Dimensional Analysis and Similarity Method Driving Self-similar Solutions of the First and Second Kind Inducing Energy

Nearly all scientists,at conjunction with simplifying a differential equation,have probably used dimensional analysis.Dimensional analysis(also called the Factor-Label Method or the Unit Factor Method)is an approach to the problem that uses the fact that one can multiply any number or expression without changing its value.This is a useful technique.However,the reader should take care to understand that chemistry is not simply a mathematics problem.In every physical problem,the result must match the real world.In physics and science,dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions.The dimension of a physical quantity is the combination of the fundamental physical dimensions(usually mass,length,time,electric charge,and temperature)which describe it;for example,speed has the dimension length/time,and may be measured in meters per second,miles per hour,or other units.Dimensional analysis is necessary because a physical law must be independent of the units used to measure the physical variables in order to be general for all cases.One of the most derivation elements from dimensional analysis is scaling and consequently arriving at similarity methods that branch out to two different groups namely self-similarity as the first one,and second kind that through them one can solve the most complex none-linear ODEs(Ordinary Differential Equations)and PDEs(Partial Differential Equations)as well.These equations can be solved either in Eulearian or Lagrangian coordinate systems with their associated BCs(Boundary Conditions)or ICs(Initial Conditions).Exemplary ODEs and PDEs in the form of none-linear can be seen in strong explosives or implosives scenario,where the results can easily be converted to induction of energy in a control forms for a peaceful purpose(i.e.,fission or fusion reactions).

Variability in total cost of vehicle ownership across vehicle and user profiles

Widespread adoption of electric vehicles(EVs)is a common and critical component of international strategies to mitigate environmental pollution,climate change and oil dependency.The ability of consumers to assess the total cost of ownership(TCO)of EVs relative to internal combustion engine vehicles(ICEVs)remains an important factor for EV uptake.The TCO of vehicles is not universal across different car segments and user profiles.We analyse and compare the TCO of ICEVs and EVs from 17 car segments across short-and long-term ownership periods,and further advance existing TCO approaches by integrating detailed activity-based driving profiles,taxation,grant structures and pricing.Results show that EV options in the most popular Irish car segments have existing battery EV options with a TCO averaging respectively 26% and 42% less than their equivalent petrol and diesel ICEV options over a 4-year ownership term when the current grant is included.This integrated method for granular TCO evaluation offers important insights for this market and affords scope to investigate how changes in travel patterns,car-segment pricing,taxation,grant policy,fuel costs,and carbon pricing and other transport policies can all affect TCO values over time across a broad range of market offerings.

Thermal Physics and Statistical Mechanics Driven Inertial Confinement Fusion(ICF)Inducing a Controlled Thermonuclear Energy

In the 1970s,scientists began experimenting with powerful laser beams to compress and heat the hydrogen isotopes to the point of fusion,a technique called ICF(Inertial Confinement Fusion).In the“direct drive”approach to ICF,powerful beams of laser light are focused on a small spherical pellet containing micrograms of deuterium and tritium.The rapid heating caused by the laser“driver”makes the outer layer of the target explode.In keeping with Isaac Newton’s Third Law“For every action,there is an equal and opposite reaction”,the remaining portion of the target is driven inwards in a rocket-like implosion,causing compression of the fuel inside the capsule and the formation of a shock wave,which further heats the fuel in the very center and results in a self-sustaining burn.The fusion burn propagates outward through the cooler,outer regions of the capsule much more rapidly than the capsule can expand.Instead of magnetic fields,the plasma is confined by the inertia of its own mass—hence the term inertial confinement fusion.A similar process can be observed on an astrophysical scale in stars and the terrestrial uber world,that have exhausted their nuclear fuel,hence inertially or gravitationally collapsing and generating a supernova explosion,where the results can easily be converted to induction of energy in control forms for a peaceful purpose(i.e.,inertial fusion reaction)by means of thermal physics and statistical mechanics behavior of an ideal Fermi gas,utilizing Fermi-Degeneracy and Thomas-Fermi theory.The fundamental understanding of thermal physics and statistical mechanics enables us to have a better understanding of Fermi-Degeneracy as well as Thomas-Fermi theory of ideal gas,which results in laser compressing matter to a super high density for purpose of producing thermonuclear energy in way of controlled form for peaceful shape and form i.e.CTR(Controlled Thermonuclear Reaction).In this short review,we have concentrated on Fundamental of State Equations by driving them as it was evaluated in book Statistical Mechanics written by Mayer,J.and Mayer,M.in this article.