Shock

A jerk or jolt. A disturbance or surprise. The impact or encounter of individuals or groups in combat. Electricity going through the body.

Shocks are discontinuities that can arise in the solution of nonlinear PDEs.

For Example... consider the nonlinear PDE

u_t + uu_x = 0

Preliminaries What path would we have to travel in x and t to stay at a constant value of u? Introduce a parameter s and let x = x(s) and t = t(s). Then u(x,t) = u(x(s),t(s)) and

du   du dx   du dt
-- = -- -- + -- --
ds   dx ds   dt ds

Since we get to pick x(s) and t(s), set

dx           dt
-- = u  and  -- = 1.
ds           ds

Then du/ds simplifies to the original PDE:

du   du     du
-- = -- u + -- = uu  + u  = 0.
ds   dx     dt     x    t

Therefore, u is constant along the curve defined by (x(s),t(s)). Integrate dx/ds and dt/ds to get

x = us + c1
t = s + c2
Letting c2 = 0 for convenience, 
x = ut + c1  ==&rt;  x - ut = c

We have found that u is constant along the characteristic lines x - ut = c.

Initial Conditions Notice that the lines along which u is constant are dependent on u itself! This is something that happens in nonlinear PDEs that doesn't happen in linear PDEs--the "behavior" is dependent on initial conditions. Suppose u at time zero looks like this:

     t                                       
     ^                                        
     |                                        
     |                                        
     |                                        
-----2-_                                     
     |  \                                   
     |   \                                    
     |    \                                     
     1     -___________                
     |                                          
     |                                         
-----0-------------------------&rt;x
     |                                         
     |                                         
     |                                         

Then the lines of constant u will be something like this:

     t                                     
     ^        /  /  /   /                     
     |       /   | /    |                     
     |      /    |/     |                     
     |     /    //     /                      
     |    /     *     |                   
     |   /     /|      |                      
     |  /     //      /                       
     | /     / |      |                       
     |/     /  |      |                       
     +     /  /      /                       
    /|    /   |      |                        
 u=2 |  u=2  u=1    u=1                        
  /  |  /    /      /            
 /   | /     |      |                          
/    |/      |      |                         
-----+--------------------------&rt;x
     |                                         
     |                                         
     |                                         

But wait, the lines where u=2 and u=1 intersect! In other words, at the location *, u is multivalued?

Shocks In reality, whatever is represented by u probably cannot be multivalued. Therefore we introduce the "weak solution" which has a shock, or discontinuity, in it. The weak solution satisfies the PDE everywhere except at the shock.

     t                                       
     ^                                        
     |                                        
     |                                        
     |                                        
-----2---------+                                   
     |         |                                 
     |         |                                 
     |         |                                
     1         +_______                
     |                                          
     |                                         
-----0-------------------------&rt;x
     |         ^                               
     |         |                              
     |       shock                            

To find the speed of the shock, integrate the PDE with resepct to x from a to b to get

             2         2
 d  a       u (a,t) - u (b,t)
-- ∫ u dx = -----------------
dt  b               2

Let a → f^- and b → f⁺, where f(t) is the location of the shock. We get

                       2      2
df   -    +        (u-) - (u+)
-- (u  - u ) + 0 = ------------
dt                      2

or,

df   (u-) + (u+)
-- = -----------
dt        2

The shock wave travels at the average of the speed on the left and the speed on the right.

To elaborate upon Webster 1913's smallish entry: In medical terms, shock means a severe state of too-low blood pressure. This can be life-threatening, because blood supplies vital chemicals (most notably oxygen) to every organ in our body, and if blood pressure is too low, it means that blood can't circulate properly and organs (most notably the brain) may end up starved of resources.

There are three main forms of shock:

• lack-of-volume shock: induced by a lack of blood, usually resulting from some kind of injury through which blood is lost. The bleeding may be internal, in which case the cause of shock is non-obvious.
• anaphylactic shock: cause by strong allergies, e.g. against bee poison. The allergic reaction can cause all the blood vessels to become wider than they should be, which also sends blood pressure tumbling. This can also happen as a result of sheer pain, compounding a lack-of-volume shock, or replacing it with some injuries (such as broken bones) where blood loss is not serious enough to cause one.
• cardiogenic shock: occurs when a malfunction of some sort weakens the heart to the point where it can't provide the necessary blood pressure.

