importantly to account for fluctuations of the chain inside the tube, see below), one has to distinguish between the tube and chain coordinates. Now we introduce the main set of variables of the tube model the 3D tube coordinates V),(t), fe = 0...Z as in the previous section plus the one-dimensional (ID) chain coordinates inside the tube Xj( ), i = 0...N. In total, we have 3(Z-r 1) -r (N-f 1) variables, and their equations of motion are coupled. The main idea of the tube theory is that the chain inside the tube moves independent of the tube coordinates, whereas the tube segments are deleted at the ends when the chain does not occupy them any more, and are created when the chain sticks out of the tube. In the pure reptation model, only the center-of-mass of X coordinates moves according to... 

---