Shock symptoms include dizziness, sickness and general weakness, leading to unconsciousness if not treated. A carciogenic shock is distinguishable from the other types by blood vessels at the throat swelling and standing out visibly. This is important becuase a cardiogenic shock must not be treated like the other types!

Shock countermeasures: usually, the best and easiest thing to do is to let the patient lie down and place his or her feet in an elevated position ("shock position") so that blood from the legs becomes available to the more vital parts of the body and supplying the brain becomes an easier job for the heart (no height difference). In case of a lack-of-volume shock, the lost blood volume should be added throug an infusion. In case of an anaphylactic shock, the patient must be given anti-allergic medicine as quickly as possible.

However, in case of a cardiogenic shock, the shock position only compounds the problem, as it places additional strain on the heart! In that case, the patient should be kept sitting.

In all cases, not only related to shock, an important aspect is psychology: keep the patient comfortable and non-frightened as far as possible, ensure him or her that everything humanly possible is being done, that help will arrive soon, etc. Rule No. 1 of first aid is: Keep talking to the patient!

There are three vascular and two nonvascular causes of shock.

Vascular causes are:

• Pump failure, i.e. the heart is damaged and cannot pump the blood effectively:
  Cardiogenic shock

• Blood/fluid loss, i.e. low volume in the circulatory system causing insufficient perfusion of the body:
  Hypovolemic shock; when due to blood loss, hemorrhagic shock; may result from trauma, burns, crush injuries or dehydration.
  Metabolic shock; due to severe untreated illness, such as diabetes, vomiting, diarrhea or excessive urination
  Septic shock; due to bacterial toxins from severe systemic infections, blood vessels become leaky and dilated, producing a combination of blood volume loss and vessel volume increase

• Dilation of the blood vessels, i.e. increase in the volume of the circulatory system resulting in proportionally less blood volume, causing insufficient perfusion of the body:
  Neurogenic shock; due to spinal cord damage, blood vessel tone below the level of injury is lost, causing general dilation of vessels and vessel volume increase
  Psychogenic shock; aka the common faint, is a temporary generalized dilation of the blood vessels due to some psychological (well, there's really no other word..) shock

Nonvascular causes are:

• Respiratory shock; due to severe chest injury or airway obstruction causing inadequate blood oxygen levels; enough blood is carried to the organs, but there is not enough oxygen in it

• Anaphylactic shock; the most severe form of allergic reaction, involving itching, flushing, hives, edema (especially of the face, lips and tongue), coughing, tightness in the chest, wheezing and dyspnea, drop in blood pressure, pallor, dizziness, fainting and coma. Anaphylactic shock is basically a type of respiratory shock, as the problems are mainly due to low blood oxygen

Symptoms of shock include:

• Restlessness and anxiety
• Rapid, weak pulse
• Cold, clammy skin
• Severe sweating
• Pallor, possibly late cyanosis (especially around the mouth)
• Shallow, rapid, labored breathing
• Dilated pupils
• Thirst
• Nausea and vomiting
• Dropping blood pressure
• Loss of consciousness

Initial treatment of shock should involve the following steps:

• Open the patient's airway and give oxygen, if possible
• Control obvious bleeding through direct pressure
• Elevate the lower extremities ca. 12 inches (if no obvious fractures are present)
• Avoid rough handling, avoid causing any unnecessary pain
• Prevent loss of body heat by placing blankets under and over the patient (do not overload)
• Keep patient lying down; if patient has difficulty breathing, allow patient to assume most comfortable position
• Do not give the patient anything by mouth - neither food or drink
• Obtain medical attention for the patient as soon as possible

It is also worth noting that the various cases of shock tend to progress in severity in three stages:

Compensatory Shock

Compensatory shock is the body's natural reaction to the trauma that it has received. During this phase, the body may cope well enough that symptoms of shock are not noticeable, or symptoms of compensatory shock may manifest themselves. These symptoms may include anxiety; cool, clammy skin; thirst; vomiting; and lightheadedness. If treatment is received during this phase of shock, prognosis is good for a full recovery.

Decompensatory (or Progressive) Shock

In this phase of shock, the body can no longer care for itself, and gradual systemic shutdown begins to occur. Symptoms of decompensatory shock may include a decreased level of consciousness; profuse sweating; Caucasian skin becomes pale white or grey, while darker skin may turn cyanotic; shallow breathing; rapid pulse; and low blood pressure. If treatment is not received now, it is likely that the patient will slip into the third stage of shock.

Irreversible Shock

In this final phase, the heart, brain, and other organs sustain major damage as a result of hypoxia. The result is usually death. Some patients may survive, but will have incurred irreversible cellular damage to vital organs. Treatment in this phase is usually ineffective, as the body is beginning to die rapidly. Symptoms of irreversible shock may include the patient becoming unresponsive; cold white or gray skin; slow or no heart rate; undetectable pulse; labored, shallow breathing; and an undetectable blood pressure.

The most efficient methods of treatment are stated above in gwenllian's writeup. There is little that an average person may do to treat shock, the most important thing is to seek professional assistance immediately, as patients suffering from shock can have their conditions rapidly deteriorate in a matter of two to three hours.

Shock (?), n. [OE. schokke; cf. OD schocke, G. schock a heap, quantity, threescore, MHG. schoc, Sw. skok, and also G. hocke a heap of hay, Lith. kugis.]

1.

A pile or assemblage of sheaves of grain, as wheat, rye, or the like, set up in a field, the sheaves varying in number from twelve to sixteen; a stook.

And cause it on shocks to be by and by set.
Tusser.

Behind the master walks, builds up the shocks.
Thomson.

2. [G. schock.] (Com.)

A lot consisting of sixty pieces; -- a term applied in some Baltic ports to loose goods.

 

© Webster 1913

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Shock, v. t.

To collect, or make up, into a shock or shocks; to stook; as, to shock rye.

 

© Webster 1913

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Shock, v. i.

To be occupied with making shocks.

Reap well, scatter not, gather clean that is shorn,
Bind fast, shock apace.
Tusser.

 

© Webster 1913

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Shock, n. [Cf. D. schok a bounce, jolt, or leap, OHG. scoc a swing, MHG. schoc, Icel. skykkjun tremuously, F. choc a shock, collision, a dashing or striking against, Sp. choque, It. ciocco a log. √161. Cf. Shock to shake.]

1.

A quivering or shaking which is the effect of a blow, collision, or violent impulse; a blow, impact, or collision; a concussion; a sudden violent impulse or onset.

These strong, unshaken mounds resist the shocks
Of tides and seas tempestuous.
Blackmore.

He stood the shock of a whole host of foes.
Addison.

2.

A sudden agitation of the mind or feelings; a sensation of pleasure or pain caused by something unexpected or overpowering; also, a sudden agitating or overpowering event. "A shock of pleasure." Talfourd.

3. (Med.)

A sudden depression of the vital forces of the entire body, or of a port of it, marking some profound impression produced upon the nervous system, as by severe injury, overpowering emotion, or the like.

4. (Elec.)

The sudden convulsion or contraction of the muscles, with the feeling of a concussion, caused by the discharge, through the animal system, of electricity from a charged body.

Syn. -- Concussion, Shock. Both words signify a sudden violent shaking caused by impact or colision; but concussion is restricted in use to matter, while shock is used also of mental states.

 

© Webster 1913

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Shock, v. t. [imp. & p. p. Shocked (?); p. pr. & vb. n. Shocking.] [OE. schokken; cf. D. schokken, F. choquer, Sp. chocar. √161. Cf. Chuck to strike, Jog, Shake, Shock a striking, Shog, n. & v.]

1.

To give a shock to; to cause to shake or waver; hence, to strike against suddenly; to encounter with violence.

Come the three corners of the world in arms,
And we shall shock them.
Shak.

I shall never forget the force with which he shocked De Vipont.
Sir W. Scott.

2.

To strike with surprise, terror, horror, or disgust; to cause to recoil; as, his violence shocked his associates.

Advise him not to shock a father's will.
Dryden.

 

© Webster 1913

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Shock, v. i.

To meet with a shock; to meet in violent encounter. "They saw the moment approach when the two parties would shock together." De Quincey.

 

© Webster 1913

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Shock, n. [Cf. Shag.]

1. (Zoöl.)

A dog with long hair or shag; -- called also shockdog.

2.

A thick mass of bushy hair; as, a head covered with a shock of sandy hair.

 

© Webster 1913

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Shock, a.

Bushy; shaggy; as, a shock hair.

His red shock peruke . . . was laid aside.
Sir W. Scott.

 

© Webster 1913

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Shock, v. t. (Physiol.)

To subject to the action of an electrical discharge so as to cause a more or less violent depression or commotion of the nervous system.

 

© Webster 1913